(182b) Convex Optimal Control of Multi-Time-Scale Systems Using Input Convex Temporal Convolutional Neural Networks

Multi-time-scale behaviors are common in chemical processes due to complex reaction and energy integration networks [1]. In response to a dynamic supply chain and the increasing complexity of process operation, modeling and controlling the multi-time-scale systems have become crucial for process safety and profitability. However, optimal control of such chemical processes is challenging due to the difficulties in modeling and optimizing nonlinear multi-time-scale systems [2].

Input convex neural networks (ICNNs) are promising data-driven modeling techniques for the optimal control of nonlinear dynamic systems [3]. They are a class of deep learning models where the outputs are constructed to be convex functions of the inputs [4]. Similar to ordinary neural networks (NNs), ICNNs can efficiently approximate all continuous Lipschitz convex functions [5]. Additionally, ICNNs can be efficiently trained on GPUs using existing deep learning packages such as PyTorch and TensorFlow. By modeling systems using ICNNs, optimal control problems on top of the system models can be solved as convex optimization problems, leading to improved performance and robustness.

Our current work proposes a special type of ICNNs that are suited for modeling nonlinear multi-time-scale behaviors in dynamic systems, named input convex temporal convolutional networks (ICTCN). This strategy incorporates temporal convolution mechanisms into ICNNs to efficiently capture multi-time-scale behaviors [6]. Unlike normal or recurrent ICNNs, the receptive field of ICTCN grows exponentially with the increasing number of network layers, capturing interesting patterns in both the short-term and long-term dynamic behaviors.

The strategy of using ICTCN for optimal control consists of three basic steps: Firstly, informative variables that contain important dynamic information are selected. Then, historical process data are used to train ICTCN-based process models offline. Lastly, the system models are integrated into the MPC framework for online optimal control. Because systems are modeled using ICTCNs, dynamics of different time scales can be captured during convex MPC calculation. Additionally, the Jacobians can be calculated using backpropagation, allowing efficient gradient-based optimization methods.

The proposed approach will be illustrated through a case study based on the vinyl acetate monomer process [7,8] , which exhibits nonlinear and multi-time-scale behaviors. The simulation results demonstrate improved approximation accuracy and control performance compared with normal ICNNs and NNs. By explicitly incorporating prior knowledge about convexity, this framework provides a good balance between the approximation power required by modeling nonlinear multi-time-scale systems, and the computational feasibility required by control and optimization.

References

[1] Jogwar, S. S., Rangarajan, S., & Daoutidis, P. (2011). Multi-time scale dynamics in energy-integrated networks: A graph theoretic analysis. IFAC Proceedings Volumes, 44(1), 6085-6090.

[2] Baldea, M., & Daoutidis, P. (2007). Control of integrated process networks—A multi-time scale perspective. Computers & Chemical Engineering, 31(5-6), 426-444.

[3] Yang, S., & Bequette, B. W. (2021). Optimization-based control using input convex neural networks. Computers & Chemical Engineering, 144, 107143.

[4] Amos, B., Xu, L., & Kolter, J. Z. (2017). Input convex neural networks. In International Conference on Machine Learning (pp. 146-155). PMLR.

[5] Chen, Y., Shi, Y., & Zhang, B. (2018). Optimal control via neural networks: A convex approach. arXiv preprint arXiv:1805.11835.

[6] Bai, S., Kolter, J. Z., & Koltun, V. (2018). An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv preprint arXiv:1803.01271.

[7] Luyben, W. L. (2011). Design and control of a modified vinyl acetate monomer process. Industrial & Engineering Chemistry Research, 50(17), 10136-10147.

[8] Ghosh. S. (2021). Human-In-The-Loop And Graph Theoretic Aspects Of A Smart Control Room. PhD Dissertation, Rensselaer Polytechnic Institute, 2021.