Ashchepkov, L. T.; Vasil’ev, O. V. Methods of nonlinear programming in the theory of singular controls. (Russian) Zbl 0597.49022 Questions of stability and optimization of dynamical systems, Collect. Artic., Irkutsk 1983, 5-23 (1983). [For the entire collection see Zbl 0571.00005.] Here is considered a terminal problem of optimal control for trajectories of a system of ordinary differential equations under moving end-points. The author presents a simple proof for necessity of conditions which must be true along Pontryagin’s extremals. This proof is based on second-order necessary conditions for extrema in problems of nonlinear programming. In essence, the paper is of methodological importance. References, fourteen in number, fully cover the stated problem. Reviewer: V.Chernyatin MSC: 49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49K15 Optimality conditions for problems involving ordinary differential equations 90C30 Nonlinear programming 93C10 Nonlinear systems in control theory 93C15 Control/observation systems governed by ordinary differential equations Keywords:singular controls; terminal problem; Pontryagin’s extremals; second-order necessary conditions Citations:Zbl 0571.00005 PDFBibTeX XML