(299g) The Integration of Relu-Based Deep Neural Networks for Explicit Model Predictive Control

Explicit model predictive control (eMPC) is an advanced control strategy where the optimal control actions are calculated offline [1]. This is achieved by solving a multiparametric optimization program, whose outcome expresses the optimal control actions as an explicit function of the states/outputs of the system. Being a model-based methodology, it requires the incorporation of a process model in the optimization formulation, to derive the optimal input trajectories to the system. Directly incorporating the -possibly nonlinear- dynamic model in the multiparametric optimization problem, makes its solution challenging [2,3]. Hence, an approximate model is required to substitute the original process model, based on which the optimal operational policy will be calculated. As it has been reported in the eMPC literature, the approximate model can have a drastic effect on the performance of the process when the optimal control actions are applied back to the original process model in closed-loop. Namely, not only can the deviation from the desired state be significant, but also the control law can lead the original system to infeasible operation [4].

Deep learning models are proven to have strong predictive capabilities to represent complex phenomena between input and output data [5]. Substituting the original process model with a deep learning model, the complexity of the system is dramatically reduced, while the desired accuracy is maintained [6,7]. In this work, we propose the integration of feedforward deep neural networks with rectified linear units (ReLU) as activations functions with eMPC. Recently, it has been shown that ReLU-based deep neural networks can be exactly recast to a mixed-integer linear program [8]. Nevertheless, the mixed-integer nature of the model makes its application in a model predictive control framework challenging. This computational complexity is alleviated by solving the resulting model predictive control problem explicitly, where the solution is calculated offline, and the optimal control actions are defined by affine functions of the states/outputs of the system [9]. The aforementioned strategy is applied to the setpoint tracking of the ACUREX solar field. Through the proposed method it is shown that the optimal operation of the solar field can be maintained in the presence of disturbances.

[1] Bemporad, A., Morari, M., Dua, V., & Pistikopoulos, E. N. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, 38(1), 3-20.

[2] Sakizlis, V., Kakalis, N. M., Dua, V., Perkins, J. D., & Pistikopoulos, E. N. (2004). Design of robust model-based controllers via parametric programming. Automatica, 40(2), 189-201.

[3] Pappas, I., Diangelakis, N.A., & Pistikopoulos, E.N. The exact solution of multiparametric quadratically constrained quadratic programming problems.

[4] Katz, J., Burnak, B., & Pistikopoulos, E. N. (2018). The impact of model approximation in multiparametric model predictive control. Chemical engineering research and design, 139, 211-223.

[5] Himmelblau, D. M. (2000). Applications of artificial neural networks in chemical engineering. Korean journal of chemical engineering, 17(4), 373-392.

[6] Bangi, M. S. F., & Kwon, J. S. I. (2020). Deep hybrid modeling of chemical process: Application to hydraulic fracturing. Computers & Chemical Engineering, 134, 106696.

[7] Wu, Z., Rincon, D., & Christofides, P. D. (2020). Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes. Journal of Process Control, 89, 74-84.

[8] Grimstad, B., & Andersson, H. (2019). ReLU networks as surrogate models in mixed-integer linear programs. Computers & Chemical Engineering, 131, 106580.

[9] Katz, J., Pappas, I., Avraamidou, S., & Pistikopoulos, E. N. (2020). Integrating Deep Learning Models and Multiparametric Programming. Computers & Chemical Engineering, 106801.