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PreprintCC BY-NC-ND 4.0arXiv

Policy iteration for Hamilton-Jacobi-Isaacs equations with control constraints and comparison with Hamilton-Jacobi-Bellman equations

  • Sudeep Kundu
  • Karl Kunisch
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Abstract

Convergence of the bilevel policy iteration algorithm for the value function, satisfying the Hamilton-Jacobi-Isaacs (HJI) equation, is analyzed in the presence of control constraints. Both first and second-order HJI equations corresponding to the deterministic and stochastic systems are considered. For numerical tests, a semi-implicit upwind scheme for backward HJI PDEs is applied and a thorough comparison between the solutions to first and second-order Hamilton-Jacobi-Bellman (HJB) equations is presented for both the unconstrained and the constrained control cases.

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Cite

BibTeXRIS
BibTeX
@misc{kundu2026policy,
  title = {{Policy iteration for Hamilton-Jacobi-Isaacs equations with control constraints and comparison with Hamilton-Jacobi-Bellman equations}},
  author = {Sudeep Kundu and Karl Kunisch},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29368},
  eprint = {2609.29368},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29368},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Policy iteration for Hamilton-Jacobi-Isaacs equations with control constraints and comparison with Hamilton-Jacobi-Bellman equations
AU  - Sudeep Kundu
AU  - Karl Kunisch
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29368
UR  - https://arxiv.org/abs/2609.29368
AB  - Convergence of the bilevel policy iteration algorithm for the value function, satisfying the Hamilton-Jacobi-Isaacs (HJI) equation, is analyzed in the presence of control constraints. Both first and second-order HJI equations corresponding to the deterministic and stochastic systems are considered. For numerical tests, a semi-implicit upwind scheme for backward HJI PDEs is applied and a thorough comparison between the solutions to first and second-order Hamilton-Jacobi-Bellman (HJB) equations is presented for both the unconstrained and the constrained control cases.
ER  -