Strategy optimization of controlled evolutionary games on a two-layer coupled network using Lebesgue sampling

This paper studies the strategy optimization for a type of evolutionary games on coupled networks under sampled-data state feedback controls (SDSFCs) with Lebesgue sampling, which is more economical than traditional state feedback controls. Firstly, using the semi-tensor product of matrices, the algebraic expression of a controlled evolutionary game on a two-layer coupled network is established. Secondly, for a given Lebesgue sampling region, a necessary and sufficient condition is presented to detect whether each player’s payoff can ultimately remain at or above its own threshold, and the corresponding SDSFCs are designed. Furthermore, for a given signal of Lebesgue sampling, an approach is provided to obtain a desired sampling region, under which each player’s payoff always meets their threshold condition after a certain time. Finally, an illustrative example is provided to support our new results.