A DISCRETE SAMPLE AVERAGE APPROXIMATION FOR UNCERTAIN MINIMAX OPTIMAL CONTROL PROBLEMS

GIANATTI, JUSTINA; LAURA S. ARAGONE; PABLO A. LOTITO; LISANDRO A. PARENTE

Comodoro Rivadavia

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

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