Event-triggered control design for networked evolutionary games with time invariant delay in strategies

Abstract

This paper investigates the dynamics and control problem for a class of networked evolutionary games with time invariant delay (DNEGs) in strategies by using a semi-tensor product based method. A number of new results are presented. First, algebraic forms are constructed for DNEGs. Second, based on the algebraic formulations, necessary and sufficient conditions for the global convergence of desired strategy profile are presented under a state feedback event-triggered controller. Furthermore, the constructive procedure and the number of all valid event-triggered state feedback controllers are derived, which can make the game converge globally. Finally, an illustrative example is given to show the effectiveness of the obtained results.

Keywords:

• Networked evolutionary games
• time invariant delay
• event-triggered control
• semi-tensor product of matrices

Disclosure statement

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

Notes

1 All necessary computations have been carried out using Matlab and the STP toolbox (Cheng et al., 2011).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (NNSF of China) under Grants 61803240, the Natural Science Foundation of Shandong Province under Grants ZR2019BF023.

Notes on contributors

Jianjun Wang

Jianjun Wang, was born in Shandong in 1991. He received his M.S. degree from the School of Mathematical Sciences, Liaocheng University, Liaocheng, China, in 2018. Since 2019 he has been pursuing his Ph.D. degree at the School of Science and Technology, University of Camerino, Camerino(MC), Italy. His research interests include game theory and application, logical dynamic systems, etc.

Renato De Leone

Renato De Leone received his degree summa cum laude from the University of Napoli (Italy) in 1981. From 1984 to 1993 he was Research Associate, Lecturer and Visiting Professor at the University of Wisconsin Madison (USA). In these years he performed research in Mathematica Programming and Optimization and taught various courses in the areas of Applied Mathematics and Operations Research. Since 1994 he is at the University of Camerino (Italy), first as Associate Professor and from 2001 as Full Professor. Since 1994 he served, among the other, as Chairman of the Mathematics and Computer Science Department, Coordinator of the Bachelor and Master courses in Mathematics, Vice Director of the School of Science and Technology, Rector Delegate for Erasmus International Mobility. From January 2007 to December 2011 he has been President of AIRO, the Italian Association of Operations Research. His main research areas are Optimization and Mathematical Programming, Mathematical Modelling, Machine Learning with special interest in Classification problems via Support Vector Machines, and Decision Support Systems (DSSs).

Shihua Fu

Shihua Fu, was born in Shandong in 1987. She received her Ph.D. degree from the School of Control Science and Engineering, Shandong University, Jinan, China, in 2018. Since 2018, she is a teacher with the School of Mathematical Sciences, Liaocheng University, China. Her research interests include the strategy regulation and optimization of networked evolutionary games, the analysis and control of logical dynamic systems, etc.

Jianwei Xia

Jianwei Xia, received his Ph.D. degree from the School of Automation, Nanjing University of Science and Technology in 2007. Since 2016, he is a professor with the School of Mathematical Sciences, Liaocheng University, China, and now the Vice Dean of the School of Mathematical Sciences, Liaocheng University. His research interests include stability analysis and control of stochastic Markov jump systems, switched systems and time-delay systems.

Lishan Qiao

Lishan Qiao, received his Ph.D. degree in computer science, from Nanjing University of Aeronautics and Astronautics, in 2010. From 2017 to 2018, he worked as a Volunteer in Samoa College, Samoa. From 2015 to 2016, he worked as a Visiting Scholar in the Department of Radiology and BRIC, University of North Carolina at Chapel hill, USA. From 2012 to 2014, he worked as a Post-doctoral Researcher in the Department of Computer Science and Technology, Nanjing University, China. His research interests include Data Analysis and Machine Learning, Pattern Recognition and Medical Image Analysis.