Computation of Maximal Admissible Robust Positive Invariant Sets for Linear Systems With Parametric and Additive Uncertainties

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2024-06-17 DOI:10.1109/LCSYS.2024.3415489
Anchita Dey;Shubhendu Bhasin
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Abstract

In this letter, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and input are subject to hard constraints, and the system parameters and the exogenous disturbance are assumed to belong to known convex polytopes. We provide necessary and sufficient conditions for the existence of the non-empty MARPI set, and explore relevant features of the set that lead to an efficient finite-time converging algorithm with a suitable stopping criterion. The analysis hinges on backward reachable sets defined using recursively computed halfspaces and the minimal RPI set. A numerical example is used to validate the theoretical development.
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具有参数和添加不确定性的线性系统的最大可容许稳健正不变集的计算
在这封信中,我们探讨了如何计算具有参数不确定性和外加扰动的离散时线性时变系统的最大容许鲁棒正不变量(MARPI)集的问题。系统状态和输入都受到硬约束,系统参数和外生扰动被假定属于已知的凸多面体。我们提供了非空 MARPI 集存在的必要条件和充分条件,并探讨了该集的相关特征,从而提出了一种具有合适停止准则的高效有限时间收敛算法。分析的关键是使用递归计算的半空间和最小 RPI 集定义的后向可达集。一个数值示例用于验证理论的发展。
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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