(391r) Control Lyapunov Barrier Function Based Predictive Control of Nonlinear Systems Using Physics-Informed Recurrent Neural Networks

In various fields, safety-critical systems require rigorous adherence to safety constraints to avoid compromising process stability, economic performance, or operational safety. Significant research has focused on verifying system safety and developing control laws with guaranteed safety properties. In this context, Control Barrier Functions (CBFs) have been introduced as a means to assess the safety of dynamical systems by confirming that a control law maintains the forward invariance of a designated safe set—much like Control Lyapunov Functions (CLFs) are used to verify stability [1-2]. CBFs can be integrated into control designs for systems with multiple objectives. For instance, in controllers based on Control Lyapunov Barrier Functions (CLBF), a CLF delineates a region of stability while a CBF identifies an unsafe region that the system’s state is prevented from entering at any time. This strategy has been further applied to nonlinear systems with input constraints, where CLBF-based control laws act as contractive constraints within a model predictive controller (MPC) framework, ensuring both closed-loop stability and safety for nonlinear processes featuring regions of both bounded and unbounded risk.

Recent ML advancements have significantly improved MPC strategies by enabling data-driven models to capture complex nonlinear dynamics more accurately. While traditional ML-based MPC approaches typically use RNNs and transformers for sequence predictions, recent trends have shifted toward physics-informed neural networks. By integrating physical laws into the model structure, physics-informed RNNs (PIRNNs) have been shown to outperform RNNs that neglect any physical constraints [3]. The model training itself has also been shown to improve when incorporating knowledge of the sequence of process units into the training in [4]. However, despite these advances, to the best of our knowledge, the integration of PIRNNs within a CLBF-MPC framework for ensuring process safety has not been investigated yet. In this work, we propose a novel CLBF-MPC approach that employs a PIRNN as the process model, demonstrating its effectiveness in preventing state trajectories from entering unsafe regions while maintaining robust performance. We develop the PIRNN-based CLBF-MPC and apply it to a two-CSTR process, wherein the traditional MPC causes the process to enter the unsafe region.

References

[1] Ames, A. D., Xu, X., Grizzle, J. W., & Tabuada, P. (2016). Control barrier function based quadratic programs for safety critical systems. IEEE Transactions on Automatic Control, 62(8), 3861-3876.

[2] Xu, X., Tabuada, P., Grizzle, J. W., & Ames, A. D. (2015). Robustness of control barrier functions for safety critical control. IFAC-PapersOnLine, 48(27), 54-61.

[3] Alhajeri, M. S., Abdullah, F., Wu, Z., & Christofides, P. D. (2022). Physics-informed machine learning modeling for predictive control using noisy data. Chemical Engineering Research and Design, 186, 34-49.

[4] Alhajeri, M. S., Ren, Y. M., Ou, F., Abdullah, F., & Christofides, P. D. (2024). Model predictive control of nonlinear processes using transfer learning-based recurrent neural networks. Chemical Engineering Research and Design, 205, 1-12.