2,516 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
Characterization of maximum hands-off control
Maximum hands-off control aims to maximize the length of time over which zero
actuator values are applied to a system when executing specified control tasks.
To tackle such problems, recent literature has investigated optimal control
problems which penalize the size of the support of the control function and
thereby lead to desired sparsity properties. This article gives the exact set
of necessary conditions for a maximum hands-off optimal control problem using
an -(semi)norm, and also provides sufficient conditions for the optimality
of such controls. Numerical example illustrates that adopting an cost
leads to a sparse control, whereas an -relaxation in singular problems
leads to a non-sparse solution.Comment: 6 page
L1 Control Theoretic Smoothing Splines
In this paper, we propose control theoretic smoothing splines with L1
optimality for reducing the number of parameters that describes the fitted
curve as well as removing outlier data. A control theoretic spline is a
smoothing spline that is generated as an output of a given linear dynamical
system. Conventional design requires exactly the same number of base functions
as given data, and the result is not robust against outliers. To solve these
problems, we propose to use L1 optimality, that is, we use the L1 norm for the
regularization term and/or the empirical risk term. The optimization is
described by a convex optimization, which can be efficiently solved via a
numerical optimization software. A numerical example shows the effectiveness of
the proposed method.Comment: Accepted for publication in IEEE Signal Processing Letters. 4 pages
(twocolumn), 5 figure
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