Discrete-Time Distributed Population Dynamics for Optimization and Control

Distributed population dynamics offer a game-theoretical framework for distributed decision making. As such, the application of these methods to the control of networked systems has been widely studied in the literature. The theoretical analyses available in the literature have only considered continuous-time formulations of distributed population dynamics. However, given that modern computers can only process information in a discrete-time fashion, the practical implementation of distributed population dynamics-based methods is inevitably discrete. In consequence, it is paramount to extend the available theory to a more implementable discrete-time approach. For that reason, in this article, we provide a discrete-time analysis of a general class of distributed population dynamics, and we derive sufficient conditions on the discretization time to ensure the asymptotic stability of the discretized dynamics. To illustrate the relevance and performance of the proposed methods, we apply the developed theory to distributed optimization and control problems, including a real multirobot platform, which consider noncomplete communication networks and coupled constraints.