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We show that artificial neural networks with rectifier units as activation functions can exactly represent the piecewise affine function that results from the formulation of model predictive control of linear time-invariant systems. The choice of deep neural networks is particularly interesting as they can represent exponentially many more affine regions compared to networks with only one hidden layer. We provide theoretical bounds on the minimum number of hidden layers and neurons per layer that a neural network should have to exactly represent a given model predictive control law.The proposed approach has a strong potential as an approximation method of predictive control laws, leading to better approximation quality and significantly smaller memory requirements than previous approaches, as we illustrate via simulation examples. Since the online evaluation of neural networks is extremely simple, the proposed approach is a perfect candidate for embedded applications.

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Model predictive control is an optimization-based strategy for high-performance control that is attracting increasing interest. While model predictive control (MPC) requires the online solution of an optimization problem, its ability to handle multivariable systems and constraints makes it a very powerful control strategy specially for MPC of embedded systems, which have an ever increasing amount of sensing and computation capabilities. We argue that the implementation of MPC on field programmable gate arrays (FPGAs) using automatic tools is nowadays possible, achieving cost-effective successful applications on fast or resource-constrained systems. The main burden for the implementation of MPC on FPGAs is the challenging design of the necessary algorithms. We outline an approach to achieve a software-supported optimized implementation of MPC on FPGAs using high level synthesis tools and automatic code generation. The proposed strategy exploits the arithmetic operations necessaries to solve optimization problems to tailor an FPGA design, which allows a trade-off between energy, memory requirements, cost, and achievable speed. We show the capabilities and the simplicity of use of the proposed methodology on two different examples and illustrate its advantages over a microcontroller implementation.

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