Stabilization of Nonlinear Stochastic Delay Differential Equations Driven by G-Brownian Motion
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摘要: 研究了一类G-Brown运动驱动的非线性随机时滞微分方程的稳定化问题.首先,在一个不稳定的G-Brown运动驱动的非线性随机时滞微分方程的漂移项中设计了时滞反馈控制, 得其相应的控制系统.其次, 利用Lyapunov函数方法给出其相应的控制系统是渐近稳定的充分条件.最后, 通过例子说明了所得的结果.
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关键词:
- 非线性随机时滞微分方程 /
- 时滞反馈控制 /
- G-Brown运动 /
- 渐近稳定性
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. -
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.
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