Adaptive parameter estimation for degenerate parabolic systems (Q1892509)

Parameter identification, or estimation, simply means the determination of unknown parameters (which may be either scalar, vector, or functional) in a proposed model for a given physical system based upon input/output data. Here, an adaptive (on-line) identification scheme for first-order in time implicit and possibly degenerate distributed parameter systems is considered. A state and parameter estimator are defined as the coupled states of an initial value problem for an infinite-dimensional non- degenerate evolution equation. The aim of the article is to establish that the state and parameter estimators asymptotically approach the true values of the corresponding parameters and the corresponding plant state. For the state convergence a Lyapunov -- like argument is used, while for the parameter convergence an additional assumption known as ``persistence of excitation'' is required. An example concerning the identification of a degenerate one-dimensional heat equation is discussed and some numerical results are provided.