(91c) Handling Correlated Data for Artificial Neural Network (ANN)-Based Model Predictive Control (MPC) Implementations

Advanced control systems play a key role in chemical process industries to achieve economic and safety objectives. However, there have been several challenging issues in developing these systems such as nonlinearity, process constraints, and multi-variable interactions. Model predictive control (MPC) is one of the optimal control techniques that can successfully handle these challenges [1]. Using an optimization problem, MPC decides which control action to implement by testing the effect of a candidate input on the process using a process model. Thus, good control performance relies on using an accurate process model. Several modeling techniques including first-principles and data-driven based approaches have been developed and used for MPC implementations. Although first-principles models have good extrapolation capabilities, they are generally difficult to develop and maintain because of uncertainty in physical parameters and unmeasured states.

With the recent development of computing and data storage technologies, there has been increasing interest in building data-driven and machine learning-based models. Among many machine learning techniques, artificial neural networks (ANNs) have received significant attention due to their ability to capture nonlinearity. ANN-based models have also been used to implement MPC [2,3]. To develop an ANN-based model, a significant amount of high-quality data is usually required because of a large number of parameters that need to be tuned. However, the presence of redundant information in some historical data can exacerbate the negative impact of the over-fitting problem. The redundancy issue usually happens when data are collected from a process operating under closed-loop conditions. In this situation, if data samples are directly used (without utilizing an appropriate data mining mechanism) to develop MPC, it may lead to a poor closed-loop performance. Therefore, additional constraints must be considered within the standard ANN-based MPC framework to maintain model validity [4].

Motivated by the above considerations, this work addresses the problem of ANN-based MPC design, where the collected closed-loop data contains correlation in both the input and output spaces. To maintain model validity, a principal component analysis (PCA)-based squared prediction error (SPE) constraint is first added to the standard ANN-based MPC formulation to make the control actions follow the same correlation as that of the training input data (constrained ANN-based MPC). Note that implementing the ANN-based MPC just by adding the PCA-based SPE constraint on the input moves does not necessarily guarantee that the outputs will track the arbitrarily prescribed set-points because of the existing correlation in the training output data. To overcome this problem, an optimization problem is used to minimize the sum of squared error between the prescribed and achievable set-points by applying a PCA-based SPE constraint, developed using the training output data. In addition, to handle the nonlinear correlation between the process outputs, an autoencoder-based optimization problem is developed to calculate the achievable set-points. The effectiveness of the proposed approaches is shown via simulation of a chemical reactor example. The results reveal the superior performance of the constrained ANN-based MPC over the standard ANN-based MPC to drive the outputs to the achievable set-points. Further improvement in closed loop performance is achieved using the achievable set-points calculated based on the autoencoder-based strategy (due to the superior performance of the autoencoder to handle the nonlinear correlation, while calculating the achievable set-points) [5].

[1] Mayne, D. Q., Rawlings, J. B., Rao, C. V. & Scokaert, P. O. (2000). Constrained model predictive control: Stability and optimality. Automatica, 36(6), 789–814.

[2] Sadeghassadi, M., Macnab, C. J., Gopaluni, B., & Westwick, D. (2018). Application of neural networks for optimal-setpoint design and MPC control in biological wastewater treatment. Computers & Chemical Engineering, 115, 150-160.

[3] Wu, Z., Rincon, D., Luo, J., & Christofides, P. D. (2021). Machine learning modeling and predictive control of nonlinear processes using noisy data. AIChE Journal, 67(4), e17164.

[4] Hassanpour, H., Corbett, B., & Mhaskar, P. (2020). Integrating dynamic neural network models with principal component analysis for adaptive model predictive control. Chemical Engineering Research and Design, 161, 26-37.

[5] Hassanpour, H., Corbett, B., & Mhaskar, P. (2022). Artificial Neural Network-Based Model Predictive Control Using Correlated Data. Industrial & Engineering Chemistry Research.