Svobodová, Hana; Vaníček, Jiří Optimal regulation. (Czech) Zbl 0143.12701 Čas. PěstováníMat. 85, 345-355 (1960). 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. Reviewer: S. Drobot (MR0130053) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page 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 Keywords:ordinary differential equations PDFBibTeX XMLCite \textit{H. Svobodová} and \textit{J. Vaníček}, Čas. Pěstování Mat. 85, 345--355 (1960; Zbl 0143.12701)