Composite learning robot control with guaranteed parameter convergence

Abstract

Parameter convergence is desirable in adaptive control as it enhances the overall stability and robustness properties of the closed-loop system. However, a stringent condition termed persistent excitation (PE) must be satisfied to guarantee parameter convergence in the conventional adaptive control. This paper provides the first result of parameter convergence without the PE condition for adaptive control of a general class of robotic systems. More specifically, we develop a composite learning robot control (CLRC) strategy to achieve fast and accurate parameter estimation under a condition termed interval excitation (IE) which is much weaker than the PE condition. In the composite learning, a time-interval integral of a filtered regressor is utilized to construct a prediction error such that the time derivation of plant states is not necessary, and both the prediction error and a filtered tracking error are employed to update the parameter estimate. The closed-loop system is proven to be globally exponentially stable under the IE condition. Robustness against external disturbances of the CLRC is analyzed in the Lyapunov sense. An illustrative example shows the effectiveness and superiority of the proposed approach.