Title: Fractional order output-feedback tube-MRAC design for a class of fractional order transfer functions with unknown parameters

Authors: Hanane Balaska; Samir Ladaci

Addresses: Department of Electrical Engineering, Skikda University, Route d'Elhadaiek, Skikda, Algeria ' Department of Automatics, National Polytechnic School of Algiers, Algiers, 16200, Algeria; SP-Lab Laboratory, Department of Electronics, University of Constantine 1, Constantine, 25000, Algeria

Abstract: In this paper, we address a class of fractional order systems defined by transfer function with unknown parameters and present a novel fractional order tube model reference adaptive control (FOTMRAC) design for their control despite the fact that the only available signals are the input and output of the system. This is the main difference with preceding authors' recent study, where the states of the system where available. Based on the output feedback, this strategy is a generalisation of the tube model reference adaptive control (TMRAC) to fractional order systems. The basic idea is to replace the single reference trajectory well known in reference model control theory by a set of admissible trajectories called tube reference. Also, an optimisation problem is resolved online in order to update the correction control signal minimising a control cost criterion. The asymptotic stability is proved using the Lyapunov extension theorem. Simulation results illustrate and confirm the effectiveness of the proposed control design.

Keywords: fractional adaptive control; fractional order linear system; model reference adaptive control; MRAC; optimisation criterion; output feedback; performance tube; unknown parameters.

DOI: 10.1504/IJAAC.2023.130572

International Journal of Automation and Control, 2023 Vol.17 No.3, pp.287 - 305

Received: 07 Jan 2022
Accepted: 05 Apr 2022

Published online: 28 Apr 2023 *

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