Piecewise Constant Tuning Gain-Based Singularity-Free MRAC With Application to Aircraft Control Systems

This article introduces an innovative singularity-free output feedback model reference adaptive control (MRAC) method that is adaptable to a wide range of continuous-time linear systems with relative degrees $n^{*} \geq 1$ and unknown high-frequency gains. 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 requiring high-frequency gain information or adding design constraints. A 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 bilinear. The linear regression form facilitates the direct estimation of all unknown parameters, thereby simplifying the adaptive control process. In the absence of any high-frequency gain information, the proposed method still maintains the boundedness of the closed-loop system signals and $\lim _{t \to \infty } (y(t)-y^{*}(t))=0$ , where $y(t)$ and $y^{*}(t)$ are the system output and any reference output, respectively. Meanwhile, this method overcomes some limitations associated with previous methods like Nussbaum and multiple-model-based methods. Finally, a simulation of the aircraft control system is conducted to validate the proposed solution.