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Optimal Constrained Stabilization of Stochastic Time-Delay Systems | IEEE Journals & Magazine | IEEE Xplore

Optimal Constrained Stabilization of Stochastic Time-Delay Systems


Abstract:

Physical systems in the real world are usually constrained due to different considerations. These constraints are closely related to the system safety and stability. In t...Show More

Abstract:

Physical systems in the real world are usually constrained due to different considerations. These constraints are closely related to the system safety and stability. In this letter we investigate the optimal stabilization control problem of stochastic time-delay systems under safety constraints. We first follow the Razumikhin approach to propose stochastic control Lyapunov and barrier functions, which result in the closed-form controllers for the stabilization and safety control individually. Next, based on the modification of the quadratic programming, an optimization problem is established to address the stabilization control under safe constraints. The optimal controller is derived explicitly in a switching form to tradeoff the stabilization and safety requirements. Finally, a numerical example is presented to illustrate the proposed control strategy.
Published in: IEEE Control Systems Letters ( Volume: 8)
Page(s): 2775 - 2780
Date of Publication: 09 December 2024
Electronic ISSN: 2475-1456

Funding Agency:


I. Introduction

In the real world physical systems are generally constrained, and the constraints range from their own limitations to the workspace and task requirements. The violation of these constraints has great impacts on the safety of physical systems; see [1] and references therein for more examples. In this respect, safety constraints are essential for physical systems, and impose strict requirements on system states/inputs to avoid system damages and economic losses. With the safety constraints in the priority place, physical systems are expected to accomplish some desired tasks, including stabilization, tracking and even temporal logic tasks [2], [3], [4]. From the control perspective, numerous approaches have been proposed and applied in the literature to deal with different tasks under safety constraints [1], [5], [6]. For instance, model predictive control (MPC) approach has been implemented to deal with motion planning and control problems of marine vehicles [6]; different energy-based functions, such as artificial potential functions, control Lyapunov and barrier functions, have been combined and mixed up to address formation, tracking and reach-avoid tasks of mobile robots [2], [5], [7].

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References

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