(711d) Predictive Control of Distributed Transportation Systems Using Physics-Informed Neural Network

As a transportation carrier for water and various energy resources, pipelines have long been an integral component of global transportation systems, enabling the efficient movement of water, oil, natural gas, and other essential resources across vast distances. The dynamic behaviours of the transient flow in pipes are typically described by a set of partial differential equations (PDE), deriving from the mass, momentum, and energy balance laws, which have gained widespread utilization as a prominent example of first principle modeling [1]. In the context of pipeline operations, the control strategy directly affects the energy scheduling and efficient transportation. Among the modern control approaches, model predictive control (MPC) stands out as a highly effective control strategy for managing pipeline operations and handling various system constraints [2-4]. The performance of MPC relies on the accurate model representation and accurate initial and boundary conditions of the governing PDE.

However, in practical pipeline systems, some boundary conditions are unknown and measured data is sparse due to the measurement cost [5]. In this case, both traditional methods fully based on physical equations and data-driven neural network methods have difficulty in accurately predicting the flow dynamics. The physics-informed neural network (PINN), introduced by Raissi [6], overcomes these challenges by simultaneously integrating measured data and physical equations into the network training process [7]. In this work, we explore a PINN-based predictive control framework for pipeline systems. Specifically, the PINN modeling strategy is introduced to combine observational data with PDE models for the development of machine learning models. Then the PINN model is incorporated into the framework of MPC, aiming to optimize process performance and ensure closed-loop stability. The efficacy and practical applicability of the proposed framework are validated through case studies.

References:

[1] Blažič, S., Matko, D. and Geiger, G., 2004. Simple model of a multi-batch driven pipeline. Mathematics and computers in simulation, 64(6), pp.617-630.

[2] Wu, Z., Tran, A., Rincon, D. and Christofides, P.D., 2019. Machine learning‐based predictive control of nonlinear processes. Part I: theory. AIChE Journal, 65(11), p.e16729.

[3] Van Pham, T., Georges, D. and Besançon, G., 2013. Predictive control with guaranteed stability for water hammer equations. IEEE transactions on automatic control, 59(2), pp.465-470.

[4] Zhang, L., Xie, J. and Dubljevic, S., 2023. Tracking model predictive control and moving horizon estimation design of distributed parameter pipeline systems. Computers & Chemical Engineering, 178, p.108381.

[5] Ye, J., Do, N.C., Zeng, W. and Lambert, M., 2022. Physics-informed neural networks for hydraulic transient analysis in pipeline systems. Water Research, 221, p.118828.

[6] Raissi, M., Perdikaris, P. and Karniadakis, G.E., 2019. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational physics, 378, pp.686-707.

[7] Zheng, Y., Hu, C., Wang, X. and Wu, Z., 2023. Physics-informed recurrent neural network modeling for predictive control of nonlinear processes. Journal of Process Control, 128, p.103005.