<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.</p>
</abstract>

The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.

An Integral and MRAC–Based Approach to the Adaptive Stabilisation of a Class of Linear Time–Delay Systems with Unknown Parameters

Center of Computing Research, National Polytechnic Institute

Department of System Engineering and Automatic Control

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with...

An Integral and MRAC–Based Approach to the Adaptive Stabilisation of a Class of Linear Time–Delay Systems with Unknown Parameters

Published Online: Mar 26, 2024

Page range: 81 - 91

Received: May 02, 2023

Accepted: Dec 17, 2023

DOI: https://doi.org/10.61822/amcs-2024-0006

Keywords
MRAC, time-delay systems, backstepping, integral operator

© 2024 Luis Felipe Ramírez Jerónimo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An Integral and MRAC–Based Approach to the Adaptive Stabilisation of a Class of Linear Time–Delay Systems with Unknown Parameters

Published Online: Mar 26, 2024

Page range: 81 - 91

Received: May 02, 2023

Accepted: Dec 17, 2023

DOI: https://doi.org/10.61822/amcs-2024-0006

KeywordsMRAC, time-delay systems, backstepping, integral operator

© 2024 Luis Felipe Ramírez Jerónimo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
MRAC, time-delay systems, backstepping, integral operator