Plenary Lecture

Finsler Optimal Control and Geometric Dynamics

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

Abstract: This paper relates the theory of optimal control to the Finsler geometry and to the geometric dynamics. Section 1 shows how we build a Finsler structure starting from an optimal control problem. Section 2 studies a dynamic system evolving over time and controlled through a Finsler control. In order to choose properly the controls, we use a payoff functional and the Pontryaguin Maximum Principle. Section 3 transforms a controlled evolution system in a Finsler geometric dynamics. Section 4 introduces the idea of the controlled Finsler gradient flows in optimization problems. Section 5 studies the Finsler optimal control attached to Rosenbrock function. Section 6 formulates a Finsler affine regulator problem. Section 7 describes a Finsler optimal growth model.

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.