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.

翻译：本研究通过为具有参数不确定性的约束线性系统构建鲁棒对应模型，推进了最大零操作稀疏控制框架的发展。由此产生的最优控制问题在不可数紧约束族下最小化$L^{0}$目标函数，因此属于非凸、非光滑的鲁棒优化问题。为解决此问题，我们将$L^{0}$目标替换为其凸$L^{1}$代理函数，并利用鲁棒庞特里亚金最大值原理的非光滑变体，证明$L^{0}$与$L^{1}$表述具有完全相同的最优解集——我们称之为鲁棒零操作原理。基于该等价性，我们提出一种算法框架——借鉴半无限鲁棒优化文献中数值可行的技术——以求解所得问题。文中提供了示例以验证该方法的有效性。