Semi-tensor product method to a class of event-triggered control for finite evolutionary networked games

Using the approach of semi-tensor product of matrices, this study studies a class of event-triggered control for finite evolutionary networked games, where the control only works at some certain individual states. First, by identifying 'control does not work' as a new specific control strategy, the controlled game dynamics is converted into an algebraic form. Second, to make the game converge globally, two necessary and sufficient conditions for the existence of event-triggered control are obtained. Meanwhile, a constructive procedure is proposed to design state feedback control strategy and an adjustment method is presented to minimise the control times. Finally, the developed theory results are illustrated by a numerical method.