Distributed feedback control of a fractional diffusion process

Ahmed Maidi (1) , Jean-Pierre Corriou (2)

1 UMMTO - Université Mouloud Mammeri [Tizi Ouzou]
2 LRGP - Laboratoire Réactions et Génie des Procédés

In this paper, a control law that enforces an output tracking of a fractional diffusion process is developed. The dynamical behavior of the process is described by a space-fractional parabolic equation. The objective is to force a spatial weighted average output to track its specified output by manipulating a control variable assumed to be distributed in the spatial domain. The state feedback is designed in the framework of geometric control using the notion of the characteristic index. Then, under the assumption that the fractional diffusion process is a minimum phase system, it is shown that the developed control law guarantees exponential stability in L2 -norm for the resulting closed loop system. Numerical simulations are performed to show the tracking and disturbance rejection capabilities of the developed controller.

Mots clés: Distributed parameter system; Geometric control; Characteristic index; Fractional diffusion; Fractional partial differential equation; Late lumping

Domaines: Automatique / Robotique

Ahmed Maidi, Jean-Pierre Corriou. Distributed feedback control of a fractional diffusion process. International Journal of Dynamics and Control, 2019, 7, pp.1091-1100. ⟨10.1007/s40435-018-0493-0⟩. ⟨hal-02130574⟩