Smooth homogeneous asymptotically stabilizing feedback controls

Hermes, 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 -