Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics

Pascal Morin; Claude Samson

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

  • Volume: 4, page 1-35
  • ISSN: 1292-8119

Abstract

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Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was first addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These controllers are more precisely described as continuous time-periodic feedbacks associated with a specific dynamic extension of the original system. Sufficient conditions which, if they are satisfied by the control law, ensure that the control is a robust exponential stabilizer for the extended system are given. Explicit and simple control expressions which satisfy these conditions in the case of n-dimensional chained systems are proposed. A constructive algorithm for the design of such control laws, which applies to any (sufficiently regular) driftless control system, is described.

How to cite

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Morin, Pascal, and Samson, Claude. "Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 1-35. <http://eudml.org/doc/197375>.

@article{Morin2010,
abstract = { Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was first addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These controllers are more precisely described as continuous time-periodic feedbacks associated with a specific dynamic extension of the original system. Sufficient conditions which, if they are satisfied by the control law, ensure that the control is a robust exponential stabilizer for the extended system are given. Explicit and simple control expressions which satisfy these conditions in the case of n-dimensional chained systems are proposed. A constructive algorithm for the design of such control laws, which applies to any (sufficiently regular) driftless control system, is described. },
author = {Morin, Pascal, Samson, Claude},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nonlinear system; asymptotic stabilization; robust control; Chen-Fliess series.; affine control system; robust exponential stability; feedback time-dependent control; periodic control; robust stabilization},
language = {eng},
month = {3},
pages = {1-35},
publisher = {EDP Sciences},
title = {Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics},
url = {http://eudml.org/doc/197375},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Morin, Pascal
AU - Samson, Claude
TI - Exponential stabilization of nonlinear driftless systems with robustness to unmodeled dynamics
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 1
EP - 35
AB - Exponential stabilization of nonlinear driftless affine control systems is addressed with the concern of achieving robustness with respect to imperfect knowledge of the system's control vector fields. In order to satisfy this robustness requirement, and inspired by Bennani and Rouchon [1] where the same issue was first addressed, we consider a control strategy which consists in applying periodically updated open-loop controls that are continuous with respect to state initial conditions. These controllers are more precisely described as continuous time-periodic feedbacks associated with a specific dynamic extension of the original system. Sufficient conditions which, if they are satisfied by the control law, ensure that the control is a robust exponential stabilizer for the extended system are given. Explicit and simple control expressions which satisfy these conditions in the case of n-dimensional chained systems are proposed. A constructive algorithm for the design of such control laws, which applies to any (sufficiently regular) driftless control system, is described.
LA - eng
KW - Nonlinear system; asymptotic stabilization; robust control; Chen-Fliess series.; affine control system; robust exponential stability; feedback time-dependent control; periodic control; robust stabilization
UR - http://eudml.org/doc/197375
ER -

References

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