Solvability of Approximate Reach-Avoid Games

Mario Gleirscher

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arXiv · 2502.04544

Solvability of Approximate Reach-Avoid Games

Mario Gleirscher

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Abstract

Objective: In a companion paper, we propose a parametric hybrid automaton model and an algorithm for the online synthesis of robustly correct and near-optimal controllers for cyber-physical system with reach-avoid guarantees. A key part of this synthesis problem is based on a weighted discretised game and solved via scope-adaptive discrete dynamic programming. Approach: This work examines proofs of key properties of the discussed algorithm. Evaluation: The main proof is by induction over the stages of a discrete Hamilton-Jacobi-Bellman system of equations. Contribution: The results include a game solvability theorem and identify necessary and sufficient conditions for its applicability.

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BibTeX RIS

Mario Gleirscher. 2025-02-06. Solvability of Approximate Reach-Avoid Games. https://arxiv.org/abs/2502.04544

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