STP-based control of networked evolutionary games with multi-channel structure

The channel delay in the game process has an important influence on its evolutionary dynamics. This paper aims to optimize the strategy game with general information delays, including the state delay in the previous work, and the control delay that is introduced for the first time to depict the time consumed by strategy propagation in reality. Specifically, the dynamics of networked evolutionary games is transformed into an algebraic form by use of the newly proposed semi-tensor product of matrices, which extends the ordinary matrix multiplication. Subsequently, according to the values of control and state delays, the strategy optimization problem can be divided into six different cases, and then via the constructed algebraic equation, we can obtain the sufficient and necessary conditions for the existence of the strategy optimization. Meanwhile, based on a reachable set method, the corresponding feedback controllers are further designed. Last, one illustrative example is taken to demonstrate the feasibility of our model. The results of this paper will be helpful to investigate the game-based control issues in the complex networked environment.