Boundary control strategy for three kinds of fractional heat equations with control-matched disturbances

• Published in: Chaos, solitons and fractals Vol. 146; p. 110886
• Main Authors: Cai, Rui-Yang, Zhou, Hua-Cheng, Kou, Chun-Hai
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2021
• Subjects: Disturbance rejection control design; Fractional heat equations with delay; Partial differential inclusion solution; Stabilization; Partial differential inclusion solution; Disturbance rejection control design; Fractional heat equations with delay; Stabilization
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2021.110886

•We design the disturbance rejection controllers for three classes of fractional heat equations.•Boundary control strategies achieve the power law type stabilization and the asymptotical stabilization for fractional heat e quations without and with time delay, respectively.•Compared with the existing control law for the same fractional heat e quations the control design introduced here is much simple. This work aims to design the disturbance rejection controllers for three classes of fractional heat equations. Based on Filippov’s theory, the existence conclusion for the partial differential inclusion solution (PDIS) is established for fractional heat equations with discontinuous boundary conditions. Boundary control strategies are designed directly without the use of any robust control method to respectively achieve the power-law type stabilization and the asymptotical stabilization for fractional heat equations without and with time delay, respectively. A numerical example is included to illustrate the obtained results.