Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

In recent years considerable attention has been devoted to the problem of using feedback to control fluid dynamic systems. This problem is complex and particularly difficult when one is faced with phenomena such as shocks. Moreover, these systems are governed by nonlinear partial differential equations so that the natural state of the system is infinite dimensional. If one assumes that “full state feedback” is necessary to design practical controllers, then one would conclude that feedback control of fluid dynamic system is “not practical”. However, it is well known that even in finite dimensional control systems one rarely has the ability to accurately sense all states, so that some form of dynamic compensation must be used.

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