The optimization of solutions of the dynamic systems with random structure. (English) Zbl 1217.93184

Růžičková, Miroslava; Dzhalladova, Irada

Abstr. Appl. Anal. 2011, Article ID 486714, 18 p. (2011).

Summary: The paper deals with the class of jump control systems with semi-Markov coefficients. The control system is given by a system of linear differential equations. Every jump of the random process implies the random transformation of solutions of the considered system. Relations determining the optimal control to minimize the functional are derived using Lyapunov functions. Necessary conditions of optimization which enables the synthesis of the optimal control are established as well.

MSC:

93E20	Optimal stochastic control
93E03	Stochastic systems in control theory (general)
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60J75	Jump processes (MSC2010)
49K45	Optimality conditions for problems involving randomness

Keywords:

jump control systems; semi-Markov coefficients; linear differential equations; Lyapunov functions; necessary conditions of optimization

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