Composite learning control with application to inverted pendulums

TL;DR

This paper introduces a novel model reference composite learning control strategy for nonlinear systems that guarantees parameter convergence without the persistent excitation condition, demonstrated on an inverted pendulum.

Contribution

It proposes a new MRCLC method that ensures parameter convergence under interval excitation, removing the need for persistent excitation in adaptive control.

Findings

Achieves global exponential-like stability

Guarantees parameter convergence without PE

Successfully applied to inverted pendulum control

Abstract

Composite adaptive control (CAC) that integrates direct and indirect adaptive control techniques can achieve smaller tracking errors and faster parameter convergence compared with direct and indirect adaptive control techniques. However, the condition of persistent excitation (PE) still has to be satisfied to guarantee parameter convergence in CAC. This paper proposes a novel model reference composite learning control (MRCLC) strategy for a class of affine nonlinear systems with parametric uncertainties to guarantee parameter convergence without the PE condition. In the composite learning, an integral during a moving-time window is utilized to construct a prediction error, a linear filter is applied to alleviate the derivation of plant states, and both the tracking error and the prediction error are applied to update parametric estimates. It is proven that the closed-loop system achieves global exponential-like stability under interval excitation rather than PE of regression functions. The effectiveness of the proposed MRCLC has been verified by the application to an inverted pendulum control problem.