<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We introduce a novel fractional order adaptive control design based on the tube model reference adaptive control (TMRAC) scheme for a class of fractional order linear systems. By considering an adaptive state feedback control configuration, the main idea is to replace the classical reference model with a single predetermined trajectory by a fractional order performance tube guidance model allowing a set of admissible trajectories. Besides, an optimization problem is formulated to compute an on-line correction control signal within specified bounds in order to update the system performance while minimizing a control cost criterion. The asymptotic stability of the closed loop fractional order control system is demonstrated using an extension of the Lyapunov direct method. The dynamical performance of the fractional order tube model reference adaptive control (FOTMRAC) is compared with the standard fractional order model reference adaptive control (FOMRAC) strategy, and the simulation results show the effectiveness of the proposed control method.</p></abstract>

We introduce a novel fractional order adaptive control design based on the tube model reference adaptive control (TMRAC) scheme for a class of fractional order linear systems. By considering an adaptive state feedback control configuration, the main idea is to replace the classical reference model with a single predetermined trajectory by a fractional order performance tube guidance model allowing a set of admissible trajectories. Besides, an optimization problem is formulated to compute an on-line correction control signal within specified bounds in order to update the system performance while minimizing a control cost criterion. The asymptotic stability of the closed loop fractional order control system is demonstrated using an extension of the Lyapunov direct method. The dynamical performance of the fractional order tube model reference adaptive control (FOTMRAC) is compared with the standard fractional order model reference adaptive control (FOMRAC) strategy, and the simulation results show the effectiveness of the proposed control method.

Fractional Order Tube Model Reference Adaptive Control for a Class of Fractional Order Linear Systems

LGEA Laboratory, Department of Electrical Engineering

Department of Electronics, Electrical Engineering and Automation, National Polytechnic School of Constantine

University of Applied Sciences (HTW) Berlin

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

We introduce a novel fractional order adaptive control design based on the tube model reference adaptive control (TMRAC) scheme for a class of fractional order...

Fractional Order Tube Model Reference Adaptive Control for a Class of Fractional Order Linear Systems

Published Online: Sep 29, 2020

Page range: 501 - 515

Received: Jan 20, 2020

Accepted: Apr 29, 2020

DOI: https://doi.org/10.34768/amcs-2020-0037

Keywords
fractional order linear system, model reference adaptive control, fractional adaptive control, optimization, performance tube, fractional order TMRAC

© 2020 Hanane Balaska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fractional Order Tube Model Reference Adaptive Control for a Class of Fractional Order Linear Systems

Published Online: Sep 29, 2020

Page range: 501 - 515

Received: Jan 20, 2020

Accepted: Apr 29, 2020

DOI: https://doi.org/10.34768/amcs-2020-0037

Keywordsfractional order linear system, model reference adaptive control, fractional adaptive control, optimization, performance tube, fractional order TMRAC

© 2020 Hanane Balaska et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
fractional order linear system, model reference adaptive control, fractional adaptive control, optimization, performance tube, fractional order TMRAC