Control problems for ensembles of differential inclusion trajectories

The paper is devoted to the study of differential inclusions with a control parameter. The problems of interest for the theory of nonsmooth optimization are considered. We study the topological properties of the set of solutions and the ensemble of trajectories of differential inclusions, the property of controllability of the ensemble of trajectories, and necessary and sufficient conditions for optimality in the speed problem and in the minimax problem of controlling the ensemble of trajectories. The results may be used in the study of control systems under conditions of incomplete information. The monograph is intended for specialists in applied mathematics and optimal control theory.