Stochastic stabilization based on kinetic-potential energy shaping for stochastic mechanical port-Hamiltonian systems

Authors

Satoshi Satoh, Kenji Fujimoto

Abstract

This paper extends a kinetic-potential energy shaping method to stochastic mechanical port-Hamiltonian systems. The kinetic-potential energy shaping brings a new class of Lyapunov function candidates involving a cross term of the position and the momentum without solving partial differential equations for deterministic port-Hamiltonian systems. However, the conventional kinetic-potential energy shaping does not necessarily work for stochastic port-Hamiltonian systems due to energy increase by stochastic noise. Therefore, we first provide a modification properly compensated by using stochastic generalized canonical transformations. Then, two stochastic stability results are presented. The first result shows a necessary condition for stochastic asymptotic stability for an equilibrium state. The other one shows a necessary condition for stochastic bounded stability for a target state, which is not necessarily an equilibrium point. GRAPHICAL

Citation

• Journal: Advanced Robotics
• Year: 2024
• Volume: 38
• Issue: 9-10
• Pages: 610–618
• Publisher: Informa UK Limited
• DOI: 10.1080/01691864.2024.2340543

BibTeX

@article{Satoh_2024,
  title={{Stochastic stabilization based on kinetic-potential energy shaping for stochastic mechanical port-Hamiltonian systems}},
  volume={38},
  ISSN={1568-5535},
  DOI={10.1080/01691864.2024.2340543},
  number={9–10},
  journal={Advanced Robotics},
  publisher={Informa UK Limited},
  author={Satoh, Satoshi and Fujimoto, Kenji},
  year={2024},
  pages={610--618}
}

Download the bib file

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