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

TL;DR

This paper introduces a novel automaton-based method to compute implicit controlled invariant sets for discrete-time linear systems with disturbances, enabling robust control design even without disturbance measurements.

Contribution

It provides closed-form expressions for invariant sets using automata, extending invariant set computation to disturbance-agnostic scenarios.

Findings

Implicit invariant sets expressed by linear inequalities

Automaton-based parameterization for disturbance-reactive controllers

Invariant set computation without disturbance measurement

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.