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Optimal regulation. (Czech) Zbl 0143.12701

The authors give a survey of the results obtained by the Soviet mathematicians in the field of optimal regulation of systems. A detailed account is given for the following problem concerning the linear system (1) \(\dot{x}=Ax+c_1u_1(t)+\cdots+c_ru_r(t)\), with a time-independent matrix \(A\) and vectors \(c_1,\cdots,c_r\): Find regulators \(u_k(t)\), among those for which \(|u_k|\leq 1\) almost everywhere, such that the solution of (1) is transferred from an arbitrary initial position to the zero solution in the shortest time.

MSC:

34H05 Control problems involving ordinary differential equations
49J15 Existence theories for optimal control problems involving ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
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