# Smooth homogeneous asymptotically stabilizing feedback controls

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 2, page 13-32
- ISSN: 1292-8119

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topHermes, H.. "Smooth homogeneous asymptotically stabilizing feedback controls." ESAIM: Control, Optimisation and Calculus of Variations 2 (2010): 13-32. <http://eudml.org/doc/197370>.

@article{Hermes2010,

abstract = {
If a smooth nonlinear affine control system has a controllable linear
approximation, a standard technique for constructing a smooth (linear)
asymptotically stabilizing feedbackcontrol is via the
LQR (linear, quadratic, regulator) method. The nonlinear system may
not have a controllable linear approximation, but instead may be shown
to be small (or large) time locally controllable via a high order,
homogeneous approximation. In this case one can attempt to construct
an asymptotically stabilizing feedback control as the optimal control,
relative to a cost functional with homogeneous integrand, for the
approximating system. Necessary, and some sufficient, conditions
for the existence of a smooth (real analytic), stabilizing feedback
control of this form are given. For some systems which satisfy
these necessary conditions, the specific form of a stabilizing
control is established.
},

author = {Hermes, H.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Stabilizing feedback control / homogeneous approximations.; asymptotic stabilization; graded approximations; value functions; homogeneous cost; homogeneous feedback},

language = {eng},

month = {3},

pages = {13-32},

publisher = {EDP Sciences},

title = {Smooth homogeneous asymptotically stabilizing feedback controls},

url = {http://eudml.org/doc/197370},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Hermes, H.

TI - Smooth homogeneous asymptotically stabilizing feedback controls

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 2

SP - 13

EP - 32

AB -
If a smooth nonlinear affine control system has a controllable linear
approximation, a standard technique for constructing a smooth (linear)
asymptotically stabilizing feedbackcontrol is via the
LQR (linear, quadratic, regulator) method. The nonlinear system may
not have a controllable linear approximation, but instead may be shown
to be small (or large) time locally controllable via a high order,
homogeneous approximation. In this case one can attempt to construct
an asymptotically stabilizing feedback control as the optimal control,
relative to a cost functional with homogeneous integrand, for the
approximating system. Necessary, and some sufficient, conditions
for the existence of a smooth (real analytic), stabilizing feedback
control of this form are given. For some systems which satisfy
these necessary conditions, the specific form of a stabilizing
control is established.

LA - eng

KW - Stabilizing feedback control / homogeneous approximations.; asymptotic stabilization; graded approximations; value functions; homogeneous cost; homogeneous feedback

UR - http://eudml.org/doc/197370

ER -

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