Interval observer design for unobservable switched nonlinear partial differential equation systems and its application

This paper designs an interval observer for switched nonlinear partial differential equation (PDE) systems. Initially, persistent dwell-time switching rules are used to model switched PDE systems with fast and slow switching phenomena. Next, for unobservable systems caused by uncertainties, the interval observer for the target PDE systems is proposed by utilizing unknown but bounded information of the initial states, boundary conditions, external disturbances, and measurement noises. Subsequently, by utilizing the estimated state's upper and lower bounds, an interval observer-based control strategy is devised to stabilize the studied systems, and sufficient conditions to ensure the stability of the target systems and the observation error dynamics are provided. Furthermore, the designed interval observer is employed to detect sensor failures in the presence of various uncertainties. Finally, two examples, including the lithium-ion battery's temperature estimation and fault detection, are utilized to demonstrate the effectiveness of the obtained methods.