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

Area of Science:

• Control Systems Engineering
• Adaptive Control Theory
• System Identification

Background:

• Traditional adaptive control methods struggle with unknown high-frequency gains, often requiring complex switching or repeated parameter estimation.
• Existing solutions like Nussbaum and multiple-model-based methods have limitations in handling these uncertainties.
• A need exists for robust adaptive control strategies that are less constrained and more computationally efficient.

Purpose of the Study:

• To introduce a novel singularity-free output feedback model reference adaptive control (MRAC) method.
• To address the challenge of unknown high-frequency gains in continuous-time linear systems.
• To develop a method that simplifies parameter estimation and avoids limitations of existing approaches.

Main Methods:

• A modified MRAC law with a piecewise constant tuning gain is proposed.
• The estimation error equation is transformed into a linear regression form, deviating from typical bilinear forms.
• Direct estimation of all unknown parameters is facilitated by the linear regression structure.

Main Results:

• The proposed method ensures boundedness of closed-loop system signals without high-frequency gain information.
• It achieves convergence of the system output to the reference output ($\lim_{t \to \infty} (y(t)-y^{*}(t))=0$).
• The method overcomes limitations associated with Nussbaum and multiple-model-based adaptive control techniques.

Conclusions:

• The developed singularity-free MRAC method offers a robust and simplified approach to adaptive control for systems with unknown high-frequency gains.
• It provides a more direct parameter estimation strategy compared to existing methods.
• Simulations, including an aircraft control system example, validate the effectiveness and practical applicability of the proposed control strategy.