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Stochastic controllability and minimum energy control of systems with multiple delays in control. (English) Zbl 1167.93008
The mathematical model of linear, stationary stochastic dynamical system with multiple constant point delays in the control is considered here. Assumed that for admissible controls, initial conditions and disturbances there exists a unique solution. Solution of the problem in integral form represented as difference between the control action and desired element in the Hilbert space is provided. Because the control operator represented in integral form is completely continuous, the convergence of corresponding solutions to the desired value follows. Minimum energy control problem also considered.

MSC:
93B05 Controllability
93C05 Linear systems in control theory
93E03 Stochastic systems in control theory (general)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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