Robust I&I Adaptive Tracking Control of Systems with Nonlinear Parameterization: An ISS Perspective

TL;DR

This paper introduces a robust, ISS-based adaptive control method for nonlinear systems with nonlinear parameterization, ensuring global stability and robustness without solving complex PDEs, demonstrated on series elastic actuators.

Contribution

A novel ISS-based I&I adaptive control framework that guarantees stability and robustness for nonlinear systems with nonlinear parameterization, avoiding PDE solutions.

Findings

Achieves uniform global asymptotic stability using ISS small-gain conditions.

Provides a filter-based approach to avoid solving PDEs in I&I design.

Demonstrates effectiveness on series elastic actuator tracking problem.

Abstract

This paper studies the immersion and invariance (I&I) adaptive tracking problem for a class of nonlinear systems with nonlinear parameterization in the ISS framework. Under some mild assumptions, a novel I&I adaptive control algorithm is proposed,leading to an interconnection of an ISS estimation error subsystem and an ISS tracking error subsystem. Using an ISS small-gain condition, the desired uniform global asymptotic stability of the resulting interconnected "error" system can be achieved and a sum-type strict Lyapunov function can be explicitly constructed. Taking advantage of this ISS-based design framework,it is shown that the corresponding robustness with respect to the input perturbation can be rendered to be ISS. To remove the need to solve the immersion manifold shaping PDE, a new filter-based approach is proposed, which preserves the ISS-based design framework. Finally, we demonstrate the validness of the proposed framework on a tracking problem for series elastic actuators.