Atlas: Uncertain Parabolic Systems and Their Optimal Control: A Games Problem by N.U. Ahmed

6th International Conference on Differential Equations and Dynamical Systems
May 22-26, 2008

Baltimore, Maryland, USA

Organizers
Xinzhi Liu, University of Waterloo; Gaston M. N'Guerekata, Morgan State University

Uncertain Parabolic Systems and Their Optimal Control: A Games Problem
by
N.U. Ahmed
University of Ottawa

In this paper we consider a class of systems governed by

semilinear Parabolic Partial Di®erential Inclusions with controls on the bound-

ary. The multifunction represents uncertainty in the dynamics. This leads to

games problem; games against natural uncertainty. We consider output feed-

back control problem and prove existence of optimal policies by proving the

existence of saddle points for the games problem. Based on the existence

theory we present necessary conditions for optimal strategies. The necessary

conditions are then used to develop a numerical algorithm for computing the

optimal strategies. We present a proof of convergence of the algorithm.

[1]. N.U. Ahmed, Optimal Output Feedback Boundary Control for Systems

Governed by Semilinear Parabolic Inclusions: Uncertain Systems, Advances in

Nonlinear Variational Inequalities, 11(1),(2008),61-79.

Date received: February 24, 2008