Adaptive control for a class of nonlinear parabolic systems via strict Lyapunov function

In this paper, the adaptive control of a class of nonlinear parabolic systems with matched external disturbances is addressed. Through the construction of the strict Lyapunov function under the persistent excitation condition, a novel adaptive control algorithm is derived such that the adaptive algorithm will estimate the true value of the parameters exponentially, which will improve the performance of the existing weak Lyapunov based adaptive control schemes,significantly. To derive the strict Lyapunov function, an observer and the linear transformation are proposed to convert the former nonlinear system into several linear parabolic systems. Due to the property of strict Lyapunov function, the proposed adaptive algorithm has the advantage in robust convergence of the closed-loop system with the external disturbances, which is not guaranteed in the existing weak Lyapunov based adaptive control strategies. Finally, a numerical example is performed to illustrate the effectiveness of the proposed adaptive control scheme and some comparisons with the weak Lyapunov based method are discussed to show the advantages of our approach.