Invariant cover: Existence, cardinality bounds, and computation

Journal article

Abstract:: An invariant cover quantifies the information needed by a controller to enforce an invariance specification. This paper investigates some fundamental problems concerning existence and computation of an invariant cover for uncertain discrete-time linear control systems subject to state and control constraints. We develop necessary and sufficient conditions on the existence of an invariant cover for a polytopic set of states. The conditions can be checked by solving a set of linear programs, one for each extreme point of the state set. Based on these conditions, we give upper and lower bounds on the minimal cardinality of the invariant cover, and design an iterative algorithm with finite-time convergence to compute an invariant cover. We further show in two examples how to use an invariant cover in the design of a coder–controller pair that ensures invariance of a given set for a networked control system with a finite communication data rate.

Files:: Gao_et_al_2021_Invariant_cover_existence.pdf

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Language:: English
Keywords:: invariant cover

invariance feedback entropy

networked control systems

FFR
Pubs id:: 1159951
Local pid:: pubs:1159951
Deposit date:: 2021-02-03

Copyright holder:: Elsevier
Notes:: This is the accepted manuscript version of the article, available under the terms of a Creative Commons, Attribution, Non-Commercial, No Derivatives licence. The final version is available online from Elsevier at: https://doi.org/10.1016/j.automatica.2021.109588

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