Stabilization of Nonlinear Stochastic Delay Differential Equations Driven by G-Brownian Motion

LI Guangjie; YANG Qigui

doi:10.21656/1000-0887.410332

Volume 42 Issue 8

Aug. 2021

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(8): 841-851

LI Guangjie, YANG Qigui. Stabilization of Nonlinear Stochastic Delay Differential Equations Driven by G-Brownian Motion[J]. Applied Mathematics and Mechanics, 2021, 42(8): 841-851. doi: 10.21656/1000-0887.410332

Citation:

PDF( 1121 KB)

Stabilization of Nonlinear Stochastic Delay Differential Equations Driven by G-Brownian Motion

doi: 10.21656/1000-0887.410332

LI Guangjie¹,
YANG Qigui^{2
,
,}

1. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, P.R.China;
2. School of Mathematics, South China University of Technology,Guangzhou 510640, P.R.China

Funds:

12071151)

The National Natural Science Foundation of China(11901398

Received Date: 2020-10-27
Rev Recd Date: 2021-02-03

Available Online: 2021-08-14

Abstract

Abstract

The stabilization problem of a class of nonlinear stochastic delay differential equations driven by G-Brownain motion (G-SDDEs) was studied. Firstly, a delay feedback control was designed in the drift term of an unstable nonlinear G-SDDE, and the controlled system was therefore obtained. Then, with the Lyapunov technique, sufficient conditions for the asymptotical stability of the controlled system were given. Finally, two examples were presented to illustrate the obtained results.
- nonlinear stochastic delay differential equation,
- delay feedback control,
- G-Brownian motion,
- asymptotical stability

FullText(HTML)

References(20)

References

MAO X. Stochastic Differential Equations and Application[M]. Chichester: Horwood Publication, 1997.

[2]HUANG Z, YANG Q, CAO J. Stochastic stability and bifurcation analysis on Hopfield neural networks with noise[J]. Expert Systems With Applications,2011,38(8): 10437-10445.

[3]ZENG C, CHEN Y, YANG Q. Almost sure and moment stability properties of fractional order Black-Scholes model[J]. Fractional Calculus and Applied Analysis,2013,16(2): 317-331.

[4]LIU L. New criteria on exponential stability for stochastic delay differential systems based on vector Lyapunov function[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems,2016,47(11): 2985-2993.

[5]GUO Q, MAO X, YUE R. Almost sure exponential stability of stochastic differential delay equations[J]. SIAM Journal on Control and Optimization,2016,54(4): 1919-1933.

[6]CHEN W, XU S, ZHANG B, et al. Stability and stabilisation of neutral stochastic delay Markovian jump systems[J]. IET Control Theory & Applications,2016,10(15): 1798-1807.

[7]XU L, DAI Z, HU H. Almost sure and moment asymptotic boundedness of stochastic delay differential systems[J]. Applied Mathematics and Computation,2019,361(15): 157-168.

[8]马丽, 马瑞楠. 一类随机泛函微分方程带随机步长的EM逼近的渐近稳定[J]. 应用数学和力学, 2019,40(1): 97-107.(MA Li, MA Ruinan. Almost sure asymptotic stability of the Euler-Maruyama method with random variable stepsizes for stochastic functional differential equations[J]. Applied Mathematics and Mechanics,2019,40(1): 97-107.(in Chinese))

[9]SHEN M, FEI C, FEI W, et al. Stabilisation by delay feedback control for highly nonlinear neutral stochastic differential equations[J]. Systems & Control Letters,2020,137: 104645.

[10]PENG S. G-expectation, G-Brownian motion and related stochastic calculus of It type[M]//Stochastic Analysis and Applications. Berlin, Heidelberg: Springer, 2007: 541-567.

[11]PENG S. Nonlinear Expectations and Stochastic Calculus Under Uncertainty[M]. Berlin, Heidelberg: Springer-Verlag, 2019.

[12]LI G, YANG Q. Convergence and asymptotical stability of numerical solutions for neutral stochastic delay differential equations driven by G-Brownian motion[J]. Computational and Applied Mathematics,2018,37(4): 4301-4320.

[13]DENG S, FEI C, FEI W, et al. Stability equivalence between the stochastic differential delay equations driven by G-Brownian motion and the Euler-Maruyama method[J]. Applied Mathematics Letters,2019,96: 138-146.

[14]YIN W, CAO J, REN Y. Quasi-sure exponential stability and stabilisation of stochastic delay differential equations under G-expectation framework[J]. International Journal of Control,2020,474(1): 276-289.

[15]ZHU Q, HUANG T. Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion[J]. Systems & Control Letters,2020,140: 104699.

[16]REN Y, YIN W, SAKTHIVEL R. Stabilization of stochastic differential equations driven by G-Brownian motion with feedback control based on discrete-time state observation[J]. Automatica,2018,95: 146-151.

[17]YANG H, REN Y, LU W. Stabilisation of stochastic differential equations driven by G-Brownian motion via aperiodically intermittent control[J]. International Journal of Control,2020,93(3): 565-574.

[18]LI X, MAO X. Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control[J]. Automatica,2020,112: 108657.

[19]FEI C, FEI W, YAN L. Existence and stability of solutions to highly nonlinear stochastic differential delay equations driven by G-Brownian motion[J]. Applied Mathematics: a Journal of Chinese Universities,2019,34(2): 184-204.

[20]LU C, DING X. Permanenceand extinction of a stochastic delay logistic model with jumps[J]. Mathematical Problems in Engineering,2014,2014(2): 1-8.

Relative Articles

Supplements(0)

Cited By

Proportional views