International Journal of Robotics and Control Systems Vol. 1, No. 3, 2021, pp. 326-337 ISSN: 2775-2658 http://pubs2.ascee.org/index.php/ijrcs Robust Fuzzy Adaptive Control with MRAC Configuration for a Class of Fractional Order Uncertain Linear Systems Bachir Bourouba a,1 , Samir Ladaci b,c,2,* , Rachid Illoul d,3 a Department of Electrical Engineering, Setif-1 University BP: El Bez, Setif 19000, Algeria b Department of E.E.A., National Polytechnic School of Constantine, BP: 75A RP, Ali Mendjeli, Constantine 25000, Algeria c SP-Lab Laboratory, University of Mentouri Constantine 1, Department of Electronics, 25000 Constantine, Algeria d Department of Automatics, National Polytechnic School of Algiers, (ENP) BP 162, Elharrach, Algiers, 16200, Algeria 1 bourouba_b@yahoo.fr; 2 samir.ladaci@enp-constantine.dz; 3 rachid.illoul@g.enp.edu.dz * Corresponding Author ARTICLE INFO Article History Received 14 August 2021 Revised 11 September 2021 Accepted 15 September 2021 Keywords Fractional order system; Adaptive MRAC control; Robustness; Fuzzy logic; Lyapunov stability ABSTRACT This paper investigates a novel robust fractional adaptive control design for a class of fractional-order uncertain linear systems. Based on the Model Reference Adaptive Control (MRAC) configuration, the objective of the proposed controller is to ensure the output of the controlled plant to track the output of a given reference model system, while maintaining the overall closed-loop stability despite external disturbances and model un- certainties. An adaptive fuzzy logic controller is employed to eliminate unknown dynamics and disturbance. Lyapunov stability analysis demon- strates and verifies the desired fractional adaptive control system stabil- ity and tracking performance. Numerical simulation results illustrate the efficiency of the proposed adaptive fuzzy control strategy to deal with un- certain and disturbed fractional-order linear systems. This is an open access article under the CC-BY-SA license. 1. Introduction Fractional calculus is a 300 years old mathematical concept, but no significant impact was achieved in science and engineering until recent years. Recently, considerable attention has been paid to fractional-order systems whose models are described by fractional-order differential equations and especially, to fractional-order control design since it provides more robustness to model uncertainties and better response in comparison with classical controllers. Many works and applications are found in fractional calculus literature [1][2] with many applications such as viscoelastic materials modeling [3], health monitoring [4], modeling and control of robotic sys- tems [5], renewable energy systems [6], chaotic systems [7] and others [8]. One has to mention particularly, that fractional order controllers have been extensively used in many applications to achieve robust performance of the systems [9][10][11]. One of the main research topics in the literature on control theory and engineering for un- http://dx.doi.org/10.31763/ijrcs.v1i3.426 ijrcs@ascee.org