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Optimal control for discrete‐time singular stochastic systems with input delay
Author(s) -
Wang Fan,
Liang Jinling,
Wang Feng
Publication year - 2016
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2237
Subject(s) - discrete time and continuous time , control theory (sociology) , multiplicative function , optimal control , controller (irrigation) , state (computer science) , mathematics , stochastic control , function (biology) , expression (computer science) , multiplicative noise , bellman equation , mathematical optimization , quadratic equation , computer science , control (management) , algorithm , statistics , artificial intelligence , agronomy , biology , computer hardware , geometry , mathematical analysis , programming language , signal transfer function , digital signal processing , evolutionary biology , analog signal
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. Copyright © 2016 John Wiley & Sons, Ltd.