Manifold control of a class of distributed parameter systems using modal expansion

The paper discusses stability analysis and design of control strategies for distributed parameter systems described by a class of partial differential equations which includes diffusions with multidimensional spatial variable. Our approach is to find a manifold in the system´s infinite dimensional state space such that if confined to the manifold the system has the desired properties. Then we design a control which makes this manifold an area of attraction for the closed loop system. The states are steered towards and maintained within the manifold. In particular we design a sliding mode controller which is well known to have strong robustness properties against matched disturbances. We study the conditions for the system dynamics within the equilibrium manifold to be stable