Louisiana Workshop on
Mathematical Control Theory

May 16-25, 2006
Louisiana State University
Baton Rouge, LA

Scope of Workshop Workshop Committee Local Information
Principal Talks Other Talks Workshop Schedule

Scope of Workshop

This meeting includes eight principal talks by Francis Clarke who is a major figure in nonsmooth analysis and optimization theory. There will also be seven additional presentations by other speakers including a keynote presentation by Zvi Artstein on relaxed controls. The workshop topics include nonsmooth analysis, Hamilton-Jacobi-Bellman equations, and feedback stabilization. It promotes interdisciplinary contact between mathematical control researchers, and provides opportunities for young researchers and graduate students interested in applied controls and optimization to meet and interact with leading figures in the field. Awards from the Louisiana Board of Regents Enhancement Program support attendance at the workshop by young researchers and participants without other means of travel support. This meeting fosters advances in mathematical control theory and increased interaction between the pure and applied mathematics communities. The workshop includes participants from several countries, including students and young faculty, furthering collaboration among research groups in different parts of the world.

Principal Talks

Title of Talks
Francis Clarke Calculus of Variations, Nonsmooth Analysis and Control Theory
Institut Camille Jordan,
Université Claude-Bernard
(Lyon I), FRANCE

Clarke's lectures will take place on each day of the workshop starting at 9AM in 116 Prescott Hall.

Abstract: This series of eight lectures begins by presenting nonsmooth analysis: what is it, and why do we need it? Next comes an introduction to the calculus of variations, from its classical roots to modern developments in optimal control. Along the way, we will see the role of the Hamilton-Jacobi equation and the Pontryagin maximum principle. We next look at the central issue in contemporary control theory, the design of feedbacks, in the context of Lyapunov methods, stabilization, and sliding modes. The final topic will be a return to the calculus of variations, but in the multiple integral setting, where the regularity theorems of Hilbert-Haar and De Giorgi will be revisited. The emphasis throughout the talks will be on basic questions, main approaches, and general principles.

Biography of Speaker: Francis Clarke was born in 1948 in Montréal. His PhD is from the University of Washington (1973); he became a full professor at the University of British Columbia in 1978. In 1984 he was named director of the Centre de Recherches Mathématiques (CRM) at l'Université de Montréal. During his nine year tenure, CRM evolved into Canada's first national research center for mathematics and its applications. Clarke was also founding director of ISM, a mathematics institute spanning Montréal's four universities. He is now a faculty member at l'Université de Lyon, in l'Institut Camille Jordan and also holds a chair in mathematical control theory at l'Institut universitaire de France. Francis Clarke's research interests lie in nonsmooth analysis (a term he coined), differential equations, control theory, optimization, and the calculus of variations. His contributions have involved the development of nonsmooth calculus, its applications to dynamic optimization, regularity and existence theory in the calculus of variations, Hamiltonian mechanics, generalized solutions of the Hamilton-Jacobi equation, and feedback control synthesis. Francis Clarke is the author of the book Optimization and Nonsmooth Analysis (Wiley 1983, now in SIAM's Classics in Applied Mathematics Series), which has been translated into Russian. A Fellow of the Royal Society of Canada, he received the Coxeter-James and the Archambault research prizes, and a Killam Fellowship. He has been a featured speaker at the International Congress of Mathematicians (Helsinki 1978), plenary speaker at the IEEE Conference on Decision and Control (Brighton 1991) and the European Control Conference (Porto 2001) and keynote speaker at the Congress of Nonlinear Analysts (Athens 1996). In 2004 he was president of the scientific committee for the first joint meeting of the six mathematical societies of Canada and France.

Other Talks

Title and Time of Talk
Zvi Artstein Relaxed Controls and Related Ideas
(May 19th, 2PM)
Department of Mathematics, Weizmann Institute of Science, ISRAËL
Abdou Dramé Semilinear Parabolic Boundary Value Problems: An Application to Bioreactors
(May 23rd, 1:30PM)
Center for Systems Engineering and Applied Mechanics (CESAME), Department of Applied Mathematics, Université Catholique de Louvain, BELGIUM
Michael Malisoff
On Strict Lyapunov Functions for Discrete Time, Continuous Time, and Hybrid Time-Varying Systems
(May 24th, 2:15PM)
Department of Mathematics, Louisiana State University, Baton Rouge
Antonio Marigonda
Differentiability Properties for a Class of Non-Lipschitz Functions and Applications
(May 23rd, 2:15PM)
Dipartimento di Matematica, Università di Roma "La Sapienza", Rome, ITALY
Chadi Nour The Hamilton-Jacobi Equation of the Minimal Time Function: The Constant Dynamic Case
(May 18th, 1:30PM)
Computer Science and Mathematics Division, Lebanese American University, Byblos, LEBANON
Norma Ortiz
The Generalized Problem of Bolza with Time Delay
(May 24th, 1:30PM)

Department of Mathematics, Virginia Commonwealth University, Richmond, VA

Vinicio Ríos The Minimal Time Function under the Monotone Lipschitz Assumption
(May 18th, 3PM)
Departamento de Matemáticas, Facultad Experimental de Ciencias, Universidad del Zulia, Maracaibo, VENEZUELA

All talks will be in 203 Prescott unless otherwise noted.

Workshop Committee

Alvaro Guevara
Assistant Organizer
Department of Mathematics,
Louisiana State University, USA
Michael Malisoff
MCT'06 Co-Chair
Department of Mathematics,
Louisiana State University, USA
Peter Wolenski
MCT'06 Chair
Department of Mathematics,
Louisiana State University, USA

Acknowledgements:  The organizers thank the LSU Department of Mathematics staff and Louisiana Travel for assisting with this workshop. This workshop has been sponsored in part by the Louisiana Board of Regents grant "Enhancement of Control Theory at LSU" (P. Wolenski, Principal Investigator).

Local Information

This workshop will take place on the main campus of Louisiana State University (LSU) in Baton Rouge. The nearest airport to LSU is Baton Rouge Metropolitan Airport (BTR), which is 8 miles away. BTR is serviced by Continental Airlines, and offers service to international airports in Atlanta, Houston, and Memphis. Participants may find it more convenient to use the New Orleans International Airport (MSY), which is 75 miles away. However, there is no passenger train service between Baton Rouge and New Orleans, and the bus service from New Orleans to LSU is very limited. To help find their way around LSU, participants can go to the LSU Visitor Information Center to get campus directions and parking instructions. An online campus map is also available. Some local attractions located near LSU include the Louisiana State Capitol and the Bluebonnet Swamp. The weather in Baton Rouge for the workshop is expected to be rain-free with highs in the 90's and lows in the 70's.

Workshop Schedule

There will be one principal talk by Francis Clarke on each day of the workshop for a total of eight principal lectures. The principal talks will take place each day in 116 Prescott Hall from 9AM to 11:30AM. There will also be afternoon sessions in 203 Prescott starting at 1:30PM.

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