Regional controllability results for Riemann–Liouville fractional control systems

Results in Control and Optimization

卷:7

F.-Z. El Alaoui¹  A. Tajani² 

[1] Corresponding author.;

[2] TSI Team, Moulay Ismail University, Faculty of Sciences, Meknes, Morocco;

关键词: Fractional calculus;    Sub-diffusion systems;    Semi-linear systems;    Regional controllability;    Fixed point theory;    Gronwall’s lemma;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper, we consider the problem of regional controllability for semi-linear time-fractional sub-diffusion systems involving Riemann–Liouville fractional derivative. Our goal is to steering the considered system into a desired state only in a sub-region of the spatial domain. In order to do that, we adapt the standard Hilbert Uniqueness Method (HUM), developed in Lions and Magenes (1968), Lions (1988), for our kind of system and we use two fixed point theorem depend to proposed assumptions. We also present some numerical simulations that illustrate the effectiveness of the proposed method, where we consider respectively zone actuator and pointwise one.

【 授权许可】

Unknown