Fractional-order PID control of tipping in network congestion

Abstract

Tracing the rapid progress of communication network, the control of dynamic evolution of network has become a central issue. There are a lot of tipping phenomena in network congestion systems. Therefore, tipping control principally centres on traditional control policies, and some advanced control approaches need to be supplemented. In this paper, a fractional-order proportional-integral-derivative (PID) controller is introduced to a network congestion model to ponder corresponding bifurcation-induced tipping regulation. First, a fractional-order congestion model with fractional-order PID controller is constructed. Then the onset of the tipping induced by Hopf bifurcation of the uncontrolled model is studied. By contrast, the tipping point can be delayed under the controller for the controlled model. Some conditions under which Hopf bifurcation occurs are given. The stable and unstable ranges of control parameters for the controlled model are also deduced. At last, some simulated examples are given to verify the theoretical results and demonstrate the superiority of the controller in tipping regulation. Moreover, the bidirectional effects of the controller are displayed by manipulating the control parameters.

Keywords:

• Network congestion
• tipping
• bifurcation
• fractional order
• PID controller

Disclosure statement

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

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant numbers 62073172, 62173214], Natural Science Foundation of Jiangsu Province of China [grant number BK20221329], Postgraduate Research and Practice Innovation Program of Jiangsu Province [grant number KYCX21_0786], and Open Research Project of the State Key Laboratory of Industrial Control Technology of Zhejiang University [grant number ICT2022B43].

Notes on contributors

Jiajin He

Jiajin He received the B.S. degree from the College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, China, in 2020, where he is currently pursuing the Ph.D. degree. His current research interests include anomalous diffusion systems, neural networks and bifurcation control.

Min Xiao

Min Xiao received the B.S. degree in mathematics and the M.S. degree in fundamental mathematics from Nanjing Normal University, Nanjing, China, in 1998 and 2001, respectively, and the Ph.D. degree in applied mathematics from Southeast University, Nanjing, China, in 2007. He was a Post-Doctoral Researcher or a Visiting Researcher with Southeast University, the City University of Hong Kong, Hong Kong, and Western Sydney University, Sydney, NSW, Australia. He is currently a Professor with the College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, China. His current research interests include information security, anomalous diffusion systems, networked control systems, tipping and control, and cyber-physical systems.

Yunxiang Lu

Yunxiang Lu received the B.S. degree from the College of Electrical Engineering, Tongda College of Nanjing University of Posts and Telecommunications, China, in 2019. He is currently pursuing the Ph.D. degree with the College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, China. His current research interests include the neural dynamics, reaction diffusion systems, tipping and control, and eco-epidemiological competition systems.

Zhen Wang

Zhen Wang received the B.S. degree in mathematics from the Ocean University of China, Qingdao, China, in 2004, and the Ph.D. degree in control theory and control engineering with the School of Automation, Nanjing University of Science and Technology, Nanjing, China, in 2014. He has been with the Shandong University of Science and Technology, Qingdao, since 2004, where he is currently a Professor and a Doctoral Supervisor. His current research interests include nonlinear control, neural networks, and network-based systems control. Prof. Wang was a recipient of the Highly Cited Researcher Award by Clarivate Analytics (formerly, Thomson Reuters) in 2020, 2021, 2022.

Wei Xing Zheng

Wei Xing Zheng received the B.Sc. degree in Applied Mathematics, the M.Sc. degree and the Ph.D. degree in Electrical Engineering from Southeast University, Nanjing, China, in 1982, 1984, and 1989, respectively. Over the years he has held various faculty/research/visiting positions at Southeast University, China; Imperial College of Science, Technology and Medicine, U.K.; University of Western Australia, Australia; Curtin University of Technology, Australia; Munich University of Technology, Germany; University of Virginia, USA; University of California at Davis, USA; etc. He is currently a University Distinguished Professor with Western Sydney University, Sydney, Australia. He has served as an Associate Editor for IEEE Transactions on Automatic Control, IEEE Transactions on Circuits and Systems-I: Regular Papers, IEEE Transactions on Fuzzy Systems, IEEE Transactions on Neural Networks and Learning Systems, IEEE Transactions on Cybernetics, IEEE Transactions on Control of Network Systems, and several other flagship journals. He was named a Highly Cited Researcher by Clarivate Analytics from 2015 to 2022 consecutively. He has been an IEEE Distinguished Lecturer of IEEE Control Systems Society. He is a Fellow of IEEE.