Presented by: 
Professor Vladimir Gaitsgory (South Australia)
Mon 14 Nov, 2:00 pm - 3:00 pm
116 in Sir Llew Edwards (14).

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 numerical examples.