Suboptimal Linear Output Feedback Control of Discrete-time Systems with Multiplicative Noises

This paper considers the fundamental problem of output feedback control for a class of discrete-time systems with multiplicative noises. It is well-known that the classical separation principle fails due to the existence of multiplicative noises in state and control variables. Thus, the traditional...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. II, Express briefs Express briefs, 2023-04, Vol.70 (4), p.1-1
Main Authors: Liang, Xiao, Zhang, Ancai, Liu, Zhi, Du, Yingxue, Qiu, Jianlong
Format: Article
Language:English
Subjects:
Algorithms
Control systems
Controllers
Covariance matrices
Difference equations
Discrete time systems
Feedback control
forward and backward stochastic difference equations (FBSDEs) and coupled forward and backward Riccati equations (CFBREs)
Iterative methods
Iterative solution
multiplicative noises
Noise measurement
Optimal control
Output feedback
Output feedback control
Principles
Riccati equation
Riccati equations
Separation
Stochastic systems
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Summary:This paper considers the fundamental problem of output feedback control for a class of discrete-time systems with multiplicative noises. It is well-known that the classical separation principle fails due to the existence of multiplicative noises in state and control variables. Thus, the traditional optimal solutions for the controller and estimator can not be obtained. Different from the previous methods of enforced separation principle, the explicit expression of the suboptimal linear controller is derived by using the solution of the forward and backward stochastic difference equations (FBSDEs) and the linear optimal estimator. However, it leads to the other mathematical difficult problem that the control gain and the estimator gain are coupled with each other. Specifically, the control gain obeys the backward Riccati equation and the estimator gain satisfies the forward Riccati equation such that the solutions can not be acquired simultaneously. A novel method of iterative solutions to the coupled backward and forward Riccati equations (CBFREs) is proposed. Numerical examples are illustrated to show that the proposed algorithms have better performance than the previous methods.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2022.3222199