Plenary Lecture

Multitime Dynamic Programming for
Multiple Integral Actions

Professor Constantin Udriste
Department of Mathematics
University Politehnica of Bucharest
Romania
E-mail: anet.udri@yahoo.com

Abstract: This paper introduces a new type of dynamic programming PDE for optimal control problems with performance criteria involving multiple integrals. The main novel feature of the multitime dynamic programming PDE, relative to the standard Hamilton-Jacobi-Bellman PDE, is that it is connected to the multitime maximum principle. In other words, we present an interesting and useful connection between the multitime maximum principle and the multitime dynamic programming, characterizing the optimal control by means of a multitime Hamilton-Jacobi-Bellman PDE system that may be viewed as a feedback law. In the case of performance criteria involving multiple integrals with quadratic integrands, the new equations lead to multitime variant of the Riccati equation.
Section 1 introduces the multitime Hamilton-Jacobi PDE from geometrical point of view. Section 2 shows how a multitime control dynamics determines the multitime Hamilton-Jacobi-Bellman PDE via the value functions. Section 3 describes the connection between multitime dynamic programming and the multitime maximum principle.

Brief Biography of the Speaker:
Important Career Positions: Dean, Director, Chair, Full Professor 1990-, University Politehnica of Bucharest, Department of Mathematics.
Number of PhD Students: 25 in due time and 13 Doctors in Mathematics.
Membership of Associations: AMS, 1987; Tensor Society, 1985; Balkan Society of Geometers, President, 1994;
Publications: over 40 books; 200 papers; 200 communications.
Honors: D. Hurmuzescu Prize, Romanian Academy, 1985; Award MEI, 1988; Correspondent Member, Academia Peloritana, Messina, 1997; Titular Member, Academy of Romanian Scientists, 2007; Honorary Member, World Scientific and Engineering Academy and Society, 2008-;
Organizer: The International Conference of Differential Geometry and Dynamical Systems, University Politehnica of Bucharest, October 5-7, 2007; 7th WSEAS International Conference on Systems Theory and Scientific Computation (ISTASC'07), Vouliagmeni Beach, Athens, Greece, August 24-26 (2007); European Computing Conference, Vouliagmeni Beach, Athens, Greece, September 24-26, 2007; 12th WSEAS International Conference on Applied Mathematics, Cairo, Egypt, Dec. 29-31, 2007; 7th WSEAS International Conference on Circuits, Systems, Electronics, Control and Signal Processing, Cairo, Egypt, Dec. 29-31, 2007; Chair-Committee: American Conference on Applied Mathematics (Math’08) and Management, Marketing and Finances (MMF’08), Cambridge, Massachusetts, USA, March 24-26, 2008; International Program Committee: The Applied Computing Conference (ACC-08), Istanbul, Turkey, May 27-30, 2008.
Fields of Interest: Differential Geometry, Optimizations on Riemannian Manifolds, Magnetic Dynamical Systems, Geometric Dynamics.