Model reference adaptive control of abstract hyperbolic distributed parameter systems

An abstract theory for the model reference adaptive control of abstract hyperbolic distributed parameter systems is developed. A feedback control law based upon estimates of the unknown parameters together with update laws for the unknown parameters are given. A Lyapunov estimate together with a version of Barbalat's lemma is used to establish that the plant's displacement and velocity track the displacement and velocity of the reference model while the closed loop input and output remain bounded. A richness or persistence of excitation condition in terms of the state of the reference model is defined and used to establish parameter convergence. An example including numerical simulation results for a one dimensional visco-elastic wave equation is presented.<
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