30 research outputs found
Maximum Hands-Off Control: A Paradigm of Control Effort Minimization
In this paper, we propose a new paradigm of control, called a maximum
hands-off control. A hands-off control is defined as a control that has a short
support per unit time. The maximum hands-off control is the minimum support (or
sparsest) per unit time among all controls that achieve control objectives. For
finite horizon control, we show the equivalence between the maximum hands-off
control and L1-optimal control under a uniqueness assumption called normality.
This result rationalizes the use of L1 optimality in computing a maximum
hands-off control. We also propose an L1/L2-optimal control to obtain a smooth
hands-off control. Furthermore, we give a self-triggered feedback control
algorithm for linear time-invariant systems, which achieves a given sparsity
rate and practical stability in the case of plant disturbances. An example is
included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear
Continuous Hands-off Control by CLOT Norm Minimization
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