通过CLOT范数最小化实现连续的手动控制
Continuous Hands-off Control by CLOT Norm Minimization
AI总结：
本文通过最小化CLOT范数实现连续的手动控制，提出了一种连续且相对稀疏的控制方法，相比传统弹性网络控制，CLOT控制更稀疏且连续。
摘要：
本文考虑通过最小化CLOT（结合L1和L2）范数实现的手动控制。最大手动控制是在所有受指定值限制且能在固定时间内将状态从初始状态转移到原点的可行控制中，L0最优（即最稀疏）的控制。通常，最大手动控制是bang-off-bang控制，取+1、-1和0值。对于许多实际应用，这种控制的不连续性是不理想的。为了获得连续但仍然相对稀疏的控制，我们提出使用CLOT范数，即L1和L2范数的凸组合。通过数值模拟，我们证明CLOT控制是连续的，并且比传统弹性网络（EN）控制更稀疏（即控制取0值的时间更长）。
英文摘要：
In this paper, we consider hands-off control via minimization of the CLOT (Combined L-One and Two) norm. The maximum hands-off control is the L0-optimal (or the sparsest) control among all feasible controls that are bounded by a specified value and transfer the state from a given initial state to the origin within a fixed time duration. In general, the maximum hands-off control is a bang-off-bang control taking values of +1, -1, and 0. For many real applications, such discontinuity in the control is not desirable. To obtain a continuous but still relatively sparse control, we propose to use the CLOT norm, a convex combination of L1 and L2 norms. We show by numerical simulation that the CLOT control is continuous and much sparser (i.e. has longer time duration on which the control takes 0) than the conventional EN (elastic net) control, which is a convex combination of L1 and squared L2 norms.
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