A Dynamic Controller for PDE-Based Systems

A dynamic controller for the generalized synchronization of system described by partial differential equations (PDE) by means of a differential algebraic approach is developed. Generalized synchronization is based on the existence of a transformation. Here, such transformation is generated through the so called differential primitive element. Since the solution of the systems treated here evolves in an infinite dimensional Hilbert space, the stability of the proposed controller is analysed from the spectral theory and semi-group theory. In order to show the effectiveness of the proposed method, an example of generalized synchronization for Gray-Scott systems is given and the corresponding numerical results are presented.