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| Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays |
| XiaoLu,QiyanZhang,XiaoLiang,HaixiaWang,ChunyangSheng,ZhiguoZhang |
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| (Shandong University of Science and Technology, Qingdao, China) |
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| DOI：https://doi.org/10.1007/s11768-021-00053-z |
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| 基金项目: |
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| Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays |
| Xiao Lu,Qiyan Zhang,Xiao Liang,Haixia Wang,Chunyang Sheng,Zhiguo Zhang |
| (Shandong University of Science and Technology, Qingdao, China) |
| Abstract: |
| This paper is concerned with the optimal linear quadratic Gaussian (LQG) control problem for discrete time-varying system
with multiplicative noise and multiple state delays. The main contributions are twofolds. First, in virtue of Pontryagin’s
maximum principle, we solve the forward and backward stochastic difference equations (FBSDEs) and show the relationship
between the state and the costate. Second, based on the solution to the FBSDEs and the coupled difference Riccati equations,
the necessary and sufficient condition for the optimal problem is obtained. Meanwhile, an explicit analytical expression is
given for the optimal LQG controller. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm. |
| Key words: LQG control · Discrete time-varying system · Multiplicative noise · Multiple state delays |
