Abstract
The authors consider the adaptive (online) estimation of parameters for a class of distributed parameter evolution systems. A combined state and parameter estimator is constructed as an initial value problem for an infinite dimensional evolution equation in a weak or variational form. State convergence is established via a Lyapunov-like estimate. The finite-dimensional notion of persistence of excitation is extended to the infinite-dimensional case and used to establish parameter convergence. Results of numerical studies on a one-dimensional parabolic system are presented to demonstrate the feasibility of the approach. >
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