  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.
