Model reference adaptive control of slowly time-varying parabolic distributed parameter systems

The model reference adaptive control for a class of slowly time-varying distributed parameter systems is considered. An adaptive controller based upon the unknown (slowly time-varying) parameters together with the 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 state tracks the state of the reference model while the closed loop input and output remain bounded. A persistence of excitation condition is introduced and used to establish parameter convergence. The result does not require a modification of the standard adaptive law for time invariant parameters. Examples that demonstrate the above theory are presented along with some numerical results. These include a parabolic system with time varying parameters and a heat equation with a slowly time-varying functional parameter