A population game approach for dynamic resource allocation problems

We consider a water distribution system as an example of resource allocation, and investigate the use of a population game for its control. We use a game-theoretic approach based on two evolutionary dynamics, the Brown-von Neumann-Nash and the Smith dynamics. We show that the closed-loop feedback interconnection of the water distribution system and the game-theoretic-based controller has a Nash equilibrium as an asymptotically stable equilibrium point. The stability analysis is performed based on passivity concepts and the Lyapunov stability theorem. An additional control subsystem is considered for disturbance rejection. We verify the effectiveness of the method by simulations under different scenarios.