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Learning Nonlinear Dynamics of Flexible Structures for Predictive Control Using Gaussian Process NARX Models.

Nasser Ayidh Alqahtani1

  • 1Department of Mechanical Engineering, College of Engineering, Qassim University, Buraidah 51452, Saudi Arabia.

Biomimetics (Basel, Switzerland)
|April 27, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a bio-inspired Bayesian approach using Gaussian Process Nonlinear Model Predictive Control (GP-NMPC) for effective structural vibration control under uncertainty. The method significantly reduces vibration amplitudes in flexible systems.

Keywords:
Gaussian Process Nonlinear AutoRegressive model with eXogenous inputadvanced process controlnonlinear model predictive controlpredictive functional control

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Area of Science:

  • Control Systems Engineering
  • Robotics and Aerospace Engineering
  • Computational Mechanics

Background:

  • Biological systems exhibit remarkable abilities in motion control and vibration suppression through adaptive and predictive strategies.
  • Flexible structures in aerospace and robotics face challenges from model uncertainty, necessitating advanced vibration mitigation techniques.
  • Bayesian system identification offers a robust framework for modeling and estimation, especially when dealing with uncertainty in structural dynamics.

Purpose of the Study:

  • To develop a data-driven control strategy for mitigating structural vibrations in systems with model uncertainty.
  • To integrate Gaussian Process (GP) models within a Nonlinear Model Predictive Control (NMPC) framework for enhanced predictive control.
  • To leverage probabilistic predictions for improved vibration suppression and system robustness.

Main Methods:

  • Implementation of a Gaussian Process Nonlinear AutoRegressive model with eXogenous input (GP-NARX) for probabilistic modeling of structural dynamics.
  • Integration of the GP-NARX predictor within an NMPC framework, enabling multi-step-ahead forecasts for control optimization.
  • Validation through simulations on various oscillator and beam models, assessing performance in regulation and tracking tasks.

Main Results:

  • Achieved an 88.2% reduction in displacement amplitude compared to uncontrolled systems.
  • Demonstrated high predictive accuracy with a Root Mean Square Error (RMSE) of 0.0031 and Standardized Mean-Squared Error (SMSE) below 0.05.
  • Confirmed the reliability of predictive uncertainty quantification through Mean Standardized Log Loss (MSLL) evaluations.

Conclusions:

  • The proposed Bayesian-predictive coupling (GP-NMPC) is a highly effective approach for high-performance structural vibration control.
  • The method successfully addresses challenges posed by model uncertainty in flexible aerospace and robotic systems.
  • This framework provides a foundation for bio-inspired mechanical design, enhancing adaptive control capabilities.