Composite learning adaptive dynamic surface control for uncertain nonlinear strict-feedback systems with fixed-time parameter estimation under sufficient excitation

This paper presents a novel practical fixed-time parameter identification algorithm and a composite learning based practical fixed-time adaptive dynamic surface control (DSC) scheme for nonlinear strict-feedback systems subject to linear-in-parameters uncertainties. The convergence of conventional parameter estimation algorithms often requires a restrictive prerequisite termed persistent excitation (PE) condition. By contrast, a new fixed-time parameter identification algorithm configured with two layer transformation technique is firstly proposed under relaxed sufficient excitation condition rather than strict PE condition. The key point of avoiding PE condition is by introducing a smooth switching function to adjust the forgetting factor in the filtered regressor dynamics. Instead of using the fractional power of the tracking errors to construct the control laws, a smooth hyperbolic tangent function based adaptive DSC scheme is designed such that the potential singular problem caused by time derivations of virtual control laws in back-stepping algorithm is avoided. Integrating the parameter identification algorithm into the adaptive DSC scheme, a composite learning based control is formed to guarantee the practical fixed-time convergence of parameter estimation errors and tracking errors. Comparative simulation results are given to illustrate the effectiveness of the proposed algorithm.