Numerical Methods for Minimax Control Problems: Deterministic and Uncertain Systems

J. GIANATTI; L.A. PARENTE; P.A. LOTITO; L.S. ARAGONE

Tandil

Workshop; V Latin American Workshop on Optimization and Control; 2016

Universidad Nacional del Centro de la Provincia de Buenos Aires

We consider minimax optimal control problems with linear dynamics. First, we study the deterministic case where, under convexity assumptions, by using non-smooth optimization techniques, we derive a set of optimality conditions. We define an approximated discrete-time problem where analogous conditions hold. One of them allows us to design an easily implementable descent method whose accumulation points are optimal.Then, we address an extension of the previous problem to a setting with parameter uncertainty, where the objective function is the expectation of a max operator and the underlying trajectory depends on stochastic parameters in such way that, for each fixed sample in a complete probability space, we recover the deterministic case. We analyze two possibles approaches and show some examples.