Adaptive Control of Uncertain Pure-feedback Nonlinear Systems

TL;DR

This paper introduces a new adaptive control method for uncertain pure-feedback nonlinear systems, ensuring global asymptotic stability despite non-linear uncertainties and unknown control coefficients.

Contribution

It develops a backstepping adaptive control approach using parameter separation and high gain techniques for a broad class of uncertain pure-feedback systems.

Findings

Proves boundedness of all closed-loop signals.

Achieves global asymptotic stabilization.

Validated with numerical and real-world examples.

Abstract

A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback nonlinear system under consideration is with non-linearly parameterised uncertainties and possibly unknown control coefficients. Based on the parameter separation technique, a backstepping controller is designed by adopting the adaptive high gain idea. The rigorous stability analysis shows that the proposed controller could guarantee, for any initial system condition, boundedness of the closed-loop signals and globally asymptotic stabilization of the state. A numerical and a realistic examples are employed to demonstrate the effectiveness of the proposed control method.