The industrial deployment of linear model predictive control requires a solution to a convex quadratic program (QP) in real-time. The explicit solution to the QP characterizes the MPC control law, that is a piecewise affine function of the state and some steady-state targets computed for offset-free control. The complexity of the explicit control law is well known to grow exponentially with the increase in the problem size, rendering an offline characterization and an on-line deployment using the explicit control law intractable for any reasonably sized industrial plant. The recent observation that deep neural networks with the rectified linear unit (ReLU) as the activation function also represent a piecewise affine function makes them an attractive candidate for obtaining accurate approximations of the explicit MPC control law. We examine the scalability of this approach via numerical experiments on large-scale chemical engineering examples.
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