Characterization, Verification and Computation of Robust Controlled Invariants for Monotone Dynamical Systems

TL;DR

This paper develops methods to compute and verify robust controlled invariants in discrete-time monotone dynamical systems, enhancing control system safety and reliability through set-based and trajectory-based characterizations.

Contribution

It introduces new characterizations and algorithms for verifying and computing robust controlled invariants tailored to different classes of monotone systems.

Findings

Effective algorithms for invariant verification and computation

Illustrative examples demonstrate approach advantages

Applicable to various classes of monotone systems

Abstract

In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and disturbances respect a given partial order. Then, we present set-based and trajectory-based characterizations of robust controlled invariants for the considered class of systems. Based on these characterizations, we propose algorithmic approaches for the verification and computation of robust controlled invariants. Finally, illustrative examples are provided showing the merits of the proposed approach.