# Parameter-Adaptive Approximate MPC: Tuning Neural-Network Controllers without Retraining

arXiv: https://arxiv.org/abs/2404.05835 · HTML: https://mlsanity.com/paper/2404.05835/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 8 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [MPC-Net: A First Principles Guided Policy Search](https://mlsanity.com/paper/1909.05197/) (2019)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Model-free Reinforcement Learning for Robust Locomotion using Demonstrations from Trajectory Optimization](https://mlsanity.com/paper/2107.06629/) (2021)
- [Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control](https://mlsanity.com/paper/1912.10360/) (2019)
- [A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version](https://mlsanity.com/paper/1910.12081/) (2019)
- [Neural Networks for Fast Optimisation in Model Predictive Control: A Review](https://mlsanity.com/paper/2309.02668/) (2023)
- [Efficient Calibration of Embedded MPC](https://mlsanity.com/paper/1911.13021/) (2019)
- [A Sensitivity-based Data Augmentation Framework for Model Predictive Control Policy Approximation](https://mlsanity.com/paper/2009.07398/) (2020)
- [Deep Learning-Based Model Predictive Control for Resonant Power Converters](https://mlsanity.com/paper/1810.04872/) (2018)
- [An Improved Data Augmentation Scheme for Model Predictive Control Policy Approximation](https://mlsanity.com/paper/2303.05607/) (2023)
- [Scaling Beyond Bandwidth Limitations: Wireless Control With Stability Guarantees Under Overload](https://mlsanity.com/paper/2104.07989/) (2021)

## Built on by (most cited first, 7 of 7)

- [On Foundation Models for Dynamical Systems from Purely Synthetic Data](https://mlsanity.com/paper/2412.00395/) (2024)
- [The Mini Wheelbot: A Testbed for Learning-based Balancing, Flips, and Articulated Driving](https://mlsanity.com/paper/2502.04582/) (2025)
- [Diffusion-Based Approximate MPC: Fast and Consistent Imitation of Multi-Modal Action Distributions](https://mlsanity.com/paper/2504.04603/) (2025)
- [Bridging the Sim-to-real Gap: A Control Framework for Imitation Learning of Model Predictive Control](https://mlsanity.com/paper/2503.19228/) (2025)
- [Feedback-MPPI: Fast Sampling-Based MPC via Rollout Differentiation -- Adios low-level controllers](https://mlsanity.com/paper/2506.14855/) (2025)
- [Zero-Shot Function Encoder-Based Differentiable Predictive Control](https://mlsanity.com/paper/2511.05757/) (2025)
- [SD-DPC: Sparse Dictionary Differentiable Predictive Control](https://mlsanity.com/paper/2610.02466/) (2026)

## Abstract (arXiv)

Model Predictive Control (MPC) is a method to control nonlinear systems with guaranteed stability and constraint satisfaction but suffers from high computation times. Approximate MPC (AMPC) with neural networks (NNs) has emerged to address this limitation, enabling deployment on resource-constrained embedded systems. However, when tuning AMPCs for real-world systems, large datasets need to be regenerated and the NN needs to be retrained at every tuning step. This work introduces a novel, parameter-adaptive AMPC architecture capable of online tuning without recomputing large datasets and retraining. By incorporating local sensitivities of nonlinear programs, the proposed method not only mimics optimal MPC inputs but also adjusts to known changes in physical parameters of the model using linear predictions while still guaranteeing stability. We showcase the effectiveness of parameter-adaptive AMPC by controlling the swing-ups of two different real cartpole systems with a severely resource-constrained microcontroller (MCU). We use the same NN across both system instances that have different parameters. This work not only represents the first experimental demonstration of AMPC for fast-moving systems on low-cost MCUs to the best of our knowledge, but also showcases generalization across system instances and variations through our parameter-adaptation method. Taken together, these contributions represent a marked step toward the practical application of AMPC in real-world systems.