Blagodatskikh, V. I.; Filippov, A. F. Differential inclusions and optimal control. (Russian) Zbl 0595.49026 Tr. Mat. Inst. Steklova 169, 194-252 (1985). This is a survey of some results in convex analysis, multifunctions, differential inclusions and optimal control theory in the finite- dimensional case. In the first part, 45 theorems are presented about different classes of multifunctions, selections and integration of set- valued mappings. The second part is devoted to differential inclusions. Here 43 theorems on existence and different properties of solutions of such inclusions (such as, for example, dependence on initial data and right-hand sides, stability, monotonicity, compactness, convexity of the set of all solutions, the existence of bounded and periodic solutions). In the last part, some optimal control problems for differential inclusions are considered. Necessary optimality conditions in form of Pontryagin’s maximum principle are given for a time-optimal problem and for a problem with integral cost functional. Some sufficient conditions of optimality are also presented. All theorems are formulated without proofs, some of them are illustrated by examples. The bibliography consists of 119 positions and is not complete. Reviewer: Z.Wyderka Cited in 1 ReviewCited in 68 Documents MSC: 93B05 Controllability 34A60 Ordinary differential inclusions 49K15 Optimality conditions for problems involving ordinary differential equations 26E25 Set-valued functions 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections 49J45 Methods involving semicontinuity and convergence; relaxation 54C60 Set-valued maps in general topology 49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control Keywords:survey; convex analysis; multifunctions; differential inclusions; Pontryagin’s maximum principle; time-optimal problem; integral cost functional PDFBibTeX XMLCite \textit{V. I. Blagodatskikh} and \textit{A. F. Filippov}, Tr. Mat. Inst. Steklova 169, 194--252 (1985; Zbl 0595.49026)