On Robust Controlled Invariants for Continuous-time Monotone Systems

TL;DR

This paper develops a new framework for computing robust controlled invariants in monotone continuous-time systems, introducing structural properties, feasibility conditions, and an algorithm, demonstrated on a coupled tank system.

Contribution

It introduces a novel approach to compute robust controlled invariants for monotone systems, including structural insights, feasibility conditions, and an algorithmic solution.

Findings

Structural properties of invariants for SM and CSM systems

Feasibility points characterize invariants effectively

Algorithm successfully applied to coupled tank problem

Abstract

This paper delves into the problem of computing robust controlled invariants for monotone continuous-time systems, with a specific focus on lower-closed specifications. We consider the classes of state monotone (SM) and control-state monotone (CSM) systems, we provide the structural properties of robust controlled invariants for these classes of systems and show how these classes significantly impact the computation of invariants. Additionally, we introduce a notion of feasible points, demonstrating that their existence is sufficient to characterize robust controlled invariants for the considered class of systems. The study further investigates the necessity of reducing the feasibility condition for CSM and Lipschitz systems, unveiling conditions that guide this reduction. Leveraging these insights, we construct an algorithm for the computation of robust controlled invariants. To demonstrate the practicality of our approach, we applied the developed algorithm to the coupled tank problem.