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arXiv · 2109.12378

Automaton-based Implicit Controlled Invariant Set Computation for Discrete-Time Linear Systems

Zexiang Liu·Tzanis Anevlavis·Necmiye Ozay·Paulo Tabuada
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Abstract

In this paper, we derive closed-form expressions for implicit controlled invariant sets for discrete-time controllable linear systems with measurable disturbances. In particular, a disturbance-reactive (or disturbance feedback) controller in the form of a parameterized finite automaton is considered. We show that, for a class of automata, the robust positively invariant sets of the corresponding closed-loop systems can be expressed by a set of linear inequality constraints in the joint space of system states and controller parameters. This leads to an implicit representation of the invariant set in a lifted space. We further show how the same parameterization can be used to compute invariant sets when the disturbance is not available for measurement.

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Zexiang Liu, Tzanis Anevlavis, Necmiye Ozay, Paulo Tabuada. 2021-09-25. Automaton-based Implicit Controlled Invariant Set Computation for Discrete-Time Linear Systems. https://arxiv.org/abs/2109.12378

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