Adaptive parameter estimation of hyperbolic distributed parameter systems: Non-symmetric damping and slowly time varying systems

Abstract

In this paper a model reference-based adaptive parameter estimator for a wide class of hyperbolic distributed parameter systems is considered. The proposed state and parameter estimator can handle hyperbolic systems in which the damping sesquilinear form may not be symmetric (or even present) and a modification to the standard adaptive law is introduced to account for this lack of symmetry (or absence) in the damping form. In addition, the proposed scheme is modified for systems in which the input operator, bounded or unbounded, is also unknown. Parameters that are slowly time varying are also considered in this scheme via an extension of finite dimensional results. Using a Lyapunov type argument, state convergence is established and with the additional assumption of persistence of excitation, parameter convergence is shown. An approximation theory necessary for numerical implementation is established and numerical results are presented to demonstrate the applicability of the above parameter estimators. © 1998 Société de Mathématiques Appliquées et Industrielles.