Kibenko, Anatolij; Gusar, Viktor On the problem of optimal stabilization for nonlinear systems. (Russian. English summary) Zbl 0573.49001 Differ. Uravn. Primen. 32, 46-56 (1982). The existence of an optimal control is proved for a nonlinear control system \[ \dot x=Rx+Qu+F(x)x \] concerning the problem of optimal stabilization with a square quality criterion. The method of successive approximations is used. MSC: 49J15 Existence theories for optimal control problems involving ordinary differential equations 93C10 Nonlinear systems in control theory 93D15 Stabilization of systems by feedback 49M99 Numerical methods in optimal control 93C15 Control/observation systems governed by ordinary differential equations Keywords:existence of an optimal control; nonlinear control system; optimal stabilization PDFBibTeX XMLCite \textit{A. Kibenko} and \textit{V. Gusar}, Differ. Uravn. Primen. 32, 46--56 (1982; Zbl 0573.49001)