Time-varying multi-objective optimisation over switching graphs via fixed-time consensus algorithms

Abstract

This paper considers distributed multi-objective optimisation problems with time-varying cost functions for network-connected multi-agent systems over switching graphs. The scalarisation approach is used to convert the problem into a weighted-sum objective. Fixed-time consensus algorithms are developed for each agent to estimate the global variables and drive all local copies of the decision vector to a consensus. The algorithm with fixed gains is first proposed, where some global information is required to choose the gains. Then, an adaptive algorithm is presented to eliminate the use of global information. The convergence of those algorithms to the Pareto solutions is established via Lyapunov theory for connected graphs. In the case of disconnected graphs, the convergence to the subsets of the Pareto fronts is studied. Simulation results are provided to demonstrate the effectiveness of the proposed algorithms.

Keywords:

• Consensus
• gradient descent
• optimisation
• distributed algorithm
• multi-agent systems

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 Facilities Council through Newton Fund under [grant number ST/N006852/1].

Notes on contributors

Zhongguo Li

Zhongguo Li received the first B. E. degree in electrical and electronic engineering from the University of Manchester, Manchester, UK and the second B. E. degree in communication engineering from Jilin University, Jilin, China, in 2017. He is currently pursuing the PhD degree in electrical and electronic engineering with the University of Manchester.

His research interests include distributed optimisation, game theory and their applications.

Zhengtao Ding

Zhengtao Ding received B. E. degree from Tsinghua University, Beijing, China, and M.Sc. degree in systems and control, and the PhD degree in control systems from the University of Manchester Institute of Science and Technology, Manchester, UK.

After working as a Lecturer with Ngee Ann Polytechnic, Singapore, for 10 years, he joined the University of Manchester in 2003, where he is currently the Professor of Control Systems with the Department of Electrical and Electronic Engineering. He is the author of the book: Nonlinear and Adaptive Control Systems (IET, 2013) and has published over 200 research articles. His research interests include nonlinear and adaptive control theory and their applications, more recently network-based control, distributed optimisation and distributed machine learning, with applications to power systems and robotics. Prof. Ding has served as an Associate Editor for the IEEE Transactions on Automatic Control, IEEE Control Systems Letters, Journal of The Franklin Institute, and several other journals.