Frequency-selective scheme for nonlinear adaptive control systems

Abstract

High-gain learning in adaptive control can enhance the error convergence rate, while triggering high-frequency oscillations or even instability. This paper will present a constructive method to manage the potential conflict between the online learning and the induced high-frequency oscillations, so as to improve the transient performance (e.g., error convergence rate, overshoot and smoothness of control signal) of adaptive control systems. A constructive frequency-selective scheme is suggested to extract the high-frequency contents in the tracking error stemming from unknown nonlinearities. The selective high-frequency dynamics are then used as a compensator superimposed on the adaptive control action, such that high-frequency oscillations in the closed-loop system can be diminished, allowing for a fairly large gain to rapidly adapt the environmental changes. The selection of frequency-selective coefficient and the compensation gain is discussed. Rigorous theoretical analysis indicates that this frequency-selective strategy can reduce the transient tracking error bound. Simulations based on a benchmark system and experiments on a helicopter show that the proposed method can retain better control response than the traditional method.