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PreprintCC BY 4.0HAL

Set-Valued Robust Control of Discretized Hamiltonian Systems

  • Félix Miranda-Villatoro
  • Fernando Castaños
  • Bernard Brogliato
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Abstract

This article investigates the robust regulation of discrete-time Hamiltonian systems via set-valued twisting-like feedback laws. We consider systems affected by matched disturbances and dissipative set-valued forces. Robust global finite-time stability is achieved through a set-valued feedback law constructed via nonsmooth potential-energy shaping and set-valued damping injection. The controller is implemented using a backward-Euler scheme, which naturally preserves the set-valued structure of the feedback and mitigates digital chattering. Finite-time stability and energy-balance properties are established. Numerical simulations on a simple nonlinear robotic system illustrate the theoretical developments.

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Cite

BibTeXRIS
BibTeX
@misc{mirandavillatoro2026setvalued,
  title = {{Set-Valued Robust Control of Discretized Hamiltonian Systems}},
  author = {Félix Miranda-Villatoro and Fernando Castaños and Bernard Brogliato},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://hal.science/hal-05785834v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Set-Valued Robust Control of Discretized Hamiltonian Systems
AU  - Félix Miranda-Villatoro
AU  - Fernando Castaños
AU  - Bernard Brogliato
PY  - 2026
DA  - 2026/10/08
PB  - HAL
UR  - https://hal.science/hal-05785834v1
AB  - This article investigates the robust regulation of discrete-time Hamiltonian systems via set-valued twisting-like feedback laws. We consider systems affected by matched disturbances and dissipative set-valued forces. Robust global finite-time stability is achieved through a set-valued feedback law constructed via nonsmooth potential-energy shaping and set-valued damping injection. The controller is implemented using a backward-Euler scheme, which naturally preserves the set-valued structure of the feedback and mitigates digital chattering. Finite-time stability and energy-balance properties are established. Numerical simulations on a simple nonlinear robotic system illustrate the theoretical developments.
ER  -