# Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators

arXiv: https://arxiv.org/abs/2109.10793 · HTML: https://mlsanity.com/paper/2109.10793/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [An Extensible Benchmark Suite for Learning to Simulate Physical Systems](https://mlsanity.com/paper/2108.07799/) (2021)

## Built on by (most cited first, 21 of 21)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Physics-informed neural networks for PDE-constrained optimization and control](https://mlsanity.com/paper/2205.03377/) (2022)
- [Certified machine learning: A posteriori error estimation for physics-informed neural networks](https://mlsanity.com/paper/2203.17055/) (2022)
- [RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network](https://mlsanity.com/paper/2209.09025/) (2022)
- [Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs](https://mlsanity.com/paper/2210.03426/) (2022)
- [Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wells](https://mlsanity.com/paper/2403.02289/) (2024)
- [Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems](https://mlsanity.com/paper/2408.14951/) (2024)
- [Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.01916/) (2025)
- [Deep Operator Neural Network Model Predictive Control](https://mlsanity.com/paper/2505.18008/) (2025)
- [Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory](https://mlsanity.com/paper/2508.12681/) (2025)
- [Actor-Critic Methods using Physics-Informed Neural Networks: Control of a 1D PDE Model for Fluid-Cooled Battery Packs](https://mlsanity.com/paper/2305.10952/) (2023)
- [Robust Neural IDA-PBC: passivity-based stabilization under approximations](https://mlsanity.com/paper/2409.16008/) (2024)
- [Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networks](https://mlsanity.com/paper/2510.04591/) (2025)
- [Adapting Physics-Informed Neural Networks for Bifurcation Detection in Ecological Migration Models](https://mlsanity.com/paper/2409.00651/) (2024)
- [Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systems](https://mlsanity.com/paper/2411.01297/) (2024)
- [Acoustic Wave Manipulation Through Sparse Robotic Actuation](https://mlsanity.com/paper/2502.08784/) (2025)
- [Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Control](https://mlsanity.com/paper/2504.20019/) (2025)
- [Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flow](https://mlsanity.com/paper/2508.07841/) (2025)
- [Learned Lyapunov Shielding for Adaptive Control](https://mlsanity.com/paper/2605.06934/) (2026)
- [Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Control](https://mlsanity.com/paper/2605.10624/) (2026)

## Abstract (arXiv)

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.