The robust maximum principle

The purpose of this chapter is to explore the possibilities of the maximum principle (MP) approach for the class of min–max control problems dealing with construction of the optimal control strategies for a class of uncertain models given by a system of ordinary differential equations with unknown parameters from a given finite set. The problem under consideration belongs to the class of optimization problems of the min–max type and consists in the design of a control providing a “good” behavior if applied to all models from a given class. Here a version of the robust maximum principle applied to the min–max Bolza problem with a terminal set is presented. The cost function contains a terminal term as well as an integral one. A fixed horizon is considered. The main result deals with finite parametric uncertain sets involved in a model description. The min–max LQ control problem is considered in detail.