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Model Predictive Control (MPC) is an optimal control algorithm with strong
stability and robustness guarantees. Despite its popularity in robotics and
industrial applications, the main challenge in deploying MPC is its high
computation cost, stemming from the need to solve an optimisation problem at
each control interval. There are several methods to reduce this cost. This
survey focusses on approaches where a neural network is used to approximate an
existing controller. Herein, relevant and unique neural approximation methods
for linear, nonlinear, and robust MPC are presented and compared. Comparisons
are based on the theoretical guarantees that are preserved, the factor by which
the original controller is sped up, and the size of problem that a framework is
applicable to. Research contributions include: a taxonomy that organises
existing knowledge, a summary of literary gaps, discussion on promising
research directions, and simple guidelines for choosing an approximation
framework. The main conclusions are that (1) new benchmarking tools are needed
to help prove the generalisability and scalability of approximation frameworks,
(2) future breakthroughs most likely lie in the development of ties between
control and learning, and (3) the potential and applicability of recently
developed neural architectures and tools remains unexplored in this field.
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