Roberto L. V. González

Relaxation of minimax optimal control problems with infinite horizon

A minimax optimal control problem with infinite horizon is studied. We analyze a relaxation of the controls, which allows us to consider a generalization of the original problem that not only has existence of an optimal control but also enables us to approximate the infinite-horizon problem with a sequence of finite-horizon problems. We give a set of conditions that are sufficient to solve directly, without relaxation, the infinite-horizon problem as the limit of finite-horizon problems.

On a system of Hamilton-Jacobi-Bellman inequalities associated to a minimax problem with additive final cost

We study a minimax optimal control problem with finite horizon and additive final cost. After introducing an auxiliary problem, we analyze the dynamical programming principle (DPP) and we present a Hamilton-Jacobi-Bellman (HJB) system. We prove the existence and uniqueness of a viscosity solution for this system. This solution is the cost function of the auxiliary problem and it is possible to get the solution of the original problem in terms of this solution.

NUMERICAL ANALYSIS OF A MINIMAX OPTIMAL CONTROL PROBLEM WITH AN ADDITIVE FINAL COST

In this paper we deal with the numerical analysis of an optimal control problem of minimax type with finite horizon and final cost. To get numerical approximations we devise here a fully discrete scheme which enables us to compute an approximated solution. We prove that the fully discrete solution converges to the solution of the continuous problem and we also give the order of the convergence rate. Finally we present some numerical results.

A Finite State Stochastic Minimax Optimal Control Problem with Infinite Horizon

We consider here a stochastic discrete minimax control problem with infinite horizon. We prove the existence of solution, we characterize it and we present iterative methods to compute it numerically.

A numerical procedure for minimizing the maximum cost

In this paper we consider the numerical solution of a minimax optimal control problem, where the cost to be minimized is the maximum of a function which depends on the state and the control. This problem arises, for example, when we want to minimize the maximum deviation of the controlled trajectories with respect to a given special trajectory. This differs from those problems usually considered in the optimal control literature, where an accumulated cost is minimized; problems of this type has received considerable interest in recent publications (see e.g. [1]). We present an approximation method which employs both discretization on time and on spatial variables. In this way, we obtain a computational implementable fully discrete problem. We give an optimal estimate for the error between the approximated solution and the optimal cost of the original problem.

Penalization techniques in L ∞ optimization problems with unbounded horizon

Abstract In this work we present a numerical procedure for the ergodic optimal minimax control problem. Restricting the development to the case with relaxed controls and using a perturbation of the instantaneous cost function, we obtain discrete solutions Uεk that converge to the optimal relaxed cost U when the relation ship between the parameters of discretization k and penalization ε is an appropriate one.