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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$L^0$-optimal (or the sparsest) control among all feasible controls that arebounded by a specified value and transfer the state from a given initial stateto the origin within a fixed time duration. In general, the maximum hands-offcontrol is a bang-off-bang control taking values of $\pm 1$ and $0$. For manyreal applications, such discontinuity in the control is not desirable. Toobtain a continuous but still relatively sparse control, we propose to use theCLOT norm, a convex combination of $L^1$ and $L^2$ norms. We show by numericalsimulations that the CLOT control is continuous and much sparser (i.e. haslonger time duration on which the control takes 0) than the conventional EN(elastic net) control, which is a convex combination of $L^1$ and squared $L^2$norms. We also prove that the CLOT control is continuous in the sense that, if$O(h)$ denotes the sampling period, then the difference between successivevalues of the CLOT-optimal control is $O(\sqrt{h})$, which is a form ofcontinuity. Also, the CLOT formulation is extended to encompass constraints onthe state variable.

CLOT Norm Minimization for Continuous Hands-off Control