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Optimal control for discrete-time singular stochastic systems with input delay. (English) Zbl 1351.93174

Summary: The finite-horizon linear quadratic regulation problem is considered in this paper for the discrete-time singular systems with multiplicative noises and time delay in the input. Firstly, the extremum principle is discussed, and a stationary condition is derived for the singular stochastic system. Then, based on the relationships established between the state and the costate variables, the stationary condition is also shown to be a sufficient criterion assuring the existence of the solution for the stochastic control problem. The optimal controller is designed as a linear function of the current state and the past inputs information, which can be recursively calculated by effective algorithms. With the designed optimal controllers, the explicit expression is also derived for the minimal value of the performance index. One numerical example is provided in the end of the paper to illustrate the effectiveness of the obtained results.

MSC:

93E20 Optimal stochastic control
49N10 Linear-quadratic optimal control problems
93C55 Discrete-time control/observation systems
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