Population Dynamics Approach for Resource Allocation Problems

In this paper, a water distribution system (WDS), as an example of resource distribution problems, is investigated. To achieve an adequate level of service to satisfy the demands, the flow of water should be controlled. A novel game-theoretic approach is utilized to keep the WDS under control. The feedback interconnection of the WDS and the game-theoretic-based controller reaches an asymptotically stable equilibrium point where its stability analysis uses passivity concepts and the Lyapunov stability theorem for the closed-loop system. Moreover, a generalization to a class of distribution problem that maintains the same stability properties is provided. The effectiveness of the method is subsequently verified by simulations under different scenarios.