Volume 9 Issue 1
Robust Consensus of Networked Evolutionary Games with Attackers and Forbidden Profiles †
Yalu Li, Xueying Ding and Haitao Li
School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
*Author to whom correspondence should be addressed.
†The research was supported by the National Natural Science Foundation of China under grants 61374065 and 61503225, and the Natural Science Fund for Distinguished Young Scholars of Shandong Province under grant JQ201613.
†The research was supported by the National Natural Science Foundation of China under grants 61374065 and 61503225, and the Natural Science Fund for Distinguished Young Scholars of Shandong Province under grant JQ201613.
Abstract
Using the algebraic state space representation, this paper studies the robust consensus of networked evolutionary games (NEGs) with attackers and forbidden profiles. Firstly, an algebraic form is established for NEGs with attackers and forbidden profiles. Secondly, based on the algebraic form, a necessary and sufficient condition is presented for the robust constrained reachability of NEGs. Thirdly, a series of robust reachable sets is constructed by using the robust constrained reachability, based on which a constructive procedure is proposed to design state feedback controls for the robust consensus of NEGs with attackers and forbidden profiles. Finally, an illustrative example is given to show that the main results are effective.
Keywords:networked evolutionary game; robust consensus; attackers; forbidden profiles; semi-tensor product of matrices