Differentially private containment control for multi-agent systems

Abstract

This paper is concerned with the differential privacy-based containment control problem for a class of discrete-time multi-agent systems (MASs) with time-varying topology. The classical containment control implementation relies on the explicit information exchange between agents, which will lead to the possible leakage of agents' private information, especially the initial states. In this paper, to prevent such data disclosure to neighbours inside the MASs and the outside eavesdroppers, uncorrelated noise is injected into the data during information transmission, which will bring about a more complicated scenario to the containment control. Under a milder assumption on the connectivity of the MAS – ‘average graph topology’, by resorting to the Lyapunov stability theory and algebraic graph theory, and utilising stochastic analysis techniques, sufficient conditions are derived to ensure that the discrete-time MAS subjecting to the privacy protection mechanism can achieve bounded containment control. Then, convergence accuracy is studied from the viewpoint of probability. Specially, Markov inequality is first utilised to estimate the lower bound of the probability that followers' states converge to the neighbourhood of the convex hull formed by leaders' states. Besides, differential privacy analysis is carried out to verify the validity of the proposed privacy protection mechanism in protecting the followers' initial states. Finally, two numerical examples are simulated to verify the theoretical results.

Keywords:

• Containment control
• differential privacy
• multi-agent systems
• average graph

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (RG-19-611-42). The authors, therefore, acknowledge DSR for technical and financial support. The work was also supported by National Natural Science Foundation of China under Grants 62173292, 61773017 and 61873230.

Notes on contributors

Zewei Yang

Zewei Yang was born in Jiangsu, China, in 1993, and received his B.Sc. degree in Information and Computer Science and the M.Sc. degree in Mathematics from Yangzhou University Yangzhou, China, in 2016 and 2019, respectively. Now he is pursuing the Ph.D. degree in Operational Research and Cybernetics at Yangzhou University, and his research interests include multi-agent systems, privacy protection and containment control.

Yurong Liu

Yurong Liu was born in Jiangsu, China, in 1964. He received the B.S. degree in Mathematics from Suzhou University, Suzhou, China, in 1986, the M.S. degree in Applied Mathematics from Nanjing University of Science and Technology, Nanjing, China, in 1989, and the Ph.D. degree in Applied Mathematics from Suzhou University, Suzhou, China, in 2001. Dr. Liu is currently a professor with the Department of Mathematics, Yangzhou University, China. He also serves as an Associate Editor of Neurocomputing. So far, he has published more than 100 papers in refereed international journals. His current interests include stochastic control, neural networks, complex networks, nonlinear dynamics, time-delay systems, multi-agent systems and chaotic dynamics.

Wenbing Zhang

Wenbing Zhang received the M.S. degree in Applied Mathematics from Yangzhou University, Jiangsu, China, and the Ph.D. degree in Pattern Recognition and Intelligence Systems from Donghua University, Shanghai, China, in 2009 and 2012, respectively. He was a Research Associate with The Hong Kong Polytechnic University, Kowloon, Hong Kong, from 2012 to 2013. From July 2014 to Aug 2014, he was a DAAD fellow with the Potsdam Institute for Climate Impact Research, Potsdam, Germany. He is currently an Associate Professor with the Department of Mathematics, Yangzhou University. His current research interests include synchronization/consensus, networked control systems and genetic regulatory networks. Dr. Zhang is a very active reviewer for many international journals.

Fawaz E. Alsaadi

Fawaz E. Alsaadi received the B.S. and M.Sc. degrees in Computer Science from King Abdulaziz University, Jeddah, Saudi Arabia, and University of Denver, Denver, CO, USA respectively. He then received the Ph.D. degree in Biometric Security from the University of Colorado Springs, Colorado Springs, USA. He is currently an Associate Professor in the Information Technology Department within the Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia. He has research interests in biometric recognition and biometric security, information security and cloud computing storage security.

Khalid H. Alharbi

Khalid H. Alharbi received the Ph.D. degree in Electrical Engineering from the University of Glasgow in 2016. He is currently an Assistant Professor in the Department of Electrical and Computer Engineering at King Abdulaziz University. His research interest includes micro/nano-fabrication technologies, millimetre wave and THz antennas, and RTD-based devices.