An Input-to-State Safety Approach Toward Safe Control of a Class of Parabolic PDEs under Disturbances

Distributed parameter systems (DPSs), modeled by partial differential equations (PDEs), are increasingly vulnerable to disturbances arising from various sources. Although the detection of disturbances in PDE systems has received considerable attention in the existing literature, safety control of PDEs under disturbances remains significantly underexplored. In this context, we explore a practical input-to-state safety (pISSf)-based control design approach for a class of DPSs modeled 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.