(207e) A Systematic Approach for Controlling Processes Outside the Training Region of Data-Driven Models

Data-driven models are increasingly being used to design controllers due to their ability to handle complex systems with many interacting variables, their lack of requirement for explicit knowledge, their computational efficiency, and their adaptability and flexibility [1-3]. However, it is important to note that data-driven models have limitations, such as their inability to accurately predict beyond their training domains. This can limit their applicability to only their training regions [4-5]. This can pose a major challenge when implementing data-driven process control in new operating settings outside the training region.

To address this challenge, we have developed a systematic approach to control a process outside the training region of its data-driven model. Our approach utilizes the operable adaptive sparse identification of systems (OASIS) algorithm, an online, adaptive version of the well-known SINDy developed by Dr. Kwon and his colleagues, to identify a model from the available historical process data [6]. We then use offline support vector machine analysis to identify the domain of applicability (DA) within the training region of the obtained OASIS model. Additionally, we evaluate the performance of the OASIS-based controller with multiple random initial conditions at different distances from the DA to identify the margin (𝜹) within which the model can effectively control the process.

In real-time control, the OASIS-based controller can effectively control the process within the identified DA+𝜹. However, when the process has to be operated outside the training region, the regular OASIS-based controller may not be able to control the process beyond the DA+𝜹 due to the activation functions inside hidden neurons. These functions are important for achieving model accuracy within the training range, but they eventually saturate to constant values as the neural network inputs go far beyond the training range. This results in the neural network being unable to accurately extrapolate the tendency of the original problem.

To address this issue, we propose evaluating only the hidden neurons related to a particular direction beyond their limit, which we call the γ-boundaries. For the hidden neuron whose γ-value is outside the corresponding γ-boundary, we perform linear extrapolation at its γ-boundary. For the other neurons whose γ-values are inside their γ-boundaries, we use the standard neuron activation function. This approach improves the overall prediction accuracy of OASIS and aids in controlling the process outside the training region [7]. We demonstrate the effectiveness of our developed method on a non-isothermal continuous stirred tank reactor (CSTR).

Literature cited:

1. Laurí, D., Rossiter, J.A., Sanchis, J. and Martínez, M., 2010. Data-driven latent-variable model-based predictive control for continuous processes. Journal of Process Control, 20(10), pp.1207-1219.
2. Hosen, M.A., Hussain, M.A. and Mjalli, F.S., 2011. Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): An experimental investigation. Control Engineering Practice, 19(5), pp.454-467.
3. Wu, Z., Tran, A., Rincon, D. and Christofides, P.D., 2019. Machine‐learning‐based predictive control of nonlinear processes. Part II: Computational implementation. AIChE Journal, 65(11), p.e16734.
4. Na, W., Liu, W., Zhu, L., Feng, F., Ma, J. and Zhang, Q.J., 2018. Advanced extrapolation technique for neural-based microwave modeling and design. IEEE Transactions on Microwave Theory and Techniques, 66(10), pp.4397-4418.
5. Bangi, M.S.F. and Kwon, J.S.I., 2022. Deep hybrid model‐based predictive control with guarantees on domain of applicability. AIChE Journal, p.e18012.
6. Bhadriraju, B., Bangi, M.S.F., Narasingam, A. and Kwon, J.S.I., 2020. Operable adaptive sparse identification of systems: Application to chemical processes. AIChE Journal, 66(11), p.e16980.
7. Zhang, L. and Zhang, Q.J., 2010. Simple and effective extrapolation technique for neural-based microwave modeling. IEEE Microwave and Wireless Components Letters, 20(6), pp.301-303.