Prescribed Performance-Based Low-Computation Adaptive Tracking Control for Uncertain Nonlinear Systems With Periodic Disturbances

In this brief, the problem of tracking control for uncertain nonlinear systems with periodic disturbances is studied. Based on the prescribed performance technology, two kinds of error transformation functions different from the traditional backstepping method are introduced, such that the proposed low-computation adaptive control method can ensure the boundedness of the signals of the closed-loop system. Meanwhile, the counter evidence method reveals that the system output can achieve accurate tracking. Compared with existing results, firstly, the complexity explosion problem is avoided without introducing a filter, making our result more applicable and less complex. Secondly, for the time-dependent periodic disturbances considered in the system, a function approximator based on Fourier series expansion can achieve accurate approximation with the least number of Gaussian basis functions. Comparative simulation results of the van der Pol oscillator illustrate the advantages of the proposed method.