Neural Networks for Fast Optimisation in Model Predictive Control: A Review

TL;DR

The paper addresses the computational bottleneck of Model Predictive Control (MPC) by surveying neural network based optimisation (NNBO) methods that replace or accelerate the MPC solver across LMPC, NMPC, and RMPC. It provides a structured taxonomy, a comprehensive literature review, and a practical selection guide, highlighting both the substantial speedups achievable and the challenges in preserving MPC guarantees. Key contributions include a classification framework (none, probabilistic, and strict guarantees) and demonstrations that while pure imitation learning yields large speedups, formal guarantees are difficult to sustain for larger problems without additional mechanisms. The work underscores the need for rigorous benchmarks, advances in theory linking control and learning, and exploration of modern neural architectures and physics-informed approaches to broaden applicability to real-time, safe MPC. Overall, the survey maps the current landscape, clarifies trade-offs, and points to open research directions essential for deploying NNBO in complex, real-world control systems.

Abstract

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.

Figures (6)

• Figure 1: Typical implementation of NNBO to replace an MPC controller.
• Figure 2: Block diagram of typical implementation and components of MPC solution.
• Figure 3: Proposed taxonomy of NNBO methods for MPC.
• Figure 4: Number of instances of different types of problems considered in literature to demonstrate the effectiveness of NNBO approximation methods for LMPC, NMPC, and RMPC.
• Figure 5: Examples of scalability estimates for frameworks by chen2022large, fabiani2022reliably, and li2022using. (a) relationship between NN size and plant size. (b) relationship between NN size and prediction horizon length. (c) relationship between approximation training time and plant size. (d) relationship between training time and amount of training data, and approximation performance and amount of training data.