Distributed population dynamics: Optimization and control applications

Abstract

Population dynamics have been widely used in the design of learning and control systems for networked engineering applications, where the information dependency among elements of the network has become a relevant issue. Classic population dynamics (e.g., replicator, logit choice, Smith, and projection) require full information to evolve to the solution (Nash equilibrium). The main reason is that classic population dynamics are deduced by assuming well–mixed populations, which limits the applications where this theory can be implemented. In this work, we extend the concept of population dynamics for non–well–mixed populations in order to deal with distributed information structures that are characterized by non–complete graphs. Although the distributed population dynamics proposed in this paper use partial information, they preserve similar characteristics and properties of their classic counterpart. Specifically, we prove mass conservation and convergence to Nash equilibrium. To illustrate the performance of the proposed dynamics, we show some applications in the solution of optimization problems, classic games, and the design of distributed controller.