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arXiv · 2609.29368

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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Sudeep Kundu, Karl Kunisch. 2026-09-24. Policy iteration for Hamilton-Jacobi-Isaacs equations with control constraints and comparison with Hamilton-Jacobi-Bellman equations. https://arxiv.org/abs/2609.29368

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