Recently, there has been an increasing interest in the control community in studying large-scale distributed systems. Several techniques have been developed to address the main challenges for these systems, such as the amount of information needed to guarantee the proper operation of the system, the economic costs associated with the required communication structure, and the high computational burden of solving for the control inputs for largescale systems.

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 paper, we extend the concept of population dynamics for nonwell-mixed populations in order to deal with distributed information structures that are characterized by noncomplete 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 controllers.

Temperature control in buildings is a dynamic resource allocation problem, which can be approached using nonlinear methods based on population dynamics (i.e., replicator dynamics). A mathematical model of the proposed control technique is shown, including a stability analysis using passivity concepts for an interconnection of a linear multivariable plant driven by a nonlinear control system. In order to illustrate our control strategy, some simulations are performed, and we compare our proposed technique with other control strategies in a model with a fixed structure. Finally, experimental results are shown in order to observe the performance of some of these strategies in a multizone temperature testbed.

Control of Urban Drainage Systems (UDS) is studied for cases in which the distribution of run-off through the channels of a system is inefficient, i.e. when the capacity of some structures is not used optimally. In this paper, a decentralized population-dynamics-based control for UDS is presented, particularly using the replicator and projection dynamics. For the design, a methodology to make a partitioning of the system is introduced, and the design of a population-dynamics-based control per each partition is proposed. Moreover, a stability analysis of the closed-loop system is made by using passivity theory. Finally, simulation results show the proposed approach performance in a segment of the Bogotá stormwater UDS case study.