Robust maximum hands-off optimal control: existence, maximum principle, and $L^{0}$-$L^1$ equivalence

• URL: http://arxiv.org/abs/2601.07256v1
• Date: Mon, 12 Jan 2026 06:50:29 GMT
• Title: Robust maximum hands-off optimal control: existence, maximum principle, and $L^{0}$-$L^1$ equivalence
• Abstract summary: This work advances the maximum hands-off control framework by developing a robust counterpart for constrained linear systems.<n>An illustrative example is provided to the effectiveness of the resulting problems.
• Score: 2.1485350418225244
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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