# Safe Control for Pursuit-Evasion with Density Functions

arXiv: https://arxiv.org/abs/2505.15718 · HTML: https://mlsanity.com/paper/2505.15718/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2025.

## Built on by (most cited first, 2 of 2)

- [Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints](https://mlsanity.com/paper/2505.22889/) (2025)
- [Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis](https://mlsanity.com/paper/2508.17142/) (2025)

## Abstract (arXiv)

This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust safe control problem. Using density functions and semi-algebraic set definitions, we derive sufficient conditions for weak eventuality and evasion, reformulating the problem into a convex sum-of-squares program solvable via standard semidefinite programming solvers. This approach avoids the computational complexity of solving the Hamilton-Jacobi-Isaacs partial differential equation, offering a scalable and efficient framework. Numerical simulations demonstrate the efficacy of the proposed method.