Controlled Invariant Sets: Implicit Closed-Form Representations and Applications

• 成果类型: Article
• 署名作者: Anevlavis, Tzanis; Liu, Zexiang; Ozay, Necmiye; Tabuada, Paulo
• 署名单位: University of California System; University of California Los Angeles; University of Michigan System; University of Michigan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3336819
• 发表日期: 2024
• 页码: 4506-4521
• 关键词: Linear systems; Economic indicators; safety; closed-form solutions; Aerospace electronics; trajectory; State feedback; Constrained control; controlled invariant sets; Linear systems; optimization; Robust control

摘要

In this article, we revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets. Moreover, by considering such representations in the space of states and finite input sequences we obtain closed-form expressions for controlled invariant sets. An immediate advantage is the ability to handle high-dimensional systems since the closed-form expression is computed in a single step rather than iteratively. To validate the proposed method, we present thorough case studies illustrating that in safety-critical scenarios the implicit representation suffices in place of the explicit invariant set. The proposed method is complete in the absence of disturbances, and we provide a weak completeness result when disturbances are present.