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