Challapalli, N and Nagahara, M and Mathukumalli, V
(2016)
Continuous Hands-off Control by CLOT Norm Minimization.
arXiv.
pp. 1-8.
Abstract
In this paper, we consider hands-off control via minimization of the C
LOT
(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 b
y a specified value and transfer
the state from a given initial state to the origin within a fixed time dura
tion. In general, the
maximum hands-off control is a bang-off-bang control taking value
s of
±
1 and 0. For many real
applications, such discontinuity in the control is not desirable. To ob
tain a continuous but still
relatively sparse control, we propose to use the CLOT norm, a conv
ex combination of
L
1
and
L
2
norms. We show by numerical simulation that the CLOT control is con
tinuous 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.
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