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On construction of asymptotic solution to linear singularly perturbed optimal control problem with degeneration of quality criterion. (Ukrainian. English summary) Zbl 1324.49020

Summary: We obtain some results concerning the investigation of construction an asymptotic solution of optimal control problem which is described by a linear singularly perturbed system of differential equations with degenerate matrix of derivatives in the case of degenerations of main matrix of criterion quality is considered. After application of the Pontryagin maximum principle the problem is reduced to a boundary value problem. Results of asymptotic analysis of general solution for a linear singularly perturbed system of differential equations with degenerations are used to investigated the problem.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
93C15 Control/observation systems governed by ordinary differential equations
93C70 Time-scale analysis and singular perturbations in control/observation systems
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