(386a) Error-Triggered on-Line Model Updates for Sparse Identification-Based Feedback Control

In the chemical process industry, numerous control loops are used to achieve operational stability, maximize product yield, and ensure process safety. Model predictive control (MPC) is an advanced control methodology that has been widely used in the chemical industry to meet such process performance metrics. However, MPC requires a dynamic process model in order to predict the process states over a prediction horizon, which is used to optimize a cost function and ensure constraint satisfaction. Since chemical processes often exhibit highly nonlinear and complex process dynamics, deriving first-principles models for industrial processes can be challenging. An alternative is to build data-driven models, which have advanced rapidly due to the surge of interest in machine learning and increased accessibility to computational power, which can then be incorporated into the design of an MPC. Sparse identification (SINDy) is a data-driven dynamic modeling method that has been used to build dynamic models for a wide range of engineering applications [1-3]. In the field of chemical engineering, SINDy has been used to build reduced-order models and subsequently MPC for hydraulic fracturing [4] and nonlinear, multiscale reactors [5]. When an adequate model cannot be obtained from a given data set, using online data during operation of a chemical process to update the model in real-time based on an error-triggering mechanism was investigated in [6]. By using ordinary least squares to reduce the computational burden and statistical measures such as the F-test to select only the most essential model terms from the previous model, a poor SINDy model was updated successively using a three-step procedure to obtain nearly the exact nonlinear system studied. However, based on our review of the literature on SINDy and control, the incorporation of SINDy into MPC with real-time model updates in the event of changes to the underlying process dynamics, such as via catalyst deactivation, have not been studied.

In this work, an error-triggered online model update approach is developed for closed-loop systems under a SINDy-based MPC. Initially, a highly accurate SINDy model is obtained offline using a large data set containing process operational data over a wide range of input conditions. Subsequently, due to changes in the underlying process dynamics such as catalyst deactivation or disturbances, the initially identified SINDy model fails to capture the dynamics. Hence, the error of the SINDy model prediction is tracked using a moving horizon error detector. When the prediction error exceeds a pre-defined threshold, the model is updated based on the most recent data to adapt to the most recent change in the process dynamics. Since the model structure and essential basis functions are identified when building the initial SINDy model, the updates can be carried out with significantly less data by allowing limited changes to the model structure and focusing on re-calculating the coefficients associated with the basis functions using the latest operational data. The proposed methodology is applied to two non-isothermal CSTRs, one operating at an unstable steady state under a Lyapunov-based MPC and the other with time-varying operation under an economic MPC in order to maximize the process yield.

References:

[1] Brunton, S.L., Proctor, J.L., Kutz, J.N., 2016. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl. Acad. Sci. 113 (15), 3932–3937.

[2] Schaeffer, H. , Caflisch, R. , Hauck, C.D. , Osher, S. , 2013. Sparse dynamics for partial differential equations. Proc. Natl. Acad. Sci. 110 (17), 6634–6639.

[3] Ozolinš, V. , Lai, R. , Caflisch, R. , Osher, S. , 2013. Compressed modes for variational problems in mathematics and physics. Proc. Natl. Acad. Sci. 110 (46), 18368–18373.

[4] Narasingam, A., Sang-Il Kwon, J., 2018. Data-driven identification of interpretable reduced-order models using sparse regression. Comp. & Chem. Eng. 119, 101–111.

[5] Abdullah, F., Wu, Z., Christofides, P.D., 2021. Data-Based Reduced-Order Modeling of Nonlinear Two-Time-Scale Processes. Chem. Eng. Res. & Des., 166, 1-9.

[6] Bhadriraju, B., Narasingam, A., Sang-Il Kwon, J., 2019. Machine learning-based adaptive model identification of systems: Application to a chemical process. Chem. Eng. Res. & Des., 152, 372-383.