International Journal of applied mathematics and computer science

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Paper details

Number 3 - September 2020
Volume 30 - 2020

Fractional order tube model reference adaptive control for a class of fractional order linear systems

Hanane Balaska, Samir Ladaci, Abdelbaki Djouambi, Horst Schulte, Bachir Bourouba

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