# Solvability of Approximate Reach-Avoid Games

arXiv: https://arxiv.org/abs/2502.04544 · HTML: https://mlsanity.com/paper/2502.04544/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2025.

## Built on by (most cited first, 1 of 1)

- [A Parametric Model for Near-Optimal Online Synthesis with Robust Reach-Avoid Guarantees](https://mlsanity.com/paper/2504.01006/) (2025)

## Abstract (arXiv)

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.