Decentralized Control for Urban Drainage Systems Using Replicator Dynamics

Abstract

This paper proposes a decentralized control scheme that mitigates floods in urban drainage systems (UDSs). First, we develop a partitioning algorithm of the UDS relying on a graph model of the system. Once this is done, we design a local controller for each partition based on the replicator dynamics model (a set of differential equations that describes the evolution of a population of players involved in a strategic game). The decentralized nature of the proposed strategy makes it suitable for applying it in largescale systems. Stability of the closed-loop system is proved by using Lyapunov theory. Furthermore, we simulate the performance of the decentralized control scheme in two case studies. One of them models part of the Bogotá (Colombia) stormwater UDS. Finally, we compare the proposed technique with two widely used methods for-real time control of UDSs, i.e., constrained linear quadratic regulator (LQR) and model predictive control (MPC).INDEX TERMS Urban drainage systems, population dynamics, decentralized control, replicator dynamics, resource allocation.

The Impact of Blue‐Green Infrastructure and Urban Area Densification on the Performance of Real‐Time Control of Sewer Networks

“…In this work, only rule-based RTC and MPC were considered. The sensitivity of distributed control procedures (e.g., Obando et al, 2022) or machine-learning based procedures (Tian et al, 2022) cannot be predicted based on the results obtained in this work, as the results were found to be RTC procedure specific.…”

“…The first step is to divide the UDS into sections, partitioning the sections based on the location of actuators (schematized in Figure 2), adjusted from the partitioning processes used for the design of a decentralized control scheme (Obando et al., 2022), though without the topological distinction. Considering the entire UDS as a graph G = ( V , E ) where V represents the manholes and E the conduits in the UDS.…”

Distribución dinámica de recursos vía juegos poblacionales y modelos dinámicos de pago

“…Finalmente, suponga que queremos que los tres tanques alberguen la misma cantidad de agua. Este sencillo problema que, de hecho, tiene aplicaciones relevantes en ingeniería, como es el caso de la prevención de inundaciones en redes de drenaje urbano (ver [19] para más detalles), nos servirá para explicar el uso de dinámicas poblacionales y modelos dinámicos de pago como mecanismo de control de sistemas.…”

“…Desde entonces, se han realizado aportes en términos de dinámicas distribuidas en tiempo continuo [3] y en tiempo discreto [13], así como la combinación con técnicas en sistemas híbridos [20]. Algunas aplicaciones en vehículos autónomos no tripulados [2] o combinando técnicas de control para aplicaciones en redes de agua [4,19] han sido parte de los temas desarrollados últimamente. Recientemente, se han venido obteniendo resultados importantes en la relación de estas dinámicas poblaciones y los equilibrios generalizados de Nash [15,16].…”