Differential Inclusion Approach for Mixed Constrained Problems Revisited

Properties of control systems described by differential inclusions are well established in the literature. Of special relevance to optimal control problems are properties concerning measurability, convexity, compactness of trajectories and Lipschitz continuity of the set valued mapping (or multifunction) defining the differential inclusion of interest. In this work we concentrate on dynamic control systems coupled with mixed state-control constraints. We characterize a class of such systems that can be described by an appropriate differential inclusion defined by a set valued mapping exhibiting “good” properties.