Economic Zone DeePC for Open Water Systems

This repository is the source code of paper Economic zone data-enabled predictive control for connected open water systems by X. Chen, X. Zhang, M. Han, A. W.-K. Law, and X. Yin.

Installation and usage

1. Install the dependencies

python -m pip install -r requirements.txt

You may choose Bonmin or Knitro as the MINLP solver. Bonmin is used by default and is included with the official CasADi binaries. Knitro is a commercial software, which requires a separate installation and a valid license. Note that the results from different solvers are different. Knitro might be more robust when solving complex MINLP problems.

2. Optimize the control target zone

We demonstrate the proposed method on a simplified water system described below. Run python zdpc_mi_main.py --help for all controller, solver, horizon, regularization, and weighting options.

Run Bayesian optimization (BO)-based control target zone optimization with:

python zdpc_mi_main.py --system {system} --BO_opt --RDeePC_flag --gdpc

The default system is watersys_simple. After it finishes, pass the generated BO directory to:

python compute_optimal_zone.py results/{system}/{res_dir}

The script reports the best evaluated zone ratio (best_observed) and the optimum of the fitted Gaussian-process posterior mean (gp_predicted).

3. Run closed-loop control

We use gp_predicted.zone_ratio as the optimized zone ratio for final evaluation. Run closed-loop economic zone DeePC controller with:

python zdpc_mi_main.py --system {system} --RDeePC_flag --gdpc --zone_ratio 0.60

Replace 0.60 with the value returned by your BO run. The control target zone ratio ranges from 0.0 (the zone center) to 1.0 (the desired zone).

4. Inspect and reproduce results

Each run creates a new numbered directory under results/{system}/. Closed-loop results include the configuration and seeds in config.json, trajectories in data/, and a summary plot in fig/; BO results additionally include bayes_opt_log.log and the shared disturbance profile. Set RUN_DIR in plot_fig.ipynb to a result directory for further visualization.

The --seed parameter deterministically controls data generation, online disturbances, process noise, and BO sampling. After each run, the offline trajectories will be stored under data/{system}/offline_data by default. Use --offline_mode load and specific --seed to reuse the data for later runs.

Method overview

The proposed economic zone DeePC approach combines three ideas:

1. Data-enabled prediction. Hankel matrices constructed from offline input-output trajectories predict future behavior directly, without identifying an explicit state-space model.
2. Lexicographic optimization. At each sampling instant, the upper level first minimizes water-level zone violation. The lower level then minimizes pump energy while constraining the zone-tracking loss to the upper-level optimum. Water-level regulation therefore has priority over energy saving.
3. BO-based target-zone selection. BO selects a contraction ratio for a control target zone nested inside the desired zone. BO evaluates the trade-off between control performance and economic cost, and fits a Gaussian process surrogate to the resulting objective values.

Simplified water system

The example contains one storage branch connected to an external river through one variable-speed outward pump and one outward sluice gate:

                    net inflow q_in
                          |
                          v
                 +-------------------+
                 | controlled branch |  water level h
                 +-------------------+
                    |            |
              pump q_pump    gate q_gate
                    |            |
                    +-----+------+
                          v
                external river h_out

Compared with the 14-branch system studied in the paper, this example uses a simplified network configuration and pump model. This example is provided to illustrate the implementation and workflow of the proposed method; it is not intended to reproduce the full case study presented in the paper.

Citation

If this code is useful in your research, please cite:

@article{chen2026economic,
  title   = {Economic zone data-enabled predictive control for connected open water systems},
  author  = {Chen, Xiaoqiao and Zhang, Xuewen and Han, Minghao and Law, Adrian Wing-Keung and Yin, Xunyuan},
  journal = {Water Research},
  volume  = {291},
  pages   = {125181},
  year    = {2026},
  doi     = {10.1016/j.watres.2025.125181}
}

Acknowledgement

The DeePC implementation is adapted from deepctools toolbox developed by Xuewen Zhang.