A differential game approach to urban drainage systems control

Abstract

Abstract-Urban drainage systems (UDSs) are complex large-scale systems that carry stormwater and wastewater throughout urban areas. During heavy rain scenarios, UDSs are not able to handle the amount of extra water that enters the network and flooding occurs. Usually, this might happen because the network is not being used efficiently, i.e., some structures remain underused while many others are overused. This paper proposes a control methology based on differential game theory that aims to efficiently use the existing network elements in order to minimize overflows and properly manage the water resource. The proposed controller is tested on a typical UDS and is compared with a centralized MPC achieving similar results in terms of flooding minimization and network usage, but only using local information on distributed controllers.

A framework for receding-horizon control in infinite-horizon aggregative games

“…For this reason -especially when addressing large-population noncooperative settings-applications of the game-theoretical framework on (model predictive) control schemes have considered noncooperative mechanisms as a means to devise distributed control laws (Scattolini, 2009;Li and Marden, 2013;Christofides et al, 2013). Starting from the work of van den Broek (2002) on receding horizon solutions for a linear quadratic game, several distributed MPC applications of Nash games have been proposed, amongst others, for robotic formation control (Gu, 2008), water distribution networks (Ramirez-Jaime et al, 2016;Grosso et al, 2017), freeway traffic control (Pisarski and de Wit, 2016), and economic process optimization (Lee and Angeli, 2014).…”

Differential Game for Resource Allocation in Energy Harvesting Wireless Sensor Networks

“…Furthermore, distributed algorithms for dynamical systems are practical and have the potential to enhance the network scalability and reduce the communication overheads [10]. DGs have been successfully selected to solve many distributed control problems such as robots formulation as [17] and urban drainage systems control [18]. In this sense, a distributed resource allocation algorithm for the operation of EH-WSNs is proposed based on a DG formulation.…”

“…Only for few DGs, the solution (NE) can be obtained analytically as discussed in [16]. For example, the analytical solution (open loop NE) for continuous-time non-constrained quadraticlinear programming DG is obtained in [18] & [17].…”

“…The proposed DG is solved using the open loop Receding Horizon Nash Control (RHNC) approach. DG framework has been used to solve several problems in different domains such as leader follower network formulation [17] and urban drainage systems control [18], but to the authors best of knowledge, this is the first time that the DG-RHNC approach is applied for the online operation of EH-WSNs 2 .…”