  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 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 $\pm 1$ 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 $L^1$ and $L^2$ norms. We show by numerical
simulations 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 $L^1$ 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 successive
values of the CLOT-optimal control is $O(\sqrt{h})$, which is a form of
continuity. Also, the CLOT formulation is extended to encompass constraints on
the state variable.
