On some MiniMax Optimal control problems

ARONNA, MARIA SOLEDAD; ARAGONE L. S.; LOTITO, PABLO; REYERO, GABRIELA

Rio de Janeiro, Brasil

Congreso; International Symposium on Mathematical Programming; 2006

Mathematical Programming Society

We consider an optimal control problem where the optimality criterium is to minimize the maximum cost given by a scalar function. The dynamic-system trajectory depends on the chosen control and the set of  admissible control policies are the essentially bounded functions into a compact set. We analyze the finite and infinite horizon cases. In the finite horizon case we have also considered an additive final cost and used the classical technique of adding an extra dimension to transform the Bolza formulation into a Mayer one. For the infinite horizon case we added a running cost in order to obtain an ergodic behavior. For each problem we propose a value function, a dynamical programming principle and the corresponding Hamilton- Jacobi-Bellman equations. We develop new numerical methods to compute the optimal costs, we analyze the numerical solutions and present numerical results.