Adiscrete sample average approximation for uncertain minimax optimal control problems

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

Comodoro Rivadavia

Congreso; VI Congreso de Matemática Aplicada, Computacional e Industrial; 2017

ASAMACI

We address an uncertain minimax optimal control problem with linear dynamics where the objective functional is the expected value of the supremum of the running cost over a time interval. We approximate the cost by a sample average function and we study the epi-convergence of the approximated objective functionals as well as the convergence of their global minimizers. Then we define an Euler discretization in time of the sample average problem and prove that the values of the discrete problems converges to the value of the sample average approximation. We show that there exists a sequence of discrete problems such that the accumulation points of the minimizers are optimal solution of the original problem. Finally we propose a convergent descent method to solve the discrete time problem.