# Calendar

Time interval: Events:

Tuesday, September 18, 2001

Posted November 17, 2003

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.

Tuesday, October 2, 2001

Posted September 14, 2003

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions and Viscosity Solutions, Part 1

Tuesday, October 16, 2001

Posted September 14, 2003

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions and Viscosity Solutions, Part 2

Tuesday, November 6, 2001

Posted September 14, 2003

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU Roy P. Daniels Professor
Lyapunov Functions and Viscosity Solutions, Part 3

Tuesday, October 22, 2002

Posted March 25, 2004

3:40 pm 381 Lockett Hall

Vinicio Rios, LSU Department of Mathematics PhD Student
A Theorem on Lipschitzian Approximation of Differential Inclusions

Tuesday, April 29, 2003

Posted September 19, 2003

3:30 pm 381 Lockett Hall

Peter Wolenski, LSU Department of Mathematics Russell B. Long Professor
Clarke's New Necessary Conditions in Dynamic Optimization

Wednesday, August 27, 2003

Posted August 26, 2003

3:40 pm - 4:30 pm Lockett 277

Jesus Pascal, Universidad del Zulia, Venezuela
Free Boundary Control Problem

Wednesday, November 19, 2003

Posted September 24, 2003

2:30 pm 240 Lockett Hall

Yuan Wang, Florida Atlantic University
A Relaxation Theorem for Differential Inclusions with Applications to Stability Properties

Abstract: The fundamental Filippov-Wazewski 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

Wednesday, November 26, 2003

Posted November 18, 2003

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.

Wednesday, March 31, 2004

Posted March 3, 2004

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.

Wednesday, April 14, 2004

Posted February 15, 2004

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.

Wednesday, April 28, 2004

Posted February 15, 2004

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.

Wednesday, September 1, 2004

Posted August 27, 2004

3:00 pm 381 Lockett Hall

Stanislav Zabic, Louisiana State University Department of Mathematics Graduate Student
Impulsive Systems

Monday, September 13, 2004

Posted September 3, 2004

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

Monday, September 20, 2004

Posted September 20, 2004

3:00 pm 381 Lockett Hall

Norma Ortiz, Mathematics Department, LSU PhD Student
An Existence Theorem for the Neutral Problem of Bolza

Monday, September 27, 2004

Posted September 21, 2004

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

Monday, October 4, 2004

Posted September 29, 2004

3:10 pm - 4:00 pm 381 Lockett Hall

Vinicio Rios, LSU Department of Mathematics PhD Student
Strong Invariance for Dissipative Lipschitz Dynamics

Monday, October 11, 2004

Posted October 6, 2004

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

Monday, October 18, 2004

Posted October 13, 2004

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

Monday, October 25, 2004

Posted October 20, 2004

3:10 pm - 4:00 pm 381 Lockett Hall

George Cazacu, LSU Department of Mathematics PhD student
Closed relations and Lyapunov functions for polysystems

Monday, November 15, 2004

Posted November 10, 2004

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).

Monday, November 22, 2004

Posted November 3, 2004

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

Monday, November 29, 2004

Posted November 25, 2004

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

Wednesday, February 23, 2005

Posted February 21, 2005

3:30 pm 2150 CEBA

Michael Malisoff, LSU Roy P. Daniels Professor
An Introduction to Input-to-State Stability

Wednesday, March 9, 2005

Posted March 8, 2005

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.

Thursday, April 7, 2005

Posted March 29, 2005

2:00 pm - 3:00 pm Lockett 381

Vladimir Gaitsgory, School of Mathematics and Statistics, University of South Australia
TBA

Friday, April 8, 2005

Posted March 29, 2005

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

Wednesday, April 13, 2005

Posted April 11, 2005

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

Wednesday, April 20, 2005

Posted April 15, 2005

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

Friday, June 24, 2005

Posted June 17, 2005

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

Friday, July 15, 2005

Posted July 15, 2005

10:00 am EE 117

Boumediene Hamzi, University of California, Davis
The Controlled Center Dynamics

Tuesday, February 21, 2006

Posted January 30, 2006

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.

Thursday, May 11, 2006

Posted April 19, 2006

3:40 pm 381 Lockett

Franco Rampazzo, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova Professor of Mathematical Analysis
Moving Constraints as Controls in Classical Mechanics

Professor Rampazzo's visit is sponsored by the Louisiana Board of Regents Grant "Enhancing Control Theory at LSU". This is one of two talks the speaker will give at LSU during May 2006. For abstracts of both talks, click here.

Thursday, September 28, 2006

Posted September 18, 2006

3:30 pm 285 Lockett

Martin Hjortso, Louisiana State University Chevron Professor of ChemE
Some Problems in Population Balance Modeling

Wednesday, January 31, 2007

Posted January 30, 2007

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.

Wednesday, February 7, 2007

Posted February 4, 2007

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.

Wednesday, February 14, 2007

Posted February 9, 2007

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.

Wednesday, February 28, 2007

Posted February 22, 2007

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.

Wednesday, March 7, 2007

Posted March 5, 2007

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.

Wednesday, March 28, 2007

Posted March 26, 2007

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.

Wednesday, April 18, 2007

Posted April 16, 2007

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.

Wednesday, April 25, 2007

Posted April 23, 2007

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.

Wednesday, May 2, 2007

Posted May 1, 2007

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.

Wednesday, September 12, 2007

Posted September 9, 2007

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

Monday, June 29, 2009

Posted June 28, 2009

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.

Tuesday, October 27, 2009

Posted October 9, 2009

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.

Tuesday, May 4, 2010

Posted January 28, 2010

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.

Thursday, September 24, 2015

Posted September 21, 2015

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.

Thursday, October 1, 2015

Posted September 28, 2015

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)

Thursday, October 8, 2015

Posted October 5, 2015

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.

Wednesday, April 3, 2019

Posted March 18, 2019

10:30 am - 11:30 am 3316E Patrick F. Taylor Hall

Trying 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/

Tuesday, May 14, 2019

Posted May 2, 2019

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.

Tuesday, November 26, 2019

Posted November 21, 2019

10:00 am 3316E Patrick F. Taylor Hall

Pavithra Prabhakar, Kansas State University
Robust Verification of Hybrid Systems

Information on ECE Seminar Web Site.

Wednesday, March 10, 2021

Posted March 4, 2021

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.

Wednesday, March 17, 2021

Posted March 10, 2021

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.

Wednesday, March 24, 2021

Posted March 2, 2021

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.

Wednesday, March 31, 2021

Posted March 10, 2021

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.

Wednesday, April 7, 2021

Posted February 20, 2021

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.

Wednesday, April 14, 2021

Posted March 22, 2021

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.

Wednesday, April 28, 2021

Posted March 5, 2021

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.

Wednesday, May 5, 2021

Posted March 18, 2021

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-goverened 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.

Friday, May 7, 2021

Posted April 1, 2021

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.

Wednesday, May 12, 2021

Posted March 18, 2021

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.

Wednesday, May 19, 2021

Posted March 15, 2021

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.

Wednesday, May 26, 2021

Posted May 19, 2021

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.