Implementation of Y-Wise Affine Neural Networks in Nonlinear Model Predictive Control Approximation

The traditional approach to resolving nonlinear model predictive control (NMPC)
involves solving a constrained, nonlinear problem at each time step to obtain the optimal control
action. This process can become computationally intensive and slow depending on the
complexity of the nonlinear system. Increasing efforts have been made to use neural networks to
resolve the long-term computational strain by approximating the control actions for NMPC.
These neural networks can also account for the real time noise and disturbances, thus creating
smoother control by fitting appropriate weights. However, NNs require large data sets for
training while not explicitly accounting for the safety constraints.

This work presents the use of neural networks as a more flexible and faster approach to
controlling nonlinear systems. The NN-based control comprises two major components: YANN
based on linearized explicit control laws generated from multi-parametric MPC, together with
trainable layers to approximate the nonlinear behavior. To develop these neural networks that can
replace the standard NMPC model, extensive training was done for a highly exothermic CSTR to
represent a real-world nonlinear system. The NMPC model works to maintain an appropriate
temperature while also remaining below safety critical temperature to prevent reactor runaway.
To train the neural network, sampling data were created from the NMPC over multiple steps with
randomly initialized points centered around normal state conditions. Each training episode stops
if the reactor violates the safety critical temperature and a penalty is added to encourage behavior
that avoids the critical temperature. These YANN-initialized NN controllers offer the following
advantages: (i) reduced training of the models by providing a baseline for training, (ii) utilize
both the explicit state and additional network layers, (iii) effectively address the safety concerns
of standard NN models and traditional NMPC models.