On Adaptive Tuning for Linear Distributed Systems using Compensator Prior Knowledge

In this paper we address the problem of adaptive controller tuning for continuous, linear time invariant (LTI) distributed systems which are stabilizable with finite dimensional LTI compensators. We use the word tuning to underscore the fact that the main task of the adaptive controller is not stabilization, but to adjust its parameters to improve performance. Our main concern is the incorporation on the adaptive controller design of frequency domain prior knowledge on LTI stabilizing parametrizations. This information is used to define a new filtered error that drives the parameter update law. First, we show that, for each stabilizing parametrization, we can always define suitable filters that yield a globally convergent adaptive algorithm. Then, for each ideal filter we derive a frequency condition that the estimator filters must satisfy to insure global convergence. No restrictions, besides linearity on the adjustable parameters, are imposed on the controller structure (or order). The results are illustrated with a simulated example of a system with unknown input delay.