Constrained regulation problem for continuous-time stochastic systems under state and control constraints

Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation proble...

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Bibliographic Details
Published in:Journal of vibration and control 2022-11, Vol.28 (21-22), p.3218-3230
Main Authors: Si, Xindong, Yang, Hongli
Format: Article
Language:English
Subjects:
Algorithms
Constraints
Control systems
Control theory
Feedback control
Invariants
Linear programming
Linear systems
Nonlinear systems
Numerical methods
Optimization
Set theory
Stochastic systems
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Summary:Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.
ISSN:1077-5463
1741-2986
DOI:10.1177/10775463211028075