Full-Form Model-Free Adaptive Control for a Family of Multivariable System

TL;DR

This paper introduces a novel model-free adaptive control method based on full-form equivalent-dynamic-linearization models for multivariable nonlinear systems, improving generality and stability analysis over existing approaches.

Contribution

It develops a full-form EDLM-based MFAC that removes denominator issues, relaxes diagonal dominance assumptions, and extends applicability beyond partial and compact forms.

Findings

Proved convergence of tracking error.

Established BIBO stability of the controlled system.

Demonstrated broader applicability of the control law.

Abstract

This correspondence proposes a kind of model-free adaptive control (MFAC) on the basis of full-form equivalent-dynamic-linearization model (EDLM) for the multivariable nonlinear system. Compared with the current MFAC, i) this control law does not have denominator, which is stemmed from the norm of the inverse matrix and it inevitably misses the coupling relationships among the inputs and outputs (I/O) of systems. ii) the current restrictive assumption of a diagonally dominant matrix is reduced to extend its application. iii) the MFAC based on full-form EDLM is more general than the current MFAC based on partial-form and compact-form EDLM. At last, the convergence of tracking error and the BIBO stability of controlled system have been proved, which is one of the open questions in MFAC.