×

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

Citations:

Zbl 0571.00005