TY - JOUR
T1 - Stabilisation of highly nonlinear hybrid systems by feedback control based on discrete-time state observations
AU - Fei, Chen
AU - Fei, Weiyin
AU - Mao, Xuerong
AU - Xia, Dengfeng
AU - Yan, Litan
N1 - © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
PY - 2020/7/31
Y1 - 2020/7/31
N2 - Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at times 0, τ, 2τ, · · · , so that the controlled hybrid SDE becomes asymptotically stable? It has been proved that this is possible if the drift and diffusion coefficients of the given hybrid SDE satisfy the linear growth condition. However, many hybrid SDEs in the real world do not satisfy this condition (namely, they are highly nonlinear) and there is no answer to the question yet if the given SDE is highly nonlinear. The aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid SDEs. Under some reasonable conditions on the drift and diffusion coefficients, we show how to design the feedback control function and give an explicit bound on τ (the time duration between two consecutive state observations), whence the new theory established in this paper is implementable.
AB - Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at times 0, τ, 2τ, · · · , so that the controlled hybrid SDE becomes asymptotically stable? It has been proved that this is possible if the drift and diffusion coefficients of the given hybrid SDE satisfy the linear growth condition. However, many hybrid SDEs in the real world do not satisfy this condition (namely, they are highly nonlinear) and there is no answer to the question yet if the given SDE is highly nonlinear. The aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid SDEs. Under some reasonable conditions on the drift and diffusion coefficients, we show how to design the feedback control function and give an explicit bound on τ (the time duration between two consecutive state observations), whence the new theory established in this paper is implementable.
KW - highly nonlinear
KW - Ito formula
KW - Markov chain
KW - asymptotic stability
KW - Lyapunov functional
U2 - 10.1109/TAC.2019.2933604
DO - 10.1109/TAC.2019.2933604
M3 - Article
VL - 65
SP - 2899
EP - 2912
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 7
ER -