Safe Control for Pursuit-Evasion with Density Functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909618819563520 |
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| author | Bozdag, Mustafa Honarpisheh, Arya Sznaier, Mario |
| author_facet | Bozdag, Mustafa Honarpisheh, Arya Sznaier, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Safe Control for Pursuit-Evasion with Density Functions Bozdag, Mustafa Honarpisheh, Arya Sznaier, Mario Optimization and Control 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. |
| title | Safe Control for Pursuit-Evasion with Density Functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.15718 |