Geometric output regulation for a class of nonlinear distributed parameter systems

We consider the output regulation problem for a special class of nonlinear distributed parameter systems (NLDPS). The main goal of this work is to show that the geometric theory of nonlinear output regulation, which has been extensively developed for lumped nonlinear systems, can be extended in a local setting to this class of NLDPS. Our approach is geometric, based on the center manifold theorem. Even for local problems, however, one must surmount technical issues that inevitably arise in the infinite dimensional setting. In this paper, we describe a particular class of nonlinear systems and exogenous systems for which center manifold methods can be used to obtain state feedback control laws for solving problems of tracking and disturbance attenuation. We also give a numerical example of set-point control for a controlled Chafee-Infante diffusion reaction equation which involves the consideration of a bounded input operator and an unbounded (point evaluation) output operator.