Arbitrarily Fast Multivariable Least-squares MRAC

TL;DR

This paper introduces a new multivariable least-squares MRAC algorithm that achieves arbitrarily fast tracking in control systems by modifying the control law and providing stability and convergence guarantees.

Contribution

It presents a novel LS-MRAC algorithm for MIMO plants with a modified control law and Lyapunov stability analysis, enabling faster tracking than previous methods.

Findings

Achieves arbitrarily fast tracking with stability guarantees

Provides Lyapunov-based stability and convergence analysis

Simulation shows significant performance improvement

Abstract

A novel least-squares model-reference direct adaptive control (LS-MRAC) algorithm for multivariable (MIMO) plants is presented. The controller parameters are directly updated based on the output tracking error. The control law is crucially modified to reduce the relative degree of the error model to zero. A complete Lyapunov-based stability analysis as well as a tracking error convergence characterization is provided demonstrating that the LS-MRAC can achieve arbitrarily fast tracking while maintaining satisfactory parameter convergence for appropriate adaptation gains. Simulation results show a significant improvement in tracking performance compared to previous methods.