Neural Adaptive Boundary Control for Switched PDE Systems With Application to Chip Temperature Control

Abstract

This article investigates a novel neural adaptive boundary control strategy for a class of switched partial differential equation (PDE) systems with persistent dwell-time (PDT) switching rules. First, a PDT switching regularity-based PDE is proposed to model systems with fast and slow switching characteristics and time-space evolutionary properties, which can overcome spatiotemporal dynamics’ switching frequency constraint. Furthermore, to eliminate the negative effects of unknown uncertainties on the system stability, a neural adaptive boundary control scheme is developed by using radial basis function neural networks. Next, through the use of mode-dependent multiple Lyapunov functions and with the help of integrating by parts, iteration, and geometric progression methods, sufficient conditions can be derived to guarantee the exponential input-to-state stability of closed-loop switched PDE systems. Finally, a practical example concerning the temperature control of semiconductor power chips is carried out to demonstrate the validity of the obtained results.