Reachability Analysis for Design Optimization
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910055194951680 |
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| author | Nguyen, Steven Cortés, Jorge Kramer, Boris |
| author_facet | Nguyen, Steven Cortés, Jorge Kramer, Boris |
| contents | We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input, planar systems with real, distinct eigenvalues. The second approach leverages convergence of the Lp-norms to L-infinity and uses Lp-norm reachable sets as an approximation of the L-infinity-norm reachable sets. Our optimal control results yield insights that make computational approximations of the Lp-norm reachable sets more tractable, and yield exact characterizations for L-infinity with the previous assumptions on the system. As an example, we incorporate our reachability analysis into the design optimization of a highly-maneuverable aircraft. Introducing constraints based on reachability allow us to factor physical limitations to desired flight maneuvers into the design process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reachability Analysis for Design Optimization Nguyen, Steven Cortés, Jorge Kramer, Boris Optimization and Control Systems and Control We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input, planar systems with real, distinct eigenvalues. The second approach leverages convergence of the Lp-norms to L-infinity and uses Lp-norm reachable sets as an approximation of the L-infinity-norm reachable sets. Our optimal control results yield insights that make computational approximations of the Lp-norm reachable sets more tractable, and yield exact characterizations for L-infinity with the previous assumptions on the system. As an example, we incorporate our reachability analysis into the design optimization of a highly-maneuverable aircraft. Introducing constraints based on reachability allow us to factor physical limitations to desired flight maneuvers into the design process. |
| title | Reachability Analysis for Design Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2603.15865 |