Asymptotic stabilisation of coupled delayed time fractional reaction diffusion systems with boundary input disturbances via backstepping sliding-mode control

Abstract

In this paper we study the asymptotic stabilisation for coupled time fractional reaction diffusion (FRD) systems with time varying delays and input disturbances by backstepping-based boundary sliding-mode control. Here, the spatially varying diffusion coefficients can be same or distinct. To stabilise the system, we first use an invertible backstepping transformation to convert an original dynamics into a target dynamics with new manipulable inputs and perturbations. Then, we employ the sliding-mode algorithm to design this discontinuous controller to suppress disturbances. In this case, we obtain the combined backstepping/sliding-mode controller of the original dynamics. By using the fractional Halanay's inequality, the delay-independent stability condition is obtained for the asymptotic stabilisation of the delayed target system and therefore of the delayed original system under the combined controller. Fractional numerical examples are given to verify the efficiency of the proposed synthesis.

Keywords:

• Time fractional reaction diffusion systems
• coupled systems
• time delays
• boundary sliding-mode control
• perturbations

Data availability

My paper has no associated data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the science and technology project of Changzhou University [grant number ZMF20020460], National Natural Science Foundation of China [grant number 61807016].

Notes on contributors

Juan Chen

Juan Chen received her Ph.D. degree in control science and engineering from school of IoT Engineering and master degree in applied mathematics from school of science, Jiangnan University, China, in 2018 and 2011. She joined the Mechatronics, Embedded Systems and Automation (MESA) Lab of the University of California, Merced, USA as an exchange Ph.D. student hosted by Prof. YangQuan Chen from March 2015 to September 2015. She was a postdoctoral researcher at Tallinn University of Technology, Estonia, from December 2018 to December 2019. She is now an assistant professor at Changzhou University, China and a Member of IEEE. Her research interests mainly focus on fractional order systems and control, and control of diffusion systems.

Bo Zhuang

Bo Zhuang received his Ph.D. degree from school of IoT Engineering of Jiangnan University, China. He joined the MESA Lab of the University of California, Merced, USA as an exchange Ph.D. student hosted by Prof. YangQuan Chen from December 2015 to June 2016. He is now an associate professor in Binzhou University, Shangdong, China. His research interests include analysis and control of distributed parameter systems, mobile agents, and coverage optimisation.

Yajuan Yu

Yajuan Yu received her Ph.D. degree in general and foundational mechanics from college of aerospace engineering, Nanjing University of Aeronautics and Astronautics, China, in 2017. She joined Changzhou University from 2004 and now is an associate professor. Her research interests contain fractional order models, dynamics systems.