Minmax control of systems with uncertainty in the intial state and in the state equations

In this paper, optimal control problems where there is uncertainty in the initial state measurement or where there are uncertain parameters in the state equations are investigated. It is assumed that nature will choose the uncertainty to maximize the cost which the controller is attempting to minimize. Thus, a minmax control is sought. Sufficient conditions for a control to be a minmax control are presented. These conditions suggest methods for finding the minmax control and such techniques are described. The application of these methods is illustrated by example problems.