LSU
Mathematics

Calendar

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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
Lyapunov Functions and Viscosity Solutions, Part 1

Tuesday, October 16, 2001

Posted September 14, 2003

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU
Lyapunov Functions and Viscosity Solutions, Part 2

Tuesday, November 6, 2001

Posted September 14, 2003

3:00 pm 381 Lockett Hall

Michael Malisoff, LSU
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 Ph.D. 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 Telephone: 011-58-414-3602104
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 Ph.D. Candidate

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
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 Ph.D. 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 Ph.D. 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 Ph.D. 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 Ph.D. 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 Ph.D. 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 Ph.D. 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
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
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
"to be announced"

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 Telephone: 011-58-414-3602104
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
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
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
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. Here is its abstract, and here are the related papers and slides.

Tuesday, October 27, 2009

Posted October 9, 2009

10:00 am 117 Electrical Engineering Building

Michael Malisoff, LSU
Constructions of Strict Lyapunov Functions: An Overview

Tuesday, May 4, 2010

Posted January 28, 2010

3:00 pm 117 Electrical Engineering

Michael Malisoff, LSU
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
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