(The seminar will begin after the Yohanan Vax scholarship presentation at 15:00, and may be a few minutes 

after the scheduled time.) 

Speaker: Prof. Vladimir Gaitsgory, Macquarie University

Title:  Linear Programming Approach to Optimal Control and Singularly Perturbed Optimal Control Problems 

Abstract: Problems of optimal control (POC) of dynamical systems arise in many applications and enjoy a great deal of attention internationally. Common theoretical tools for analysis and solution of POC are Pontryagin maximum principle and Hamilton-Jacobi-Bellman equations. In this presentation, we will discuss a much less conventional approach to POC. Namely, we will show that, based on occupational measures relaxation, the POC can be “equivalently” reformulated as an infinite-dimensional linear programming (IDLP) problem. We will indicate a way how this IDLP problem and its dual can be solved numerically and how their obtained numerical solutions can be used for a construction of a near optimal control of the underlying POC.  A special attention will be paid to analysis of so-called singularly perturbed POC, in which the state variables change their values with rates of different order of magnitude (so that some of them can be considered to be fast/slow with respect to others). Theoretical developments will be illustrated with some numerical examples.