Coalitional model predictive control of an irrigation canal

TL;DR

The paper addresses coordinating large-scale canal networks under communication costs by introducing a two-layer coalitional MPC. The top layer selects an appropriate network topology from a manageable set using LMIs to ensure stable, near-optimal performance, while the bottom layer runs decentralized MPC within coalitions, aided by a Kalman observer to estimate inter-coalition disturbances. The approach yields suboptimal yet scalable performance close to centralized MPC, with explicit control over communication overhead and robustness to link failures, demonstrated on a Dez canal model in SOBEK. The work advances practical, distributed control of civil infrastructure by enabling dynamic topology adaptation, parallelizable topology evaluation, and improved resilience without requiring full-system centralized computation.

Abstract

We present a hierarchical control scheme for large-scale systems whose components can exchange information through a data network. The main goal of the supervisory layer is to find the best compromise between control performance and communicational costs by actively modifying the network topology. The actions taken at the supervisory layer alter the control agents' knowledge of the complete system, and the set of agents with which they can communicate. Each group of linked subsystems, or coalition, is independently controlled based on a decentralized model predictive control (MPC) scheme, managed at the bottom layer. Hard constraints on the inputs are imposed, while soft constraints on the states are considered to avoid feasibility issues. The performance of the proposed control scheme is validated on a model of the Dez irrigation canal, implemented on the accurate simulator for water systems SOBEK. Finally, the results are compared with those obtained using a centralized MPC controller.

Figures (11)

• Figure 1: Functional diagram of the coalitional MPC.
• Figure 2: Longitudinal layout of the first 44 km of the west main canal of the Dez irrigation network.
• Figure 3: Simplified profile of a reach. The inflow $q_{i}(k)$ crosses the uniform flow section in a time $d_i$. The flow $q_{i}(k-d_i)$ enters the backwater section inducing a change in the water level $h_i(k)$. The water demand is $q_{\mathrm{offtake},i}(k)$, while $q_{i+1}(k)$ is the flow passing to the downstream reach.
• Figure 4: Scenario 1: At $k = 72$ reaches 4, 9, 10 and 13 undergo a step decrease in the offtake flows. The upper plot shows how the controller regulates the water level errors along the canal. Each blue line in the bottom plot represents an active data link between two control agents. Starting from a centralized configuration, links are deactivated one at a time until the variation in the offtakes is sensed. Then links are enabled to form coalitions among the most concerned control agents, until the disturbance is eventually rejected.
• Figure 5: Scenario 1: Water flows in input to each reach.

Theorems & Definitions (7)

• Remark 1
• Definition 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Remark 6