A Nonlinear Predictive Control Approach for Urban Drainage Networks Using Data-Driven Models and Moving Horizon Estimation

Krisztian Mark Balla*, Christian Schou, Jan Dimon Bendtsen, Carlos Ocampo-Martinez, Carsten Kallesøe

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Real-time control (RTC) of urban drainage networks (UDNs) is a complex task where transport flows are non-pressurized and therefore impose flow-dependent time delays in the system. Unfortunately, the installation of flow sensors is economically out of reach at most utilities, although knowing volumes and flows are essential to optimize system operation. In this article, we formulate joint parameter and state estimation based on level sensors deployed inside manholes and basins in the network. We describe the flow dynamics on the main pipelines by the level variations inside manholes, characterized by a system of coupled partial differential equations (PDEs). These dynamics are approximated with kinematic waves where the network model is established with the water levels being the system states. Moving horizon estimation (MHE) is developed where the states and parameters are obtained via the levels and estimated flow data, utilizing the topological layout of the network. The obtained model complexity is kept within practically achievable limits, suitable for nonlinear predictive control. The effectiveness of the control and estimation method is demonstrated on a high-fidelity model of a drainage network, acting as virtual reality. We use real rain and wastewater flow data and test the controller against the uncertainty in the disturbance forecasts.

Original languageEnglish
Article number10.1109/TCST.2021.3137712
JournalI E E E Transactions on Control Systems Technology
Pages (from-to)1-16
Number of pages16
Publication statusE-pub ahead of print - 6 Jan 2022


  • Receding horizon control
  • Transport delays
  • Partial Differential Equations
  • Urban drainage networks
  • data-driven modeling
  • Real Time Control
  • Moving horizon estimation
  • Predictive Control
  • structure-preserving modeling
  • graph network
  • high-fidelity model
  • large-scale systems
  • multiple shooting
  • optimization
  • System Identification
  • Periodic disturbances
  • nonlinear MPC
  • State Estimation


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