Plenary Lecture

Controllability and observability of multi-time linear PDE systems

Professor Constantin Udriste
University Politehnica of Bucharest
Faculty of Applied Sciences
Department of Mathematics
Splaiul Independentei 313
060042, Bucharest, ROMANIA
Email: udriste@mathem.pub.ro,
c_udriste@yahoo.com

Abstract: Since the obstruction of complete integrability conditions (path independent curvilinear integrals) is very strong, the control problems for multi-time first order PDEs were studied only in the discrete context. Now, to preserve the geometrical character of the problem, we present a continuous approach for the controllability and observability properties of multi-time completely integrable linear PDEs systems (holonomic evolution), overcoming the extant mathematical prejudices regarding the importance of a multi-time evolution. Our geometrical arguments show that each basic theorem has a correspondent in the case of single-time linear controlled ODEs system.

The main results include controllability criteria and the equivalence between controllability of a PDEs system and the observability of the dual PDEs system. All of these show that the passing from controlled single-time evolution to the controlled multi-time evolution is not trivial. Changing the geometrical language, the case of nonholonomic evolution can be recovered easily from our theory.
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Brief Biography of the Speaker:
Constantin Udriste was born in Turceni, Gorj, Romania on January 22, 1940. He earned his professor title from University of Timisoara in 1963 and his PhD from University Babes-Bolyai from Cluj-Napoca in 1971. Now he is Full Professor of Mathematics and Dean of the Faculty of Applied Sciences at University Politehnica of Bucharest. Also it is President of Balkan Society of Geometers.
Udriste has served on many advisory committees and editorial boards, and was the main organizer of over 10 International Mathematical Meetings. He is author and contributor of over 40 books, over 200 articles to mathematical journals and over 200 papers to mathematical meetings. Topics: group of motion, properties of the tangent bundle, almost coquaternion metric manifolds, variational calculus on Riemannian manifolds, Finsler-Lagrange-Hamilton manifolds, Riemannian convexity and optimization, magnetic dynamical systems, geometric dynamics and optimal control, the theory of spatial mechanisms, solar tower concentrator. A person of incredible energy and entusiasm, Udriste has trained 12 PhD students, many of whom are now faculty members.
Udriste has been the recipient of the following honors and awards: Dragomir Hurmuzescu Prize, Academy of Romania, 1985; Award for Distinguished Didactic and Scientific Activity, Ministry of Education and Instruction of Romania, 1988; Correspondent Member of the Academia Peloritana dei Pericolanti, 1997-; Member Research Board of Advisors, ABI, 1999-. Prize COPIRO - 2000 for Exact Sciences; Premio Anassilaos International 2002, Arte Cultura Scienze.