(594e) Learning-Based Economic Deepc of Wastewater Treatment Plants

Wastewater treatment plays a vital role in sustainable development and the protection of human health, as it removes hazardous components from used water and converts it into a less infective form [1]. A wastewater treatment plant (WWTP) typically comprises several interconnected units in which complex biological and chemical processes take place. Its dynamic behavior is described by a large-scale nonlinear system influenced by considerable external disturbances. Improving effluent quality while optimizing the operating cost through advanced control methods is one of the primary objectives in wastewater treatment [2].

Economic model predictive control (EMPC) is a promising approach for optimizing the operational performance of industrial processes [3,4]. By explicitly considering economic costs, EMPC can help reduce the energy and chemical consumption in wastewater treatment while ensuring satisfactory effluent quality [2]. While EMPC provides an effective control solution for WWTPs, its performance is sensitive to the accuracy of the first-principles model. Incomplete or inaccurate models may lead to the failure of the EMPC approach. Meanwhile, most of the existing EMPC methods rely on full-state measurements for online control, which is usually impractical since not all key state variables are available for real-time measurement in real-world applications [5].

The data-enabled predictive control (DeePC) scheme offers a potential approach that bypasses the need for system modeling and full-state measurements [6]. It is an input-output control framework that achieves setpoint tracking for linear time-invariant systems by leveraging historical input and output data, where the input trajectories satisfy the condition of persistent excitation [6,7]. Existing studies have demonstrated the potential of applying the DeePC framework to nonlinear systems [8,9]. Xie et al. extended DeePC to an economic version by adopting an economic cost function as the optimization objective [10]. However, applying this design to WWTPs may face challenges. Due to the nonlinearity of the designed economic cost function, a non-convex optimization problem needs to be solved in real time, leading to increased computational complexity.

Building on these considerations, we aim to propose a reinforcement learning-based economic DeePC approach for wastewater treatment processes with improved computational efficiency. During the training of the proposed computationally efficient economic DeePC framework, the DeePC operator is modeled as a random variable with time-varying parameters generated by neural networks to enable sufficient exploration. By interacting with the environment, the probability of obtaining control actions that optimize process operation performance is increased gradually. In online implementation, the distribution of the DeePC operator is determined by the output of neural networks at each sampling instant, allowing faster computation of control inputs.

References
[1] K. S. Naik and M. K. Stenstrom. Evidence of the influence of wastewater treatment on improved public health. Water Science and Technology, 66(3):644–652, 2012.
[2] J. Zeng and J. Liu. Economic model predictive control of wastewater treatment processes. Industrial & Engineering Chemistry Research, 54(21):5710–5721, 2015.
[3] M. Ellis, H. Durand, and P. D. Christofides. A tutorial review of economic model predictive control methods. Journal of Process Control, 24(8):1156–1178, 2014.
[4] M. Ellis, J. Liu, and P. D. Christofides. Economic model predictive control. Springer, 5(7):65, 2017.
[5] X. Yin and J. Liu. Subsystem decomposition of process networks for simultaneous distributed state estimation and control. AIChE Journal, 65(3):904–914, 2019.
[6] J. Coulson, J. Lygeros, and F. Dörfler. Data-enabled predictive control: In the shallows of the DeePC. European Control Conference, 307–312, 2019.
[7] J. C. Willems, P. Rapisarda, I. Markovsky, and B. L. De Moor. A note on persistency of excitation. Systems & Control Letters, 54(4):325–329, 2005.
[8] Y. Lian, R. Wang, and C. N. Jones. Koopman based data-driven predictive control. arXiv preprint arXiv:2102.05122, 2021.
[9] X. Zhang, K. Zhang, Z. Li, and X. Yin. Deep DeePC: Data-enabled predictive control with low or no online optimization using deep learning. AIChE Journal, 71(3):e18644, 2025.
[10] Y. Xie, J. Berberich, and F. Allgöwer. Linear Data-Driven Economic MPC with Generalized Terminal Constraint. IFAC-PapersOnLine, 56(2):5512–5517, 2023.