Reduction of controller complexity in nonlinear H∞ control

This paper deals with measurement feedback H_∞ control. Here one must solve a state estimator online and this often is a driven PDE and so it is infinite dimensional. While in common constructions this appears to be a PDE on the state space of the plant, in this article we find that this PDE in practice sits on a space of much lower dimension k (often 1 or 2). Thus the online computational burden for measurement feedback H_∞ control might not be prohibitive. More precisely if the plant is strictly hyperbolic and k=k(as) is the dimension of its unstable manifold, our construction produces a controller whose state dynamics is a driven PDE on R/sup k(as/). This extends results of Ball and Helton (1989, 1992) (discrete time) which “construct” finite dimensional H_∞ controllers for systems with stable plants