Properties of the infinite dimensional linear programming problem, which along with its dual allow one to characterize the optimal value of the deterministic long-run average optimal control problem are discussed. The novelty of the consideration is that it is focused on the general case, when this optimal value may depend on initial conditions of the system. The talk is based on results that have been recently obtained in collaboration with V. Borkar and I. Shvartsman.
Vladimir Gaitsgory received his M.Sc. degree in automatic control from the Department of Control Processes at Leningrad Polytechnic Institute in 1973 and his Ph.D. in applied mathematics from the Institute for System Studies of the USSR Academy of Science in 1978. He is currently a Professor in the Department of Mathematics and Statistics at Macquarie University. Vladimir is an applied mathematician with broad areas of interest in control, optimization, dynamical systems and games theories, and their applications. His most important contributions are in the areas of singularly perturbed (SP) controlled dynamical systems and SP Markov Decision processes and mathematical programming problems.