Considering the stochastic nonlinear control system dxₜ= f₀(x_t,u) dt +∑_j=1^p f_j(x_t,u) dW_t^j (x ∈ \bbfRⁿ, control u ∈ \bbfR^m, smooth coefficients f_j), the authors give Jurdjevic-Quinn type conditions for global asymptotic stabilization in probability by a feedback control u(x) not exceeding any prescribed bound. The feedback control is represented explicitely. The results generalize the stabilization theorem of Jurdjevic and Quinn for deterministic control systems that are linear with respect to the state and affine in the control as well as generalizations thereof to affine deterministic (Outbib and Sallet 1992) and stochastic (Florchinger 1994) control systems.
Publié le : 2000-07-04
Classification:
state feedback law,
stochastic stability,
Stochastic nonlinear control systems,
Lyapunov functions,
La Salle's invariance principle,
stochastic control system,
stabilization by feedback,
stability in probability,
nonlinear control system,
Jurdjevic-Quinn conditions,
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC],
[SPI.AUTO]Engineering Sciences [physics]/Automatic
@article{hal-01860798,
author = {Bensoubaya, Mohamed and Ferfera, Abdelhak and Iggidr, Abderrahman},
title = {A Jurdjevic-Quinn-type theorem for stochastic nonlinear control systems.},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01860798}
}
Bensoubaya, Mohamed; Ferfera, Abdelhak; Iggidr, Abderrahman. A Jurdjevic-Quinn-type theorem for stochastic nonlinear control systems.. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-01860798/