# Efficient model predictive control for nonlinear systems modelled by deep neural networks

arXiv: https://arxiv.org/abs/2405.10372 · HTML: https://mlsanity.com/paper/2405.10372/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 8 of 8)

- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Perception and Navigation in Autonomous Systems in the Era of Learning: A Survey](https://mlsanity.com/paper/2001.02319/) (2020)
- [Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes](https://mlsanity.com/paper/2207.02715/) (2022)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [Stability and feasibility of neural network-based controllers via output range analysis](https://mlsanity.com/paper/2004.00521/) (2020)
- [Nonlinear MPC design for incrementally ISS systems with application to GRU networks](https://mlsanity.com/paper/2309.16428/) (2023)
- [An Iterative LQR Controller for Off-Road and On-Road Vehicles using a Neural Network Dynamics Model](https://mlsanity.com/paper/2007.14492/) (2020)
- [Sampling-Based Nonlinear MPC of Neural Network Dynamics with Application to Autonomous Vehicle Motion Planning](https://mlsanity.com/paper/2205.04506/) (2022)

## Abstract (arXiv)

This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex nonlinearity of the system state and control input, the MPC problem is nonlinear and challenging to solve for real-time control. This paper proposes two types of methods for solving the MPC problem: the mixed integer programming (MIP) method which produces an exact solution to the nonlinear MPC, and linear relaxation (LR) methods which generally give suboptimal solutions but are much computationally cheaper. Extensive numerical simulation for an inverted pendulum system modelled by ReLU NNs of various sizes is used to demonstrate and compare performance of the MIP and LR methods.