Abstract
This paper investigates the algebraic formulation and control for a class of networked evolutionary games with finite memories and time-varying networks by using the semi-tensor product method and presents a number of new results. Firstly, a kind of algebraic expressions is formulated for the given networked evolutionary games, and the dynamics of the given game is expressed as a finite homogenous Markov chain, based on which, the behaviors of the players in the corresponding evolutionary games are analyzed. Then, the control problem of the given games is studied. Under certain assumptions, the relationship between the strict Nash equilibriums and the fixed points of the given networked evolutionary games is revealed, and a free-type control sequence is designed to guarantee the Nash equilibrium reachable globally. Finally, an illustrative example is studied to support our new results.