Least-squares learning control with guaranteed parameter convergence

Abstract

Parameter convergence is of great importance as it enhances the overall stability and robustness properties of adaptive control systems. However, a stringent persistent-excitation (PE) condition usually has to be satisfied to achieve parameter convergence in adaptive control. In this paper, a least-squares learning control strategy without regressor filtering is presented to achieve parameter convergence at the absence of the PE condition. An additional modified modeling error that utilizes online recorded data is constructed to update parametric estimates, and an integral transformation is derived to avoid the time differentiation of plant states in the computation of the modified modeling error. An indirect adaptive control law equipped with a novel filtering-free least-squares estimation is proposed to guarantee exponential convergence of both tracking errors and parameter estimation errors by an interval-excitation (IE) condition which is much weaker than the PE condition. An illustrative example has verified effectiveness of the proposed approach.