Posted November 17, 2003

Control and Optimization Seminar Questions or comments?

3:00 pm James E. Keisler Lounge (Room 321 Lockett)
Stanislav Zabic, Louisiana State University Department of Mathematics
Graduate Student

Optimizing the Design of the Michelin PAX Tire System

Abstract: This talk analyzes a problem encountered by the Michelin Corporation in the design of a \'run-flat\', or PAX, tire system. A PAX tire system consists of an aluminum wheel of larger-than-conventional radius, a low-profile tire, and a special rubber support ring inside and concentric with the tire. The goal of the support ring is to provide a safe driving transition in case of a flat tire. After the air has deflated from the tire, the support ring carries the entire load of the car. We will discuss ways to optimize the design of the support ring. This research was carried out during the summer of 2001, while the speaker was a visitor at North Carolina State University.

Posted September 14, 2003

Last modified May 3, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall
Michael Malisoff, LSU
Roy P. Daniels Professor

Lyapunov Functions and Viscosity Solutions, Part 1

Posted September 14, 2003

Last modified May 3, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall
Michael Malisoff, LSU
Roy P. Daniels Professor

Lyapunov Functions and Viscosity Solutions, Part 2

Posted September 14, 2003

Last modified May 3, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall
Michael Malisoff, LSU
Roy P. Daniels Professor

Lyapunov Functions and Viscosity Solutions, Part 3

Posted March 25, 2004

Last modified March 26, 2004

Control and Optimization Seminar Questions or comments?

3:40 pm 381 Lockett Hall
Vinicio Rios, LSU Department of Mathematics
PhD Student

A Theorem on Lipschitzian Approximation of Differential Inclusions

Posted September 19, 2003

Last modified March 2, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm 381 Lockett Hall
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

Clarke's New Necessary Conditions in Dynamic Optimization

Posted August 26, 2003

Control and Optimization Seminar Questions or comments?

3:40 pm - 4:30 pm Lockett 277
Jesus Pascal, Universidad del Zulia, Venezuela

Free Boundary Control Problem

Posted September 24, 2003

Last modified January 10, 2022

Control and Optimization Seminar Questions or comments?

2:30 pm 240 Lockett Hall
Yuan Wang, Florida Atlantic University

A Relaxation Theorem for Differential Inclusions with Applications to Stability Properties

The fundamental Filippov-Ważewski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz differential inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In this talk, I will discuss a complementary result which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. To illustrate the motivations for studying such approximation results, I will briefly discuss some quick applications of the result to various stability and uniform stability properties.

Visit supported by Visiting Experts Program in Mathematics, Louisiana
Board of Regents. LEQSF(2002-04)-ENH-TR-13

Posted November 18, 2003

Last modified November 24, 2003

Control and Optimization Seminar Questions or comments?

2:30 pm 240 Lockett Hall
Tzanko Donchev, University of Architecture and Civil Engineering, BULGARIA

Singular Perturbations in Infinite Dimensional Control Systems

Abstract: We consider a singularly perturbed control system involving differential inclusions in Banach spaces with slow and fast solutions. Using the averaging approach, we obtain sufficient conditions for the Hausdorff convergence of the set of slow solutions in the sup norm. We present applications of the theorem to prove convergence of the fast solutions in terms of invariant measures and convergence of equi-Lipschitz solutions. We also present some illustrative examples.

Posted March 3, 2004

Control and Optimization Seminar Questions or comments?

2:30 pm 240 Lockett Hall
Zhijun Cai, Department of Mechanical Engineering, LSU
PhD Candidate

Adaptive Stabilization of Parametric Strict-Feedback Systems with Additive Disturbance

Abstract: This talk deals with the output regulation of uncertain, nonlinear, parametric strict-feedback systems in the presence of additive disturbance. A new continuous adaptive control law is proposed using a modified integrator backstepping design that ensures the output is asymptotically regulated to zero. Despite the disturbance, the adaptation law does not need the standard robustifying term (e.g., sigma-modification or e1-modification) to ensure the aforementioned stability result. A numerical example illustrates the main result.

Posted February 15, 2004

Last modified March 1, 2004

Control and Optimization Seminar Questions or comments?

2:30 pm Lockett Hall, Room 240
Frederic Mazenc, Institut National de Recherche en Informatique et en Automatique, FRANCE

Stabilization of Nonlinear Systems with Delay in the Input

Abstract: We present three results on the problem of globally uniformly and locally exponentially stabilizing nonlinear systems with delay in the input through differentiable bounded feedbacks: 1) We solve the problem for chains of integrators of arbitrary length. No limitation on the size of the delay is imposed. An exact knowledge of the delay is not required. 2) We solve the problem for an oscillator with an arbitrary large delay in the input. A first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term. Next, it is shown through a Lyapunov analysis that the stabilization can be achieved as well when the distributed terms are neglected.
It turns out that this main result is intimately related to the output feedback stabilization problem. 3) We solve the problem for a family of nonlinear feedforward systems when there is a delay in the input. No limitation on the size of the delay is imposed. An exact knowledge of the delay is not required.

This visit is supported by the Visiting Experts Program in Mathematics, Louisiana Board of Regents Grant LEQSF(2002-04)-ENH-TR-13.

Posted February 15, 2004

Last modified March 26, 2004

Control and Optimization Seminar Questions or comments?

2:30 pm Lockett Hall, Room 240
Michael Malisoff, LSU
Roy P. Daniels Professor

Remarks on the Strong Invariance Property for Non-Lipschitz Dynamics

Abstract: Topics in flow invariance theory provide the foundation for considerable current research in modern control theory and optimization.Starting from strong invariance and its Hamiltonian characterizations, one can develop uniqueness results and regularity theory for proximal solutions of Hamilton-Jacobi-Bellman equations, stability theory, infinitesimal characterizations of monotonicity, and many other applications. On the other hand, it is well appreciated that many important dynamics are non-Lipschitz, and may even be discontinuous, and therefore are beyond the scope of the known strong invariance characterizations. Therefore, the development of conditions guaranteeing strong invariance under less restrictive assumptions is a problem that is of considerable ongoing research interest. In this talk we will report on some recently developed sufficient conditions for strong invariance for discontinuous differential inclusions. This talk is based in part on the speaker\'s joint work with Mikhail Krastanov and Peter Wolenski.

Posted August 27, 2004

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall
Stanislav Zabic, Louisiana State University Department of Mathematics
Graduate Student

Impulsive Systems

Posted September 3, 2004

Last modified September 10, 2004

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall Originally scheduled for 3:00 pm, Wednesday, September 8, 2004
Stanislav Zabic, Louisiana State University Department of Mathematics
Graduate Student

Impulsive Systems, Part II

Posted September 20, 2004

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall
Norma Ortiz, Mathematics Department, LSU
PhD Student

An Existence Theorem for the Neutral Problem of Bolza

Posted September 21, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm Lockett 381
Norma Ortiz, Mathematics Department, LSU
PhD Student

An existence theorem for the neutral problem of Bolza, Part II

Posted September 29, 2004

Last modified October 1, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm 381 Lockett Hall
Vinicio Rios, LSU Department of Mathematics
PhD Student

Strong Invariance for Dissipative Lipschitz Dynamics

Posted October 6, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm 381 Lockett Hall
Vinicio Rios, LSU Department of Mathematics
PhD Student

Strong Invariance for Dissipative Lipschitz Dynamics, Part II

Posted October 13, 2004

Last modified October 14, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm 381 Lockett Hall
George Cazacu, LSU Department of Mathematics
PhD student

A characterization of stability for dynamical polysystems via Lyapunov functions

Posted October 20, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm 381 Lockett Hall
George Cazacu, LSU Department of Mathematics
PhD student

Closed relations and Lyapunov functions for polysystems

Posted November 10, 2004

Last modified May 8, 2021

Control and Optimization Seminar Questions or comments?

3:00 pm 381 Lockett Hall
Michael Malisoff, LSU
Roy P. Daniels Professor

New Constructions of Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems

This talk is based on the speaker's joint work “Further Remarks on Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems” with Frederic Mazenc (arXiv math.OC/0411150).

Posted November 3, 2004

Last modified November 17, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm 381 Lockett Hall
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

Introduction to control Lyapunov functions and feedback

Posted November 25, 2004

Control and Optimization Seminar Questions or comments?

3:10 pm - 4:00 pm 381 Lockett Hall
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

Introduction to control Lyapunov functions and feedback, Part II

Posted February 21, 2005

Last modified February 25, 2005

Control and Optimization Seminar Questions or comments?

3:30 pm 2150 CEBA
Michael Malisoff, LSU
Roy P. Daniels Professor

An Introduction to Input-to-State Stability

Posted March 8, 2005

Last modified March 9, 2005

Control and Optimization Seminar Questions or comments?

3:30 pm - 4:30 pm 2150 CEBA
Rafal Goebel, University of California, Santa Barbara

Hybrid dynamical systems: solution concepts, graphical convergence, and robust stability

Hybrid dynamical systems, that is systems in which some variables evolve continuously while other variables may jump, are an active area of research in control engineering. Basic examples of such systems include a bouncing ball (where the velocity \"jumps\" every time the ball hits the ground) and a room with a thermostat (where the temperature changes continuously while the heater is either \"on\" or \"off\"), much more elaborate cases are studied for example in robotics and automobile design.

The talk will present some challenges encountered on the way to a successful stability theory of hybrid systems, and propose a way to overcome them. In particular, we will motivate the use

of generalized time domains, show how the nonclassical notion of graphical convergence appears to be the correct concept to treat sequences of solutions to hybrid systems, and how various other tools of set-valued and nonsmooth analysis may and need to be used.

Posted March 29, 2005

Last modified March 2, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm - 3:00 pm Lockett 381
Vladimir Gaitsgory, School of Mathematics and Statistics, University of South Australia

TBA

Posted March 29, 2005

Last modified March 30, 2005

Control and Optimization Seminar Questions or comments?

3:30 pm - 4:30 pm CEBA 2150
Vladimir Gaitsgory, School of Mathematics and Statistics, University of South Australia

Limits of Occupational Measures and Averaging of Singularly Perturbed

Posted April 11, 2005

Control and Optimization Seminar Questions or comments?

3:40 pm - 4:40 pm Lockett 381
Jesus Pascal, Universidad del Zulia, Venezuela

On the Hamilton Jacobi Bellman Equation for a Deterministic Optimal Control Problem

Posted April 15, 2005

Control and Optimization Seminar Questions or comments?

3:30 pm - 4:30 pm CEBA 2150
Steven Hall, Louisiana State University, Department of Biological and Agricultural Engineering

Challenges in Measurement and Control with Biological Systems

Posted June 17, 2005

Control and Optimization Seminar Questions or comments?

10:30 am EE117
Li Qiu, Hong Kong University of Science and Technology

Perturbation Analysis beyond Singular Values -- A Metric Geometry on the Grassmann Manifold

Posted July 15, 2005

Control and Optimization Seminar Questions or comments?

10:00 am EE 117
Boumediene Hamzi, University of California, Davis

The Controlled Center Dynamics

Posted January 30, 2006

Last modified February 16, 2006

Control and Optimization Seminar Questions or comments?

10:00 am EE 117
Patrick De Leenheer, Department of Mathematics, University of Florida

Bistability and Oscillations in the Feedback-Controlled Chemostat

The chemostat is a biological reactor used to study the dynamics of species competing for nutrients. If there are n>1 competitors and a single nutrient, then at most one species survives, provided the control variables of the reactor are constant. This result is known as the competitive exclusion principle. I will review what happens if one of the control variables--the dilution rate--is treated as a feedback variable. Several species can coexist for appropriate choices of the feedback. Also, the dynamical behavior can be more complicated, exhibiting oscillations or bistability.

Posted April 19, 2006

Last modified February 2, 2022

Control and Optimization Seminar Questions or comments?

3:40 pm 381 Lockett
Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova

Moving Constraints as Controls in Classical Mechanics

In most applications of control theory to mechanics the *control* is identified with a force, or with a torque. However, in some concrete situations, the forces are in fact unknown, whereas what one is actually controlling is the *position of part of the system*. More precisely, if the state space consists of the product $\mathcal{Q} \times \mathcal{C}$ of two manifolds $\mathcal{Q}$ and $\mathcal{C}$, one can regard $\mathcal{Q}$ as the actual (reduced) state space by identifying $\mathcal{C}$ with a set of controls. As an example, one can think of a mathematical pendulum whose pivot is constrained on a vertical line. In this case $\mathcal{Q} = S^1$ and $\mathcal{C} = \mathbf{R}$. (The title of the talk refers to the fact that a control function $\mathbf{c}(·)$ defined on a time-interval $I$ can be considered as a time dependent
(i.e., *moving*) state-constraint acting on the original state space $\mathcal{Q} \times \mathcal{C}$.)

To begin with, we will illustrate some remarkable geometric aspects, which
involve, in particular, the metric induced by the kinetic energy on the manifold
$\mathcal{Q} \times \mathcal{C}$ and its relation with the foliation $\{\mathcal{Q} \times \{\mathbf{c}\} \,|\, \mathbf{c} \in \mathcal{C} \}$ .

Secondly, we will address the question of the closure of the set of solutions
for unbounded control systems, and we will see how this issue is connected with
our mechanical problems.

Finally, we will show how some well-known mechanical questions—including
the vibrational stabilization of the so-called *inverted pendulum*—can actually be regarded as instances of problems involving moving constraints as controls.

Professor Rampazzo's visit is sponsored by the Louisiana Board of Regents Grant
"Enhancing Control Theory at LSU".

Posted September 18, 2006

Last modified September 17, 2021

Control and Optimization Seminar Questions or comments?

3:30 pm 285 Lockett
Martin Hjortso, Louisiana State University
Chevron Professor of ChemE

Some Problems in Population Balance Modeling

Posted January 30, 2007

Last modified January 31, 2007

Control and Optimization Seminar Questions or comments?

11:30 am - 12:30 pm Lockett 301D (Conference Room)
Michael Malisoff, LSU
Roy P. Daniels Professor

On the Stability of Periodic Solutions in the Perturbed Chemostat

We study the chemostat model for one species competing for one nutrient using a Lyapunov-type analysis. We design the dilution rate function so that all solutions of the chemostat converge to a prescribed periodic solution. In terms of chemostat biology, this means that no matter what positive initial levels for the species concentration and nutrient are selected, the long-term species concentration and substrate levels closely approximate a prescribed oscillatory behavior. This is significant because it reproduces the realistic ecological

situation where the species and substrate concentrations oscillate. We show that the stability is maintained when the model is augmented by additional species that are being driven to extinction. We also give an input-to-state stability result for the chemostat-tracking equations for cases where there are small perturbations acting on the dilution rate and initial concentration. This means that the long-term species concentration and substrate behavior enjoys a

highly desirable robustness property, since it continues to approximate the prescribed oscillation up to a small error when there are small unexpected changes in the dilution rate function. This talk is based on the speaker\'s joint work with Frederic Mazenc and Patrick De Leenheer.

Posted February 4, 2007

Control and Optimization Seminar Questions or comments?

11:30 am - 12:30 pm 239 Lockett
Michael Malisoff, LSU
Roy P. Daniels Professor

Further Results on Lyapunov Functions for Slowly Time-Varying Systems

We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model. This talk is based on the speaker\'s joint work with Frederic Mazenc.

Posted February 9, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm Lockett 239
Jimmie Lawson, Mathematics Department, LSU

The Symplectic Group and Semigroup and Riccati Differential

Abstract: We develop close connections between important control-theoretic matrix Riccati differential equation and the symplectic matrix group and its symplectic subsemigroup. We use this example as a case study to demonstrate how the Lie theory of the subsemigroups of a matrix group can be applied to problems in geometric control theory. As an application we derive from this viewpoint the existence of a solution for the Riccati equation for all $t\\geq 0$ under quite general hypotheses.

Posted February 22, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm Lockett 239
Jimmie Lawson, Mathematics Department, LSU

The Symplectic Group and Semigroup and Riccati Differential (Part II)

Abstract: We develop close connections between important control-theoretic matrix Riccati differential equation and the symplectic matrix group and its symplectic subsemigroup. We use this example as a case study to demonstrate how the Lie theory of the subsemigroups of a matrix group can be applied to problems in geometric control theory. As an application we derive from this viewpoint the existence of a solution for the Riccati equation for all $t\\geq 0$ under quite general hypotheses.

Posted March 5, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm Lockett 239
Jimmie Lawson, Mathematics Department, LSU

The Symplectic Group and Semigroup and Riccati Differential Equations (Part III)

Abstract: We develop close connections between important control-theoretic matrix Riccati differential equation and the symplectic matrix group and its symplectic subsemigroup. We use this example as a case study to demonstrate how the Lie theory of the subsemigroups of a matrix group can be applied to problems in geometric control theory. As an application we derive from this viewpoint the existence of a solution for the Riccati equation for all $t\\geq 0$ under quite general hypotheses.

Posted March 26, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm 239 Lockett
Feng Gao, LSU Department of Mechanical Engineering

A Generalized Approach for the Control of MEM Relays

Abstract: We show that voltage-controlled, electrostatic and electromagnetic micro-relays have a common dynamic structure. As a result, both types of microelectromechanical (MEM) relays are subject to the nonlinear phenomenon known as pull-in, which is usually associated with the electrostatic case. We show that open-loop control of MEM relays naturally leads to pull-in during the relay closing. Two control schemes - a Lyapunov design and a feedback linearization design - are presented with the objectives of avoiding pull-in during the micro-relay closing and improving the transient response during the micro-relay opening. Simulations illustrate the performance of the two control schemes in comparison to the typical open-loop operation of the MEM relay.

Posted April 16, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm Room 239 Lockett
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

The role of convexity in optimization and control theory.

Abstract: This talk will broadly survey the role of convexity in optimization theory, and outline its special place in optimal control. Roughly speaking, convexity plays the role in optimization analogous to that enjoyed by linearity in dynamical system theory. We shall illustrate this by discussing the features of local vs. global statements, generalized differentiation, duality, and representation formulas.

Posted April 23, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm Room 239 Lockett
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

The role of convexity in optimization and control theory (Part II)

Abstract: This talk will broadly survey the role of convexity in optimization theory, and outline its special place in optimal control. Roughly speaking, convexity plays the role in optimization analogous to that enjoyed by linearity in dynamical system theory. We shall illustrate this by discussing the features of local vs. global statements, generalized differentiation, duality, and representation formulas.

Posted May 1, 2007

Control and Optimization Seminar Questions or comments?

11:40 am - 12:30 pm Room 239 Lockett
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

The role of convexity in optimization and control theory (Part III)

Abstract: This talk will broadly survey the role of convexity in optimization theory, and outline its special place in optimal control. Roughly speaking, convexity plays the role in optimization analogous to that enjoyed by linearity in dynamical system theory. We shall illustrate this by discussing the features of local vs. global statements, generalized differentiation, duality, and representation formulas.

Posted September 9, 2007

Control and Optimization Seminar Questions or comments?

2:30 pm - 3:30 pm Prescott 205
Alvaro Guevara, Dept of Mathematics, LSU

Student Seminar on Control Theory and Optimization

Introduction to Convex Analysis II

Posted June 28, 2009

Last modified May 8, 2021

Control and Optimization Seminar Questions or comments?

10:00 am Lockett 301D (Conference Room)
Michael Malisoff, LSU
Roy P. Daniels Professor

Strict Lyapunov Function Constructions under LaSalle Conditions with an Application to Lotka-Volterra Systems

This informal seminar is by special request of Guillermo Ferreyra and is open to all faculty and graduate students. See abstract and related papers and slides.

Posted October 9, 2009

Last modified May 8, 2021

Control and Optimization Seminar Questions or comments?

10:00 am 117 Electrical Engineering Building
Michael Malisoff, LSU
Roy P. Daniels Professor

Constructions of Strict Lyapunov Functions: An Overview

Information on ECE Seminar Web Site.

Posted January 28, 2010

Last modified April 22, 2010

Control and Optimization Seminar Questions or comments?

3:00 pm 117 Electrical Engineering
Michael Malisoff, LSU
Roy P. Daniels Professor

New Lyapunov Function Methods for Adaptive and Time-Delayed Systems

Lyapunov functions are an important tool in nonlinear control systems theory. This talk presents new Lyapunov-based adaptive tracking control results for nonlinear systems in feedback form with multiple inputs and unknown high-frequency control gains. Our adaptive controllers yield uniform global asymptotic stability for the error dynamics, which implies parameter estimation and tracking for the original systems. We demonstrate our work using a tracking problem for a brushless DC motor turning a mechanical load. Then we present a new class of dilution rate feedback controllers for two-species chemostat models with Haldane uptake functions where the species concentrations are measured with an unknown time delay. This work is joint with Marcio de Queiroz and Frederic Mazenc.

Posted September 21, 2015

Last modified September 22, 2015

Control and Optimization Seminar Questions or comments?

12:30 pm - 1:30 pm 381 Lockett Hall
Michael Malisoff, LSU
Roy P. Daniels Professor

Control of Neuromuscular Electrical Stimulation: A Case Study of Predictor Control under State Constraints

We present a new tracking controller for neuromuscular electrical stimulation, which is an emerging technology that artificially stimulates skeletal muscles to help restore functionality to human limbs. The novelty of our work is that we prove that the tracking error globally asymptotically and locally exponentially converges to zero for any positive input delay, coupled with our ability to satisfy a state constraint imposed by the physical system. Also, our controller only requires sampled measurements of the states instead of continuous measurements and allows perturbed sampling schedules, which can be important for practical purposes. Our work is based on a new method for constructing predictor maps for a large class of time-varying systems, which is of independent interest. See http://dx.doi.org/10.1002/rnc.3211.

Posted September 28, 2015

Control and Optimization Seminar Questions or comments?

12:30 pm - 1:30 pm Room 284 Lockett Hall
Cristopher Hermosilla, Department of Mathematics, LSU

On the Construction of Continuous Suboptimal Feedback Laws

An important issue in optimal control is that optimal feedback laws (the minimizers) are usually discontinuous functions on the state, which yields to ill-posed closed loop systems and robustness problems. In this talk we show a procedure for the construction of a continuous suboptimal feedback law that allows overcoming the aforesaid problems. The construction we exhibit depends exclusively on the initial data that could be obtained from the optimal feedback. This is a joint work with Fabio Ancona (Universita degli Studi di Padova, Italy)

Posted October 5, 2015

Last modified October 8, 2015

Control and Optimization Seminar Questions or comments?

12:30 pm - 1:30 pm Room 284 Lockett Hall
Hugo Leiva, Visiting Professor, Louisiana State University

Semilinear Control Systems with Impulses, Delays and Nonlocal Conditions.

Mathematical control theory is the area of applied mathematics dealing

with the analysis and synthesis of control systems. To control a system

means to influence its behavior so as to achieve a desired goal such as

stability, tracking, disturbance rejection or optimality with respect to

some performance criterion. For many control systems in real life,

impulses and delays are intrinsic phenomena that do not modify their

controllability. So we conjecture that, under certain conditions,

perturbations of the system caused by abrupt changes and delays do not

affect certain properties such as controllability.

In this investigation we apply Fixed Point Theorems to prove the

controllability of Semilinear Systems of Differential

Equations with Impulses, delays and Nonlocal Conditions.

Specifically, Under additional conditions we prove the following statement:

If the linear $\\acute{z}(t) = A(t)z(t) + B(t)u(t)$ is controllable on $[0, \\tau]$,

then the semilinear system $z^{\\prime}(t) = A(t)z(t) + B(t)u(t)+f(t,z(t),u(t))$

with impulses, delays, and nonlocal conditions is also controllable on $[0, \\tau]$.

Moreover, we could exhibit a control steering the semilinear system from an

initial state $z_0$ to a final state $z_1$ at time $\\tau >0$.

This is a recent research work with many questions and open problems.

Posted March 18, 2019

Control and Optimization Seminar Questions or comments?

10:30 am - 11:30 am 3316E Patrick F. Taylor HallTrying to Keep it Real: 25 Years of Trying to Get the Stuff I Learned in Grad School to Work on Mechatronic Systems

See https://www.lsu.edu/eng/ece/seminar/

Posted May 2, 2019

Last modified May 3, 2019

Control and Optimization Seminar Questions or comments?

3:00 pm - 4:00 pm 1263 Patrick F. Taylor Hall
Laurent Burlion, Rutgers University

Advanced Nonlinear Control Methods to Push Aerospace Systems to Their Limits

Abstract: Although often neglected in the design of flight control laws, nonlinearities must be taken into account either to get the best performance or to enlarge the flight envelope of controlled aerospace systems. Indeed, every system has a limited control authority and is subject to some safety constraints which impose limits on certain variables. In this talk, we will first present an overview of our recent applications of nonlinear control design methods to aerospace systems. Then, we will illustrate advanced nonlinear control techniques, including bounded backstepping, anti-windup and extended command governors, that were developed to execute an aircraft vision based landing on an unknown runway. Finally, we will discuss some ongoing research activities being conducted to provide drones with new capabilities, leading to a dramatic improvement in safety.

Posted November 21, 2019

Last modified November 24, 2019

Control and Optimization Seminar Questions or comments?

10:00 am 3316E Patrick F. Taylor Hall
Pavithra Prabhakar, Kansas State University

Robust Verification of Hybrid Systems

Information on ECE Seminar Web Site.

Posted March 4, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to get password)
Michael Malisoff, LSU
Roy P. Daniels Professor

Delay Compensation in Control Systems

Control systems are a class of dynamical systems that contain forcing terms. When control systems are used in biological or engineering applications, the forcing terms are often used to represent different possible forces that can be applied to the systems. Then the feedback control problem consists of finding formulas for the forcing terms, which are functions that can depend on the state of the systems, and which ensure a prescribed qualitative behavior of the dynamical systems, such as global asymptotic convergence towards an equilibrium point. Then the forcing terms are called feedback controls. However, many control systems in biology or engineering are subject to input delays, which preclude the possibility of using current values of the states of the control systems in the expressions for the feedback controls. One approach to solving feedback control problems under input delays involves solving the problems with the delays set equal to zero, and then computing upper bounds on the input delays that the systems can tolerate while still realizing the desired objective. For longer delays, the reduction model approach is often used but can lead to implementation challenges because it leads to distributed terms in the controls. A third approach to delay compensation involves sequential predictors, which can compensate for arbitrarily long input delays using stacks of differential equations instead of distributed terms. This talk reviews recent developments in this area, and is based in part on the speaker's collaborations with Miroslav Krstic, Frederic Mazenc, Fumin Zhang, and students. The talk will be understandable to those familiar with the basic theory of ordinary differential equations. No prerequisite background in systems and control will be needed to understand and appreciate this talk.

Posted March 10, 2021

Last modified March 11, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to get password)
Peter Wolenski, LSU Department of Mathematics
Russell B. Long Professor

Introduction to Convex Analysis via the Elvis Problem

The Elvis problem was introduced into the undergraduate mathematical literature by Timothy Pennings whose dog (named Elvis) enjoyed fetching an object thrown from the shore of Lake Michigan into the water. Elvis was observed to retrieve the object by going in a path that resembled how light would refract in isotropic mediums according to Snell's Law. We retain the problem's "Elvis" nomenclature but greatly generalize the problem by considering anisotropic mediums and use the tools of Convex Analysis to provide a complete description of optimal movement. The velocity sets are closed, bounded convex sets containing the origin in its interior, whereas the original problem used only centered balls. Further generalizations are considered with faster movement allowed on the interface and with more than two mediums.

Posted March 2, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to get password)
Romain Postoyan, CNRS Researcher

A Short Introduction to Event-Triggered Control

Control systems are increasingly implemented on digital platforms, which typically have limited power and computing and communication resources. In this context, the classical implementation of sampled-data control systems may not be suitable. Indeed, while the periodic transmission of data simplifies the analysis (in general) and the implementation of the control law, the induced use of the platform resources may be too demanding. An alternative consists of defining the transmission instants between the plant and the controller based on the actual system needs, and not the elapsed time since the last transmission. This alternative is the basis of event-triggered control. With this paradigm, a transmission occurs whenever a state/output-dependent criterion is violated. The key question is then how to define this triggering rule to ensure the desired control objectives, while guaranteeing the existence of a strictly positive minimum time between any two communications, which is essential in practice. In this presentation, we review basic techniques of the field, with particular attention to nonlinear systems, and compare them on examples. We also explain the interest of introducing auxiliary variables to define the transmission criterion, in which case we talk of dynamic event-triggered control. Finally, we conclude with some open problems.

Posted March 10, 2021

Last modified March 26, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Summer Atkins, University of Florida

Solving Singular Control Problems in Mathematical Biology, Using PASA

We will demonstrate how to use a non-linear polyhedral constrained optimization solver called the Polyhedral Active Set Algorithm (PASA) for solving a general optimal control problem that is linear in the control. In numerically solving for such a problem, oscillatory numerical artifacts can occur if the optimal control possesses a singular subarc. We consider adding a total variation regularization term to the objective functional of the problem to regularize these oscillatory artifacts. We then demonstrate PASA's performance on three singular control problems that give rise to different applications of mathematical biology.

Posted February 20, 2021

Last modified March 26, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Warren Dixon, University of Florida Department of MAE
Department Chair, Fellow of ASME and IEEE

Assured Autonomy: Uncertainty, Optimality, and Data Intermittency

Autonomous systems can provide advantages such as access, expendability, and scaled force projection in adversarial environments. However, such environments are inherently complex in the sense they are uncertain and data exchanges for sensing and communications can be compromised or denied. This presentation provides a deep dive into some feedback control perspectives related to uncertainty, optimality, and data intermittency that provide foundations for assured autonomous operations. New results will be described for guaranteed deep learning methods that can be employed in real-time with no data. These efforts include methods for (deep) reinforcement learning based approaches to yield approximate optimal policies in the presence of uncertainty. The presentation will conclude with examples of intermittent feedback that explore the data exchange limits for guaranteed operation, including purposeful intermittency to enable new capabilities. Specific examples include intermittency due to occlusions in image-based feedback and intermittency resulting from various network control problems.

Posted March 22, 2021

Last modified March 26, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Jean-Michel Coron, Universite Pierre et Marie Curie, France
Member of Institut Universitaire de France

Boundary Stabilization of 1-D Hyperbolic Systems

Hyperbolic systems in one space dimension appear in various real life applications, such as navigable rivers and irrigation channels, heat exchangers, plug flow chemical reactors, gas pipe lines, chromatography, and traffic flow. This talk will focus on the stabilization of these systems by means of boundary controls. Stabilizing feedback laws will be constructed. This includes explicit feedback laws which have been implemented for the regulation of the rivers La Sambre and La Meuse. The talk will also deal with the more complicated case where there are source terms.

Posted March 5, 2021

Last modified January 10, 2022

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Vincent Andrieu, CNRS

An Overview of Asymptotic Observer Design Methods

Dynamic observers are estimation algorithms allowing us to reconstruct missing data from a model of a dynamic system and information obtained from the measurements. In this presentation, we present the main methods allowing the synthesis of an asymptotic observer. Starting from necessary conditions inspired by Luenberger's work, we show the importance of contraction properties. Then, we give different existing methods. Finally, we give an overview of open issues in the field.

Posted March 18, 2021

Last modified January 10, 2022

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Lars Gruene, University of Bayreuth, Germany

On Turnpike Properties and Sensitivities and their Use in Model Predictive Control

Model predictive control (MPC) is one of the most popular modern control techniques. It generates a feedback-like control input from the iterated solution of open-loop optimal control problems. In recent years, there was a lot of progress in answering the question when MPC yields approximately optimal solutions. In this talk we will highlight the role of the turnpike property for this analysis. Moreover, we will show that for PDE-governed control problems the turnpike property can be seen as a particular instance of a more general sensitivity property. This can be used in order to obtain efficient discretization schemes for the numerical solution of the optimal control problems in the MPC algorithm.

Posted April 1, 2021

Last modified April 26, 2021

Control and Optimization Seminar Questions or comments?

10:00 am https://lsu.zoom.us/j/94269991036 (Contact Prof. Malisoff to request password)
Hiroshi Ito, Kyushu Institute of Technology

Constructions of Lyapunov Functions for Input-to-State Stability and Control of SIR Model

To predict the spread of infectious diseases, mathematical models have been playing an essential role. The most popular model, called the SIR model, describes the behavior of the relationship between populations of susceptible, infected and recovered individuals. The model exhibits bifurcation resulting in the emergence of the endemic equilibrium when the disease transmission rate is large, or the net flow of susceptible individuals entering the region is large. In many cases, societies cannot make the inflow small enough to directly eradicate a disease of high transmission rate. Investigating and confirming stability and robustness properties of both disease-free and endemic equilibria are important and useful for the prediction and control of infectious diseases. This presentation first provides a brief induction to the stability analysis, and then limitations of standard tools and results in mathematical epidemiology are explained from the standpoint of a control theorist. The presentation focuses on the theory of construction and the use of Lyapunov functions for the specific nonlinear dynamical system. Major attention is paid to strictness of Lyapunov functions specialized to disease models. A new result allows one to establish robustness of the SIR model with respect to the inflow perturbation in terms of input-to-state stability. The usefulness to be demonstrated in this presentation includes designing feedback control laws for infectious diseases with mass vaccination.

Posted March 18, 2021

Last modified April 17, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
George Avalos, University of Nebraska

Mathematical Analysis of Interactive Fluid and Multilayered Structure PDE Dynamics

We discuss our recent work on a certain multilayered structure-fluid interaction (FSI) which arises in the modeling of vascular blood flow. The coupled PDE system under consideration mathematically accounts for the fact that mammalian veins and arteries are typically composed of various layers of tissues. Each layer will generally manifest its own intrinsic material properties, and will be separated from the other layers by thin elastic laminae. Consequently, the resulting modeling FSI system will manifest an additional PDE, which evolves on the boundary interface, to account for the thin elastic layer. (This is in contrast to the FSI PDEs which appear in the literature, wherein elastic dynamics are largely absent on the boundary interface.) As such, the PDE system will constitute a coupling of 3D fluid-2D wave-3D elastic dynamics. For this multilayered FSI system, we will in particular present results on well-posedness and stability. This is joint work with Pelin Guven Geredeli and Boris Muha.

Posted March 15, 2021

Last modified May 17, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Francesco Bullo, University of California, Santa Barbara
IEEE, IFAC, and SIAM Fellow

Non-Euclidean Contraction Theory and Network Systems

In this talk we discuss recent work on contraction theory and its application to network systems. First, we introduce weak semi-inner products as an analysis tool for non-Euclidean norms and establish equivalent characterizations of contraction and incremental stability. We also review robustness and network stability in this new setting. Second, we discuss the notion of weakly and semi-contracting systems. For weakly contracting systems we prove a dichotomy for asymptotic behavior of their trajectories and show asymptotic stability for certain non-Euclidean norms. For semi-contracting systems we study convergence to invariant subspaces and applications to networks of diffusively-coupled oscillators. This is joint work with Pedro Cisneros-Velarde, Alexander Davydov, and Saber Jafarpour.

Posted May 19, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Francesco Bullo, University of California, Santa Barbara
IEEE, IFAC, and SIAM Fellow

Non-Euclidean Contraction Theory and Network Systems

This is a continuation of last week’s Control and Optimization Seminar by the same speaker.

Posted September 21, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Michael Malisoff, LSU
Roy P. Daniels Professor

Event-Triggered Control Using a Positive Systems Approach

Control systems are a class of dynamical systems that contain forcing terms. When control systems are used in engineering applications, the forcing terms can represent forces that can be applied to the systems. Then the feedback control problem consists of finding formulas for the forcing terms, which are functions that can depend on the state of the systems, and which ensure a prescribed qualitative behavior of the dynamical systems, such as global asymptotic convergence towards an equilibrium point. Then the forcing terms are called feedback controls. Traditional feedback control methods call for continuously changing the feedback control values, or changing their values at a sequence of times that are independent of the state of the control systems. This can lead to unnecessarily frequent changes in control values, which can be undesirable in engineering applications. This motivated the development of event-triggered control, whose objective is to find formulas for feedback controls whose values are only changed when it is essential to change them in order to achieve a prescribed system behavior. This talk summarizes the speaker's recent research on event-triggered control theory and applications in marine robotics, which is collaborative with Corina Barbalata, Zhong-Ping Jiang, and Frederic Mazenc. The talk will be understandable to those familiar with the basic theory of ordinary differential equations. No prerequisite background in systems and control will be needed to understand and appreciate this talk.

Posted September 28, 2021

Last modified October 26, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Magnus Egerstedt, University of California, Irvine
Stacey Nicholas Dean of Engineering, IEEE Fellow, IFAC Fellow

Constraint-Based Control Design for Long Duration Autonomy

When robots are to be deployed over long time scales, optimality should take a backseat to “survivability”, i.e., it is more important that the robots do not break or completely deplete their energy sources than that they perform certain tasks as effectively as possible. For example, in the context of multi-agent robotics, we have a fairly good understanding of how to design coordinated control strategies for making teams of mobile robots achieve geometric objectives, such as assembling shapes or covering areas. But, what happens when these geometric objectives no longer matter all that much? In this talk, we consider this question of long duration autonomy for teams of robots that are deployed in an environment over a sustained period of time and that can be recruited to perform a number of different tasks in a distributed, safe, and provably correct manner. This development will involve the composition of multiple barrier certificates for encoding tasks and safety constraints through the development of non-smooth barrier functions, as well as a detour into ecology as a way of understanding how persistent environmental monitoring can be achieved by studying animals with low-energy life-styles, such as the three-toed sloth. Biography of Magnus Egerstedt.

Posted October 5, 2021

Last modified October 25, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Alberto Bressan, Penn State
Eberly Family Chair Professor

Optimal Control of Propagation Fronts and Moving Sets

We consider a controlled reaction-diffusion equation, modeling the spreading of an invasive population. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. The first part of the talk will focus on the optimal control of 1-dimensional traveling wave profiles. Using Stokes' formula, explicit solutions are obtained, which in some cases require measure-valued optimal controls. In turn, this leads to a family of optimization problems for a moving set, related to the original parabolic problem via a sharp interface limit. In connection with moving sets, in the second part of the talk I will present some results on controllability, existence of optimal strategies, and necessary conditions. Examples of explicit solutions and several open questions will be also discussed. This is a joint research with Maria Teresa Chiri and Najmeh Salehi.

Posted September 21, 2021

Last modified October 11, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Ilya Kolmanovsky, University of Michigan
IEEE Fellow, AACC Eckman Awardee

Reference Governors for Control of Systems with Constraints

As systems are downsized and performance requirements become more stringent, there is an increasing need for methods that are able to enforce state and control constraints as a part of the control design. The constraints can represent actuator range and rate limits, safety and comfort limits, and obstacle avoidance requirements. Reference governors are add-on supervisory algorithms that monitor and, if necessary, modify commands that are passed to the nominal controller/closed-loop system to ensure that pointwise-in-time state and control constraints are not violated. Approaches to the construction of reference governors will be described along with the supporting theory. Recent extensions of reference governors, such as a controller state and reference governor (CSRG) that in addition to modifying references can reset the controller states, and opportunities for the application of reference governors to ensure feasibility of model predictive controllers, will be discussed. The learning reference governor, which integrates learning into the reference governor operation, to handle constraints in uncertain systems, will also be touched upon. The potential for the practical applications of reference governors will be illustrated with several examples.

Posted August 25, 2021

Last modified October 26, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Kyriakos Vamvoudakis, Georgia Institute of Technology

Learning-Based Actuator Placement and Receding Horizon Control for Security against Actuation Attacks

Cyber-physical systems (CPS) comprise interacting digital, analog, physical, and human components engineered for function through integrated physics and logic. Incorporating intelligence in CPS, however, makes their physical components more exposed to adversaries that can potentially cause failure or malfunction through actuation attacks. As a result, augmenting CPS with resilient control and design methods is of grave significance, especially if an actuation attack is stealthy. Towards this end, in the first part of the talk, I will present a receding horizon controller, which can deal with undetectable actuation attacks by solving a game in a moving horizon fashion. In fact, this controller can guarantee stability of the equilibrium point of the CPS, even if the attackers have an information advantage. The case where the attackers are not aware of the decision-making mechanism of one another is also considered, by exploiting the theory of bounded rationality. In the second part of the talk, and for CPS that have partially unknown dynamics, I will present an online actuator placement algorithm, which chooses the actuators of the CPS that maximize an attack security metric. It can be proved that the maximizing set of actuators is found in finite time, despite the CPS having uncertain dynamics. Biography of Kyriakos Vamvoudakis.

Posted September 27, 2021

Last modified November 3, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Silviu-Iulian Niculescu, Laboratoire des Signaux et Systèmes (L2S)

Delays in Interconnected Dynamical Systems: A Qualitative Analysis

It is well-known that interconnections of two or more dynamical systems lead to an increasing complexity of the overall systems’ behavior, due to the effects induced by the emerging dynamics (which may include feedback loops) in significant interactions (involving sensing and communication) with environmental changes. One of the major problems appearing in such interconnection schemes is related to the propagation, transport, and communication of delays acting through, and inside, the interconnections. The aim of this talk is to briefly present user-friendly methods and techniques (based in part on frequency-domain approaches) for the analysis and control of dynamical systems in the presence of delays. The presentation is as simple as possible, focusing on the main intuitive (and algebraic and geometric) ideas to develop theoretical results, and their potential use in practical applications. Single and multiple delays will be considered. The talk ends with illustrative examples.

Posted August 18, 2021

Last modified October 31, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Kirsten Morris, University of Waterloo
IEEE Fellow, SIAM Fellow

Optimal Controller and Actuator Design for Partial Differential Equations

Control can be very effective in altering dynamics. One issue for partial differential equations is that performance depends not only on the controller, but also on its location and spatial design. Existence of a concurrent optimal controller and spatial distribution has been established for several classes of partial differential equations and objectives. Some of these results will be discussed and illustrated with examples.

Posted September 20, 2021

Last modified November 12, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Sonia Martinez, University of California, San Diego
IEEE Fellow

Data-Driven Dynamic Ambiguity Sets: Precision Tradeoffs under Noisy Measurements

Stochastic and robust optimization constitute natural frameworks to solve decision-making and control problems subject to uncertainty. However, these fall short in addressing real-world scenarios for which models of the uncertainty are not available. Data-driven approaches can be of help to approximate such models, but typically require large amounts of data in order to produce performance-guaranteed results. Motivated by settings where the collection of data is costly and fast decisions need to be made online, we present recent work on the construction of dynamic ambiguity sets for uncertainties that evolves according to a dynamical law. In particular, we characterize the tradeoffs between the amount of progressively assimilated data and its future adequacy, due to its gradual precision loss in its predicted values.

Posted September 8, 2021

Last modified October 11, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Jorge Cortes, University of California, San Diego
IEEE Fellow, SIAM Fellow

Resource-Aware Control and Coordination of Cyberphysical Systems

Trading computation and decision making for less communication, sensing, or actuator effort offers great promise for the autonomous operation of both individual and interconnected cyberphysical systems. Resource-aware control seeks to prescribe, in a principled way, when to use the available resources efficiently while still guaranteeing a desired quality of service in performing the intended task. This talk describes advances of this paradigm along three interconnected thrusts: the design of triggering criteria that balance the trade-offs among performance, efficiency, and implementability; the synthesis of distributed triggers in network systems that can be evaluated by individual agents; and the benefits of flexibly interpreting what constitutes a resource. Throughout the presentation, we illustrate our discussion with applications to stabilization under information constraints, opportunistic actuation of safety-critical systems, and information exchanges in the coordination of multi-agent systems.

Posted September 27, 2021

Last modified October 11, 2021

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request passcode)
Yacine Chitour, Laboratoire des Signaux et Systèmes (L2S)

Worst Exponential Decay Rate for Degenerate Gradient Flows Subject to Persistency of Excitation

In this talk, I will present results for the estimation of the worst rate of exponential decay of degenerate gradient flows $\dot x = −Sx$, issued from adaptive control theory. Under persistent excitation assumptions on the positive semi-definite matrix $S$, upper bounds for this rate of decay consistent with previously known lower bounds are provided and analogous stability results for more general classes of persistently excited signals. The strategy of proof consists in relating the worst decay rate to optimal control questions and studying in detail their solutions. As a byproduct of our analysis, estimates for the worst $L_2$-gain of the time-varying linear control systems $\dot x = −cc^{\scriptscriptstyle T}x$ are obtained, where the signal $c$ is persistently excited. This is a joint work with Paolo Mason and Dario Prandi.

Posted January 13, 2022

Last modified January 17, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Joel Rosenfeld, University of South Florida

Dynamic Mode Decompositions for Control Affine Systems

We will review the machine learning technique of dynamic mode decomposition (or DMD) for continuous time systems and show how this may be extended to produce models for the state of an unknown control-affine systems using trajectory data. Trajectory data in this setting comes as a pair of control signals and the corresponding control trajectory, and the DMD method for control-affine systems enables the prediction of the action of the system in response to a previously unobserved control signal. This will require a discussion of reproducing kernel Hilbert spaces (or RKHSs), vector valued RKHSs, control Liouville operators, and multiplication operators.

Posted February 3, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Michele Palladino, University of L’Aquila

Optimal Control of the Moreau’s Sweeping Process

We present recent and new results on the optimal control of Moreau’s sweeping process (SP). We will present a novel approach for proving a version of the Pontryagin Maximum Principle in a general setting. Such an approach exploits a kind of small-time local controllability property which the SP dynamics naturally satisfies in a neighborhood of the moving constraint. Open problems and further research directions will be extensively discussed.

Posted January 13, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Emmanuel Trelat, Sorbonne Universite, Paris, France

On the Turnpike Property

The turnpike property was discovered in the 50's by Nobel prize winner Samuelson in economics. It stipulates that the optimal trajectory of an optimal control problem in large time remains essentially close to a steady state, itself being the optimal solution of an associated static optimal control problem. We have established the turnpike property for general nonlinear finite and infinite dimensional optimal control problems, showing that the optimal trajectory is, except at the beginning and the end of the time interval, exponentially close to some (optimal) stationary state, and that this property also holds for the optimal control and for the adjoint vector coming from the Pontryagin maximum principle. We prove that the exponential turnpike property is due to a hyperbolicity phenomenon which is intrinsic to the symplectic feature of the extremal equations. We infer a simple and efficient numerical method to compute optimal trajectories in that framework, in particular an appropriate variant of the shooting method. The turnpike property turns out to be ubiquitous and the turnpike set may be more general than a single steady-state, like for instance a periodic trajectory. We also show the shape turnpike property for PDE models in which a subdomain evolves in time according to some optimization criterion. These works are in collaboration with Gontran Lance, Can Zhang, and Enrique Zuazua.

Posted February 8, 2022

Last modified February 21, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Cameron Nowzari, George Mason University

Implementable Event-Triggered Controllers for Networked Cyber-Physical Systems

Rapid development of technology is quickly leading us to an increasingly networked and wireless world. With massive wireless networks on the horizon, the efficient coordination of such large networks becomes an important consideration. To efficiently use the available resources, it is desirable to limit wireless communication to only the instances when the individual subsystems actually need attention. Unfortunately, classical time-triggered control systems are based on performing sensing, actuation, and even communication actions periodically in time rather than when it is necessary. This motivates the need to transcend this prevailing paradigm in exchange for event-triggered control (ETC); where individual subsystems must decide for themselves when to take different actions based on local information. The concept of ETC has been proposed as early as the 1960's but now we are starting to see practical applications. Since then, the idea of ETC has been surging in popularity to now essentially stand alone in the area of systems and control. This then begs the question: why is ETC not yet more mainstream and why has industry still not adopted it in most actual control systems? In this talk we look at this question and argue that the majority of ETC algorithms being proposed today are too theoretical to be useful. We then show how we are addressing this problem by developing a standard set of tools and methodologies for co-designing efficient event-triggered communication and control algorithms for networked systems that can actually be used by practitioners; with quantifiable benefits, performance guarantees, and robustness properties. This talk identifies numerous shortcomings between theoretical concepts and what is actually needed in practice for the theory to be useful, and discusses how we might close this gap. Finally, this talk will cover specific challenges we encountered in applying the state of-the-art event-triggered control algorithms to a wireless clock synchronization problem, and how we overcame them.

Posted February 3, 2022

Last modified February 24, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Pauline Bernard, MINES ParisTech

Observer Design for Continuous-Time Dynamical Systems

We review the main techniques of state observer design for continuous-time dynamical systems. Starting from necessary conditions for the existence of such asymptotic observers, we classify the available methods depending on the detectability/observability assumptions they require. We show how each class of observer relies on transforming the system dynamics into a particular normal form which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. A particular focus will be given to the promising theory of KKL or nonlinear Luenberger observers.

Posted January 29, 2022

Last modified February 1, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Luc Jaulin, ENSTA-Bretagne

Interval Contractors to Solve Dynamical Geometrical Equations with Application to Underwater Robotics

In Euclidean space, the separation between distinct points corresponds to their distance and is purely spatial and positive. In space-time, the separation between events takes into account not only spatial separation between the events, but also their temporal separation. We will consider problems involving geometrical constraints in space-time in an underwater robotics context. The motion of the robots will be described by differential equations, and the clocks attached to each robot are not synchronized. An interval contractor based technique is used to solve the distributed state estimation problem. The method is illustrated on the localization of a group of underwater robots with unsynchronized clocks. In this problem, the travel time of the sound that gives us the distances between robots cannot be neglected.

Posted January 28, 2022

Last modified March 9, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Anton Selivanov, University of Sheffield, UK

Time-Delay Implementation of Derivative-Dependent Control

Time delays in input or output channels often lead to instability and, therefore, are usually avoided. However, there are systems where delays have a stabilizing effect. This happens because time-delays allow one to approximate output derivatives and use them in the feedback law. In this talk, I will consider an LTI system that can be stabilized using only output derivatives. The derivatives are approximated by finite differences, leading to time-delayed feedback. I will present a method for designing and analyzing such feedback under continuous-time and sampled measurements. It will be shown that, if the derivative-dependent control exponentially stabilizes the system, then its time-delayed approximation stabilizes the system with the same decay rate provided the time delay is small enough.

Posted January 13, 2022

Last modified February 21, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Pierdomenico Pepe, University of L'Aquila

Sampled-Data Event-Based Stabilization of Retarded Nonlinear Systems

We present an event-based controller for the stabilization of nonlinear retarded systems. The main features of the controller we provide are that (i) only sampled-data measures of the Euclidean internal variable are needed, thus avoiding continuous-time monitoring of the state in infinite dimensional spaces, ii) the event function is only evaluated at sampling instants, and involves a finite number of most recent measures, and iii) discontinuous feedbacks and non- uniform sampling are allowed. The controller guarantees semi-global practical asymptotic stability to an arbitrarily small final target ball around the origin, by suitably fast sampling.

Posted January 31, 2022

Last modified April 6, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova

Goh and Legendre-Clebsch Conditions for Non-Smooth Optimal Control Problems

Various generalizations of the original Maximum Principle (Pontryagin et al., 1956) have been produced in different theoretical frameworks in the literature, starting from the pioneering works of F. Clarke in the 1970s up to recent papers. For an end-point constrained optimal control problem with control affine dynamics, I will present ideas (from a work in progress with F. Angrisani) in the direction of adding higher order necessary conditions to the Maximum Principle. In particular, one can generalize the classical Goh condition and the Legendre-Clebsch condition (which include Lie brackets) to the case where the data are nonsmooth. In fact, the recently introduced notion of Quasi Differential Quotient (Palladino and R., 2020) allows one to treat two simultaneous kinds of non-smoothness, namely the one concerning the adjoint inclusion and the one connected with the set-valued Lie brackets (R. and Sussmann 2001), within the same framework.

Posted February 6, 2022

Last modified February 18, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Xiaobo Tan, Michigan State University
MSU Foundation Professor & Richard M. Hong Endowed Chair in Electrical Engineering

Modeling and Control of Hysteresis Using Minimal Representations

Hysteresis remains a key nonlinearity in magnetic and smart material actuators that challenges their control performance. High-fidelity modeling and effective compensation of hysteresis, yet with low computational complexity, are of immense interest. In this talk I will share some recent advances in this direction via several examples. First, I will present the optimal reduction problem for a Prandtl-Ishlinskii (PI) operator, one of the most popular hysteresis models, where an optimal approximation of the original operator with fewer constituent elements (play operators) is obtained via efficient dynamic programming. Second, I will discuss adaptive estimation of play radii, instead of their weights, as an alternative means for accurate modeling of hysteresis with a PI operator of low complexity. Finally, I will report a dynamic inversion approach to hysteresis compensation that requires minimal, qualitative conditions on the system model. Throughout the talk I will use experimental results from smart materials to illustrate the methods.

Posted January 27, 2022

Last modified February 15, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Andrea Serrani, Ohio State University
Editor-in-Chief of IEEE-TCST, Interim Chair of Department of ECE

Adaptive Feedforward Compensation of Harmonic Disturbances for Convergent Nonlinear Systems

Rejecting periodic disturbances occurring in dynamical systems is a fundamental problem in control theory, with numerous technological applications such as control of vibrating structures, active noise control, and control of rotating mechanisms. From a theoretical standpoint, any design philosophy aimed at solving this problem reposes upon a specific variant of the internal model principle, which states that regulation can be achieved only if the controller embeds a copy of the exogenous system generating the periodic disturbance. In the classic internal model control (IMC), the plant is augmented with a replica of the exosystem, and the design is completed by a unit which provides stability of the closed loop. In a somewhat alternative design methodology, referred to as adaptive feedforward compensation (AFC), a stabilizing controller for the plant is computed first and then an observer of the exosystem is designed to provide asymptotic cancelation of the disturbance at the plant input. In particular, the parameters of the feedforward control are computed adaptively by means of pseudo-gradient optimization, using the regulated error as a regressor. Contrary to IMC, which has been the focus of extensive investigation, application of AFC methods to nonlinear systems has remained so far elusive. This talk aims at presenting results that set the stage for a theory of AFC for nonlinear systems by providing a nonlinear equivalent of the condition for the solvability of the problem in the linear setting, and by re-interpreting classical linear schemes in a fully nonlinear setting. To this end, the problem is approached by combining methods from output regulation theory with techniques for semi-global stabilization.

Posted January 26, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click "Questions or comments?" to request Zoom link)
Sophie Tarboureich, Laboratoire d'Analyse et d'Architecture des Systèmes (LAAS), France

Algorithms for Event-Triggered Control

Event-triggered control consists of devising event-triggering mechanisms leading to only seldom control updates. In the context of event-triggered control, two objectives that can be pursued are (1) emulation, whereby the controller is a priori predesigned and only the event-triggering rules have to be designed and (2) co-design, where the joint design of the control law and the event-triggering conditions has to be performed. Control systems are connected to generic digital communication networks for implementation, transmission, coding, or decoding. Therefore, event-triggered control strategies have been developed to cope with communication, energy consumption, and computation constraints. The talk is within this scope. Considering linear systems, the design of event-triggering mechanisms using local information is described through linear matrix inequality (or LMI) conditions. From these conditions, the asymptotic stability of the closed loop system, together with the avoidance of Zeno behavior, are ensured. Convex optimization problems are studied to determine the parameters of the event-triggering rule with the goal of reducing the number of control updates.

Posted February 2, 2022

Control and Optimization Seminar Questions or comments?

9:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Monica Motta, Università di Padova, Italy

Stabilizability in Optimal Control

We address the stabilizability of nonlinear control systems, in an optimal control theoretic framework. First, we extend the nowadays classical concepts of sampling and Euler solutions that were developed by F. Clarke, Y. Ledyaev, E. Sontag, A. Subbotin, and R.J. Stern (1997, 2000) for control systems associated to discontinuous feedbacks, by also considering corresponding costs, given by integrals of a nonnegative Lagrangian. In particular, we introduce the notions of sample and Euler stabilizability to a closed target set with regulated cost, which require the existence of a stabilizing feedback that keeps the cost of all sampling and Euler solutions starting from the same point below the same level. Then, under mild regularity hypotheses on the dynamics and on the Lagrangian, we prove that the existence of a special control Lyapunov function, to which we refer to as a minimum restraint function (or MRF), implies not only stabilizability, but also that all sample and Euler stabilizing trajectories have regulated costs. The proof is constructive, being based on the synthesis of appropriate feedbacks derived from the MRF. As in the case of classical control Lyapunov functions, this construction requires that the MRF is locally semiconcave. However, by generalizing an earlier result by L. Rifford (2000) we establish that it is possible to trade regularity assumptions on the data with milder regularity assumptions on the MRF. In particular, we show that if the dynamics and the Lagrangian are locally Lipschitz up to the boundary of the target, then the existence of a mere locally Lipschitz MRF provides sample and Euler stabilizability with regulated cost. This talk is based on a joint work with Anna Chiara Lai (from University Roma La Sapienza, Rome, Italy), which is part of an ongoing, wider investigation of global asymptotic controllability and stabilizability from an optimal control perspective.