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PreprintCC BY-NC-ND 4.0arXiv

Two-Player Zero-Sum Hybrid Games with Set-Valued Dynamics

  • Santiago J. Leudo
  • Francesco Ferrante
  • Ricardo G. Sanfelice
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Abstract

In this paper, we formulate a two-player zero-sum game under dynamic constraints defined in terms of a hybrid inclusion. The game consists of a min-max problem involving a cost functional that depends on the actions and corresponding (potentially non-unique) solutions, defined as functions of hybrid time and, hence, can flow or jump. We present sufficient conditions given in terms of Hamilton-Jacobi-Isaacs-like equations to establish a bound and to exactly evaluate the worst-case cost under the optimal strategy. Under additional conditions, we show that the proposed optimal state-feedback laws render a set of interest pre-asymptotically stable for the resulting hybrid closed-loop system. The results are illustrated in an application with sporadic jumps and linear quadratic hybrid dynamics.

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Cite

BibTeXRIS
BibTeX
@misc{leudo2026twoplayer,
  title = {{Two-Player Zero-Sum Hybrid Games with Set-Valued Dynamics}},
  author = {Santiago J. Leudo and Francesco Ferrante and Ricardo G. Sanfelice},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04999},
  eprint = {2611.04999},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04999},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Two-Player Zero-Sum Hybrid Games with Set-Valued Dynamics
AU  - Santiago J. Leudo
AU  - Francesco Ferrante
AU  - Ricardo G. Sanfelice
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04999
UR  - https://arxiv.org/abs/2611.04999
AB  - In this paper, we formulate a two-player zero-sum game under dynamic constraints defined in terms of a hybrid inclusion. The game consists of a min-max problem involving a cost functional that depends on the actions and corresponding (potentially non-unique) solutions, defined as functions of hybrid time and, hence, can flow or jump. We present sufficient conditions given in terms of Hamilton-Jacobi-Isaacs-like equations to establish a bound and to exactly evaluate the worst-case cost under the optimal strategy. Under additional conditions, we show that the proposed optimal state-feedback laws render a set of interest pre-asymptotically stable for the resulting hybrid closed-loop system. The results are illustrated in an application with sporadic jumps and linear quadratic hybrid dynamics.
ER  -