LQR and stabilization for discrete-time systems with multiplicative noises and input delays

Wang，Hongxia1; Zhang，Huanshui1; Li，Lin2; Fu，Minyue3

2023

10.1109/TAC.2023.3307218

IEEE Transactions on Automatic Control   影响因子和分区

0018-9286

1558-2523

This paper is concerned with linear quadratic regulation (LQR) and stabilization problems for discrete-time stochastic systems with multiple input channels and input delays. In comparison with single-input-channel problems, a key difficulty, induced by the different delays in different input channels, is that the information sets for multiple controllers are required to be asymmetric and coupled. A novel technique, referred to as orthogonal decomposition-reorganization, is proposed to conquer the coupling between channels. After the technique is used, a new method based on some refined decompositions is provided to solve the delayed forward-backward stochastic difference equations(D-FBSDEs), which overcomes the asymmetry and amounts to finding the solvability condition of the underlying LQR problems. The complete solutions of the finite- and infinite-horizon LQR problems are given by newly developing Riccati-type equations. Also, a necessary and sufficient stabilizing condition is obtained for the system restricted by a performance index. Finally, the effectiveness of the results is evaluated by a numerical example.

Costs Delay effects Delays Discrete-time systems input delays LQR multiplicative noise networked control Stochastic processes stochastic system Stochastic systems Symmetric matrices

SCI ; EI

英语

其他

20233514640037

Difference equations ; Digital control systems ; Discrete time control systems ; Networked control systems ; Phase noise ; Random processes ; Riccati equations ; Stabilization ; Stochastic control systems

Magnetism: Basic Concepts and Phenomena:701.2 ; Control Systems:731.1 ; Control System Applications:731.2 ; Calculus:921.2 ; Numerical Methods:921.6 ; Probability Theory:922.1 ; Systems Science:961

ENGINEERING

2-s2.0-85168725167

Scopus

1.School of Electrical and Automation Engineering, Shandong University of Science and Technology, Qingdao, China
2.School of Information Science and Engineering, Shandong Agricultural University, Taian, China
3.Shenzhen Key Laboratory of Control Theory and Intelligent Systems and Centre for Control Science and Technology, Southern University of Science and Technology, Shenzhen, China

Wang，Hongxia,Zhang，Huanshui,Li，Lin,et al. LQR and stabilization for discrete-time systems with multiplicative noises and input delays[J]. IEEE Transactions on Automatic Control,2023,PP(99):1-16.

Wang，Hongxia,Zhang，Huanshui,Li，Lin,&Fu，Minyue.(2023).LQR and stabilization for discrete-time systems with multiplicative noises and input delays.IEEE Transactions on Automatic Control,PP(99),1-16.

Wang，Hongxia,et al."LQR and stabilization for discrete-time systems with multiplicative noises and input delays".IEEE Transactions on Automatic Control PP.99(2023):1-16.