An Input-to-State Safety Approach Towards Safe Control of a Class of Parabolic PDEs Under Disturbances

TL;DR

This paper introduces a novel input-to-state safety control framework for linear parabolic PDE systems, ensuring safety and stability under disturbances, demonstrated through thermal control of battery modules.

Contribution

It develops a control design method combining control Lyapunov and barrier functionals for PDEs, addressing safety under disturbances, which is under-explored in current literature.

Findings

Effective safety control of PDEs demonstrated through simulations.

Framework guarantees safety and stability in disturbed PDE systems.

Applicable to thermal management in battery modules.

Abstract

Distributed Parameter Systems (DPSs), modelled by partial differential equations (PDEs), are increasingly vulnerable to disturbances arising from various sources. Although detection of disturbances in PDE systems have received considerable attention in existing literature, safety control of PDEs under disturbances remains significantly under-explored. In this context, we explore a practical input-to-state safety (pISSf) based control design approach for a class of DPSs modelled by linear Parabolic PDEs. Specifically, we develop a control design framework for this class of system with both safety and stability guarantees based on control Lyapunov functional and control barrier functional. To illustrate our methodology, we apply our strategy to design a thermal control system for battery modules under disturbance. Several simulation studies are done to show the efficacy of our method.