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 heat equation with unknown time-varying coefficients and spatiotemporally varying disturbance is investigated. In the adaptive control of time-varying plants, the derivative of a Lyapunov function candidate, which allows the derivation of adaptation laws, is not negative semi-definite in general. Under the assumption that the disturbance is uniformly bounded, the proposed robust 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 additional persistence of excitation condition, the parameter estimation errors are shown to converge near to zero as well. Simulation results are provided.