Semi-tensor product approach to minimal-agent consensus control of networked evolutionary games

How to find the minimum number of control agents needed to guarantee the strategy consensus of networked evolutionary games (NEGs) is studied. First, the minimal-agent consensus control (MACC) problem is formulated, and given a set of control agents, a necessary and sufficient condition is presented for the consensus of NEGs based on the algebraic form. Second, using the necessary and sufficient condition, an algorithm is established to solve the MACC problem. Third, the consensus of NEGs with switching topology is considered, and a necessary and sufficient condition is presented by introducing the concept of switching reachability. Finally, three illustrative examples are given to show the effectiveness of the obtained results.