Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems Based on Stochastic Control Lyapunov Functions
Summary :
In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffusion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.8 pp.1695-1702
- Publication Date
- 2013/08/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.1695
- Type of Manuscript
- PAPER
- Category
- Systems and Control
Authors
Yuki NISHIMURA
Kagoshima University
Kanya TANAKA
Yamaguchi University
Yuji WAKASA
Yamaguchi University
Yuh YAMASHITA
Hokkaido University
Keyword
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Yuki NISHIMURA, Kanya TANAKA, Yuji WAKASA, Yuh YAMASHITA, "Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems Based on Stochastic Control Lyapunov Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 8, pp. 1695-1702, August 2013, doi: 10.1587/transfun.E96.A.1695.
Abstract: In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffusion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1695/_p
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@ARTICLE{e96-a_8_1695,
author={Yuki NISHIMURA, Kanya TANAKA, Yuji WAKASA, Yuh YAMASHITA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems Based on Stochastic Control Lyapunov Functions},
year={2013},
volume={E96-A},
number={8},
pages={1695-1702},
abstract={In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffusion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.},
keywords={},
doi={10.1587/transfun.E96.A.1695},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - Stochastic Asymptotic Stabilizers for Deterministic Input-Affine Systems Based on Stochastic Control Lyapunov Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1695
EP - 1702
AU - Yuki NISHIMURA
AU - Kanya TANAKA
AU - Yuji WAKASA
AU - Yuh YAMASHITA
PY - 2013
DO - 10.1587/transfun.E96.A.1695
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2013
AB - In this paper, a stochastic asymptotic stabilization method is proposed for deterministic input-affine control systems, which are randomized by including Gaussian white noises in control inputs. The sufficient condition is derived for the diffusion coefficients so that there exist stochastic control Lyapunov functions for the systems. To illustrate the usefulness of the sufficient condition, the authors propose the stochastic continuous feedback law, which makes the origin of the Brockett integrator become globally asymptotically stable in probability.
ER -
English
