Synchronizing controller design for networked heat equations with boundary structured time-varying perturbations and general disturbances

Abstract

State synchronization with uncertain disturbances is an important issue in networked heat equations, especially in certain industrial production processes. A synchronizing controller based on active disturbances rejection control (ADRC) is developed to deal with this work. First, an observer is designed rely on the boundary output information of each subsystem to estimate/offset the total disturbances which are made of structured time-varying perturbations and unknown disturbances. Then, an adaptive gain controller based on consensus protocol is used to achieve synchronization between each subsystem and the reference system. Plus, the convergence of the networked heat equations to the reference systems’ state is established by using Lyapunov functional method, and the well-posedness of the closed-loop system is shown by using established results on an analytic semigroup approach. The simulation example of five networked heat equations with different time-varying disturbances, demonstrates the effectiveness and robustness of the proposed method.