提出鲁棒零范数控制新方法，确保不确定系统下的最优稀疏控制。
Robust maximum hands-off optimal control: existence, maximum principle, and $L^{0}$-$L^1$ equivalence
- 用L1近似替代L0目标函数，实现稀疏控制优化
- 证明在不确定条件下L0与L1解集完全相同
- 适用于对鲁棒性要求高的工程控制场景
本文针对具有参数不确定性的线性系统，推进了最大无干预稀疏控制框架。所提出的最优控制问题以L0为目标函数，受制于不可数个紧约束的集合，属于非凸、非光滑的鲁棒优化问题。为求解，将L0目标替换为其凸的L1代理，并利用非光滑鲁棒庞特里亚金最大值原理，证明了在鲁棒条件下L0与L1的最优解集完全一致——即鲁棒无干预原则。基于该等价性，提出一种算法框架，借鉴半无限鲁棒优化中的数值可行技术来求解。通过一个示例验证了方法的有效性。
原文摘要 · Abstract (English)
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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