Constrained distributed optimization: A population dynamics approach

Large-scale network systems involve a large number of states, which makes the design of real-time controllers a challenging task. A distributed controller design allows to reduce computational requirements since tasks are divided into different systems, allowing real-time processing. This paper proposes a novel methodology for solving constrained optimization problems in a distributed way inspired by population dynamics. This methodology consists of an extension of a population dynamics equation and the introduction of a mass dynamics equation. The proposed methodology divides the problem into smaller sub-problems, whose feasible regions vary over time achieving an agreement to solve the global problem. The methodology also guarantees attraction to the feasible region and allows to have few changes in the decision-making design when a network suffers the addition/removal of nodes/edges. Then, distributed controllers are designed with the proposed methodology and applied to the large-scale Barcelona Drinking Water Network (BDWN). Some simulations are presented and discussed in order to illustrate the control performance.