Energy‐based stabilisation and robust stabilisation of stochastic non‐linear systems

Authors

Yan‐Hong Liu, Gui‐Zhou Cao, Shu‐Xia Tang, Xiu‐Shan Cai, Jin‐Zhu Peng

Abstract

This study proposes a constructive stabilisation and robust controller design method for stochastic non‐linear systems from a novel dissipation analysis and energy point of view. First, the authors propose a sufficient condition for the dissipation of stochastic Hamiltonian systems and discuss the energy property of the systems, which will be used for the stability analysis and feedback controller design. Then, the authors show that the system is (asymptotically) stable in probability if it is (strictly) dissipative. By completing the Hamiltonian realisation of the stochastic non‐linear systems, a feedback controller is proposed to stabilise the system under the condition of dissipation and zero state detectability. For stochastic non‐linear systems subjected to external disturbances, an energy‐based controller was proposed by choosing the Hamiltonian function to construct a solution of Hamiltonian–Jacobi inequality. Finally, the effectiveness of the proposed method was illustrated via the inverted pendulum systems.

Citation

Journal: IET Control Theory & Applications
Year: 2018
Volume: 12
Issue: 2
Pages: 318–325
Publisher: Institution of Engineering and Technology (IET)
DOI: 10.1049/iet-cta.2017.0392

BibTeX

@article{Liu_2018,
  title={{Energy‐based stabilisation and  robust stabilisation of stochastic non‐linear systems}},
  volume={12},
  ISSN={1751-8652},
  DOI={10.1049/iet-cta.2017.0392},
  number={2},
  journal={IET Control Theory &amp; Applications},
  publisher={Institution of Engineering and Technology (IET)},
  author={Liu, Yan‐Hong and Cao, Gui‐Zhou and Tang, Shu‐Xia and Cai, Xiu‐Shan and Peng, Jin‐Zhu},
  year={2018},
  pages={318--325}
}

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