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The proposed book is devoted to proving necessary and sufficient optimality conditions for some classes of optimal control of discrete systems with a variable structure. The book consists of an introduction and two chapters. The first chapter has six sections The main results of the presented book are the followings: 1) Necessary optimality conditions of first order for two classes of discrete control problem with delay and variable structure with free right end of the trajectory. 2) The necessary conditions for optimality of like a discrete maximum principle for discrete control problem with variable structure in the presence of functional constraints as equality and inequalities type. 3) Necessary optimality conditions of first order for a class of step discrete systems with controlled switching conditions. 4) A sufficient condition for optimality type Krotov. 5) Necessary conditions for optimality of singular, in the sense of Pontryagin maximum principle controls for certain classes of discrete systems with variable structure. 6) Necessary conditions for optimality,of singular controls for a class of discrete control systems with varying structure.
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