LINEAR TIME-INVARIANT CONTROL-PROBLEMS WITH PERTURBATIONS

We deal with a class of control problems whose (uncertain) mathematical model is given by a linear differential equation with control parameters and perturbation parameters influencing the dynamics of an object under consideration. All we know about the perturbations is that their values belong to a given compact set Q. We show how to find both lower and upper bounds for the value function of our original perturbed system in terms of the value functions of two simplified unperturbed control problems. We also give explicit formulae for ε-optimal policies in the class of so-called step-guided strategies. In the last section the results above are extended to the infinite horison setting. © 1990.