Observer design for time fractional reaction–diffusion systems with spatially varying coefficients and weighted spatial averages measurement

Abstract

In this paper, we consider an observer design problem of a time fractional reaction–diffusion system with space-dependent coefficients and measurement of weighted spatial averages. Different from the boundary measurement, here, the output is a weighted spatial average of the state over the entire spatial domain. In order to apply the backstepping approach to obtain the observer gains, we first use a conversion of weighting functions to transform the error system into an intermediate system. With a change of variable, this intermediate system is then converted into the final target system with boundary measurement where backstepping is easily applicable. The resultant observer realises Mittag-Leffler convergence of the error system. Finally, numerical simulations are provided to check the effectiveness of the proposed observer.

Keywords:

• Fractional order systems
• reaction–diffusion systems
• observer design
• weighted spatial averages measurement
• space-dependent coefficients

Disclosure statement

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

Data availability statement

My paper has no associated data.

Additional information

Funding

This work was supported in part by Science and Technology Project of Changzhou University [grant number ZMF20020460], Changzhou Science and Technology Agency [grant number CE20205048], and the National Natural Science Foundation of China [grant number 61807016].

Notes on contributors

Yanxin Zhang

Yanxin Zhang received M.S. degree in Computational Mathematics from School of Mathematical Sciences, Nanjing Normal University, China, in 2004. He joined Changzhou University from 2004 and now is a lecture. His research interests contain marching learning, intelligent systems, fractional-order systems.

Juan Chen

Juan Chen received her Ph.D. degree in Control Science and Engineering from the 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 currently working as 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 the 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.