Robust adaptive control of a time-varying heat equation with unknown bounded disturbance

In this paper, a robust model reference adaptive control of a radiative hea t equation with unknown time-varying coefficients and spatiotemporally vary ing disturbance is investigated. In the adaptive control of time-varying pl ants, the derivative of a Lyapunov function candidate, which allows the der ivation of adaptation laws, is not negative semi-definite in general. Under the assumption that the disturbance is uniformly bounded, the proposed rob ust adaptive scheme guarantees the boundedness of all signals in the closed loop system and the convergence of the state error near to zero. With an a dditional persistence of excitation condition, the parameter estimation err ors are shown to converge near to zero as well. Simulation results are prov ided.