Plenary Lecture

Multi-Time Optimal Control

Professor Constantin Udriste
University Politehnica of Bucharest
Faculty of Applied Sciences
Department of Mathematics, Splaiul Independentei 313
Bucharest 060042, Romania

Abstract: This lecture joins some concepts (adjointness, Hamiltonian systems, duality, Riemannian manifolds) that appears in Mechanics, Field Theory, Differential Geometry, and Control Theory in order to create a multi-time maximum principle.
Near the classical theory we introduce new types of Euler-Lagrange or Hamilton PDEs for optimal control problems with performance criteria involving curvilinear or multiple integrals and evolutions of multidimensional flow type. The main novel feature of the anti-trace multi-time Euler-Lagrange or Hamilton PDEs is that they are connected to the multi-time maximum principle.
The topics include: variational calculus with gradient variations and curvilinear or multiple integral functionals, properties of multi-time Euler-Lagrange operator (changing of the Lagrangian by addition and multiplication, anti-trace multi-time Euler-Lagrange PDEs and new conservation laws), the conversion to multi-time Hamilton PDEs (canonical variables, first kind and second kind of anti-trace multi-time Hamilton PDEs), the multi-time maximum principle approach of anti-trace multi-time Euler-Lagrange or Hamilton PDEs.

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.