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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.07256 |
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| _version_ | 1866918283385503744 |
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| author | Ganguly, Siddhartha Kashima, Kenji |
| author_facet | Ganguly, Siddhartha Kashima, Kenji |
| contents | This work advances the maximum hands-off sparse control framework by developing a robust counterpart for constrained linear systems with parametric uncertainties. The resulting optimal control problem minimizes an $L^{0}$ objective subject to an uncountable, compact family of constraints, and is therefore a nonconvex, nonsmooth robust optimization problem. To address this, we replace the $L^{0}$ objective with its convex $L^{1}$ surrogate and, using a nonsmooth variant of the robust Pontryagin maximum principle, show that the $L^{0}$ and $L^{1}$ formulations have identical sets of optimal solutions -- we call this the robust hands-off principle. Building on this equivalence, we propose an algorithmic framework -- drawing on numerically viable techniques from the semi-infinite robust optimization literature -- to solve the resulting problems. An illustrative example is provided to demonstrate the effectiveness of the approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07256 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust maximum hands-off optimal control: existence, maximum principle, and $L^{0}$-$L^1$ equivalence Ganguly, Siddhartha Kashima, Kenji Optimization and Control Numerical Analysis Robotics Systems and Control This work advances the maximum hands-off sparse control framework by developing a robust counterpart for constrained linear systems with parametric uncertainties. The resulting optimal control problem minimizes an $L^{0}$ objective subject to an uncountable, compact family of constraints, and is therefore a nonconvex, nonsmooth robust optimization problem. To address this, we replace the $L^{0}$ objective with its convex $L^{1}$ surrogate and, using a nonsmooth variant of the robust Pontryagin maximum principle, show that the $L^{0}$ and $L^{1}$ formulations have identical sets of optimal solutions -- we call this the robust hands-off principle. Building on this equivalence, we propose an algorithmic framework -- drawing on numerically viable techniques from the semi-infinite robust optimization literature -- to solve the resulting problems. An illustrative example is provided to demonstrate the effectiveness of the approach. |
| title | Robust maximum hands-off optimal control: existence, maximum principle, and $L^{0}$-$L^1$ equivalence |
| topic | Optimization and Control Numerical Analysis Robotics Systems and Control |
| url | https://arxiv.org/abs/2601.07256 |