LMI Framework for Set Reachability Inclusion in Discrete-Time LTI Systems

• 成果类型: Article
• 署名作者: Hadizadeh Kafash, Sahand; Ruths, Jusin
• 署名单位: University of Texas System; University of Texas Dallas; University of Texas System; University of Texas Dallas
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3091412
• 发表日期: 2022
• 页码: 2997-3004
• 关键词: Ellipsoids; shape; Linear systems; safety; Linear matrix inequalities; trajectory; system analysis and design; Ellipsoidal approximation; linear time-invariant (LTI) systems; linear matrix inequality (LMI); reachable set

摘要

In this article, we present a convex optimization framework to verify the reachability of a desired set for discrete-time linear time-invariant systems. Given elliptically bounded inputs, the set of reachable states in N time steps is the Minkowski sum of a finite number of ellipsoids. We formulate the inclusion verification problem as a chain of constraints in the form of linear matrix inequalities. As the time horizon grows, the number of constraints becomes unwieldy, and we present a technique to achieve a similar level of accuracy with far fewer terms, significantly reducing the computational cost of the method. Numerical examples presented in this article show that the method is highly adaptable.