Piecewise constant tuning gain based singularity-free MRAC with application to aircraft control systems

TL;DR

This paper presents a novel singularity-free MRAC method with a piecewise constant tuning gain for aircraft control systems, enabling direct parameter estimation without prior gain knowledge or complex switching mechanisms.

Contribution

It introduces a linear regression-based MRAC approach that avoids singularities and simplifies adaptive control for LTI systems with unknown high-frequency gains.

Findings

Ensures closed-loop stability and asymptotic output tracking.

Demonstrates effectiveness through aircraft control system simulations.

Circumvents issues of existing Nussbaum and multi-model methods.

Abstract

This paper introduces an innovative singularity-free output feedback model reference adaptive control (MRAC) method applicable to a wide range of continuous-time linear time-invariant (LTI) systems with general relative degrees. Unlike existing solutions such as Nussbaum and multiple-model-based methods, which manage unknown high-frequency gains through persistent switching and repeated parameter estimation, the proposed method circumvents these issues without prior knowledge of the high-frequency gain or additional design conditions. The key innovation of this method lies in transforming the estimation error equation into a linear regression form via a modified MRAC law with a piecewise constant tuning gain developed in this work. This represents a significant departure from existing MRAC systems, where the estimation error equation is typically in a bilinear regression form. The linear regression form facilitates the direct estimation of all unknown parameters, thereby simplifying the adaptive control process. The proposed method preserves closed-loop stability and ensures asymptotic output tracking, overcoming some of the limitations associated with existing methods like Nussbaum and multiple-model based methods. The practical efficacy of the developed MRAC method is demonstrated through detailed simulation results within an aircraft control system scenario.