Adaptive Spatial PID and PD Coupling in Synchronization Control of Collocated Infinite and Finite Dimensional Systems

This paper presents an entirely different approach for the synchronization of identical networked infinite dimensional systems. With a large class of infinite dimensional systems representing partial differential equations (PDEs), the concept of a functional form of the consensus protocol used for synchro-nization is applied here and incorporates spatial derivatives and spatial averages of the differences of the PDE states. This leads to spatial PD-type of consensus protocols for synchronization of PDEs. When the networked PDEs are tasked with following a leader, also described by a PDE of the same type, an added component of the controller is incorporated to ensure leader following. The proposed PD-coupling in the synchronization control of infinite dimensional systems attains a new form for the finite dimensional case, where now a temporal PID coupling in the consensus protocol is implemented. Simulation studies for both the infinite and the finite dimensional cases are included to demonstrate the effects of the non-traditional coupling in the synchronization control of networked systems.