mlsanityData to 7 Oct 2026

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

arXiv 2109.10793 ↗First posted 22 Sep 2021math.OC cs.LG cs.ROcited by 21

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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.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 4 of its 25 references that are in the map. First posted on arXiv 22 Sep 2021.

Builds on

4 of 25 references.

References · 4

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2015Automatic differentiation in machine learning: a surveycited by 846
  3. 2018Learning an Approximate Model Predictive Controller with Guaranteescited by 54
  4. 2021An Extensible Benchmark Suite for Learning to Simulate Physical Systemscited by 24

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 2; 2024: 6; 2025: 7; 2026: 2.

21 papers.

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  1. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  2. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  3. 2022Physics-informed neural networks for PDE-constrained optimization and controlcited by 19
  4. 2022Certified machine learning: A posteriori error estimation for physics-informed neural networkscited by 15
  5. 2022RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Networkcited by 12
  6. 2022Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNscited by 8
  7. 2024Physics-Informed Neural Networks with Skip Connections for Modeling and Control of Gas-Lifted Oil Wellscited by 4
  8. 2024Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systemscited by 4
  9. 2025Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networkscited by 3
  10. 2025Deep Operator Neural Network Model Predictive Controlcited by 3
  11. 2025Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theorycited by 3
  12. 2023Actor-Critic Methods using Physics-Informed Neural Networks: Control of a 1D PDE Model for Fluid-Cooled Battery Packscited by 2
9 more
  1. 2024Robust Neural IDA-PBC: passivity-based stabilization under approximationscited by 1
  2. 2025Data-Driven Adaptive PID Control Based on Physics-Informed Neural Networkscited by 1
  3. 2024Adapting Physics-Informed Neural Networks for Bifurcation Detection in Ecological Migration Modelscited by 0
  4. 2024Receding Hamiltonian-Informed Optimal Neural Control and State Estimation for Closed-Loop Dynamical Systemscited by 0
  5. 2025Acoustic Wave Manipulation Through Sparse Robotic Actuationcited by 0
  6. 2025Modelling of Underwater Vehicles using Physics-Informed Neural Networks with Controlcited by 0
  7. 2025Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flowcited by 0
  8. 2026Learned Lyapunov Shielding for Adaptive Controlcited by 0
  9. 2026Hierarchical Causal Abduction: A Foundation Framework for Explainable Model Predictive Controlcited by 0