Robust Strategy Optimization of Networked Evolutionary Games with Disturbance Inputs

This paper investigates the robust strategy optimization problem for networked evolutionary games (NEGs) with pseudo-players and disturbance inputs using semi-tensor product of matrices, and presents a number of new results. First, we convert the evolutionary dynamics of the NEGs into an algebraic formulation. Secondly, we calculate the profile set in which the total payoff of the game will not less than a given value, and give two algorithms to find the largest robust profile control invariant set and the robust convergence region of this invariant set. Thirdly, the design method of profile feedback control, which can be used to regulate the strategies of the pseudo-players, is given to make the overall benefit of the game reach a certain threshold. Finally, an illustrative example is given to show the effectiveness of our main results.