时滞神经网络随机抽样控制的状态估计
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摘要
研究了时滞神经网络随机抽样控制的状态估计问题.首先,给出了随机抽样区间和抽样输入时滞的统一概率结构.基于此结构,构造了一个包含新的锯齿结构项的Lyapunov泛函.然后,运用不等式放缩技术,得到了误差系统随机稳定的保守性更低的标准,并设计出了合适的状态估计器.最后,数值仿真算例验证了所得结果的优势和有效性.
The problem of the state estimation for delayed neural networks with stochastic sampled-data control was studied. First,a unified probability framework involving the stochastic sampling interval and the sampling input delay was proposed. Second,based on this unified probability framework,a new LyapunovKrasovskii functional( LKF) with some new terms was constructed. Third,with this LKF and some inequality technologies,a less conservative criterion was established,which can ensure the stochastic stability of the error system. The desired state estimator was designed. Finally,numerical simulation results show the effectiveness and advantages of the proposed method.
The problem of the state estimation for delayed neural networks with stochastic sampled-data control was studied. First,a unified probability framework involving the stochastic sampling interval and the sampling input delay was proposed. Second,based on this unified probability framework,a new LyapunovKrasovskii functional( LKF) with some new terms was constructed. Third,with this LKF and some inequality technologies,a less conservative criterion was established,which can ensure the stochastic stability of the error system. The desired state estimator was designed. Finally,numerical simulation results show the effectiveness and advantages of the proposed method.
引文
[1]ZENG D Q,ZHANG R M,ZHONG S M,et al.Sampled-data synchronization control for Markovian delayed complex dynamical networks via a novel convex optimization method[J].Neurocomputing,2017,266:606-618.
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[8]RATNAVELU K,MANIKANDAN M,BALASUBRAMANIAM P.Design of state estimator for BAMfuzzy cellular neural networks with leakage and unbounded distributed delays[J].Information Sciences,2017,397:91-109.
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[12]WANG Z S,WANG J D,WU Y M.State estimation for recurrent neural networks with unknown delays:a robust analysis approach[J].Neurocomputing,2017,227:29-36.
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[16]LIU Y J,GUO B Z,PARK J H,et al.Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control[J].IEEE Transactions on Neural Networks and Learning Systems,2018,29(1):118-128.
[17]LI Q,SHEN B,WANG Z D,et al.A sampled-data approach to distributed H∞resilient state estimation for a class of nonlinear time-delay systems over sensor networks[J].Journal of The Franklin Institute,2017,354(15):7139-7157.
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[19]ZHANG R M,ZENG D Q,ZHONG S M,et al.Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays[J].Applied Mathematics and Computation,2017,310:57-74.
[20]ANBUVITHYA R,MATHIYALAGAN K,SAKTHIVEL R,et al.Sampled-data state estimation for genetic regulatory networks with time-varying delays[J].Neurocomputing,2015,151:737-744.
[21]ALI M S,GUNASEKARAN N,ZHU Q.State estimation of T-S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control[J].Fuz z y Sets&Systems,2017,306:87-104.
[22]LIU Y J,LEE S M.Sampled-data synchronization of chaotic Lur’e systems with stochastic sampling[J].Circuits,Systems,and Signal Processing,2015,34(12):3725-3739.
[23]SHI K B,LIU X Z,ZHU H,et al.On designing stochastic sampled-data controller for master-slave synchronization of chaotic Lur’e system via a noel integral inequality[J].Communications in Nonlinear Science and Numerical Simulation,2016,34:165-184.
[24]GAO H,WU J,SHI P.Robust sampled-data H∞control with stochastic sampling[J].Automatica,2009,45(7):1729-1736.
[25]SHEN B,WANG Z D,LIU X H.Sampled-data synchronization control of dynamical networks with stochastic sampling[J].IEEE Transactions on Automatic Control,2012,57(10):2644-2650.
[26]RAKKIYAPPAN R,DHARANI S,ZHU Q X.Synchronization of reaction-diffusion neural networks with time-varying delays via stochastic sampled-data controller[J].Nonlinear Dynamics,2015,79(1):485-500.
[27]LEE T H,PARK J H,LEE S M,et al.Robust synchronization of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control[J].International Journal of Control,2013,86(1):107-119.
[28]WU Z G,SHI P,SU H,et al.Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data[J].IEEE Transactions on Cybernetics,2013,43(6):1796-1806.
[29]YANG F S,ZHANG H G,WANG Y C.An enhanced input-delay approach to sampled-data stabilization of T-S fuzzy systems via mixed convex combination[J].Nonlinear Dynamics,2014,75(3):501-512.
[30]BOYD S,GHAOUI L E,FERON E,et al.Linear Matrix Inequalities in System and Control Theory[M].USA:Society for Industrial and Applied Mathematics,1994.
[2]王利敏,宋乾坤,赵振江.基于忆阻的分数阶时滞复值神经网络的全局渐进稳定性[J].应用数学和力学,2017,38(3):333-346.(WANG Limin,SONG Qiankun,ZHAO Zhenjiang.Global asymptotic stability of memristor-based fractional-order complex-valued neural networks with time delays[J].Applied Mathematics and Mechanics,2017,38(3):333-346.(in Chinese))
[3]舒含奇,宋乾坤.带有时滞的Clifford值神经网络的全局指数稳定性[J].应用数学和力学,2017,38(5):513-525.(SHU Hanqi,SONG Qiankun.Global stability of Clifford-valued recurrent neural networks with mixed time-varying delays[J].Applied Mathematics and Mechanics,2017,38(5):513-525.(in Chinese))
[4]ZHANG R M,ZENG D Q,ZHONG S M.Novel master-slave synchronization criteria of chaotic Lur’e systems with time delays using sampled-data control[J].Journal of The Franklin Institute,2017,354(12):4930-4954.
[5]LEE T,PARK J H,KWON O M,et al.Stochastic sampled-data control for state estimation of timevarying delayed neural networks[J].Neural Networks,2013,46(5):99-108.
[6]ZENG D Q,ZHANG R M,ZHONG S M,et al.Novel Lebesgue-integral-based approach to improved results for neural networks with additive time-varying delay components[J].Journal of The Franklin Institute,2017,354(16):7543-7565.
[7]SHI K B,LIU X Z,TANG Y Y,et al.Some novel approaches on state estimation of delayed neural networks[J].Information Sciences,2016,372:313-331.
[8]RATNAVELU K,MANIKANDAN M,BALASUBRAMANIAM P.Design of state estimator for BAMfuzzy cellular neural networks with leakage and unbounded distributed delays[J].Information Sciences,2017,397:91-109.
[9]ALI M S,SARAVANAN S,ARIK S.Finite-time H∞state estimation for switched neural networks with time-varying delays[J].Neurocomputing,2016,207:580-589.
[10]LIU Y C,WANG T,CHEN M S,et al.Dissipativity-based state estimation of delayed static neural networks[J].Neurocomputing,2017,247:137-143.
[11]XIAO J Y,LI Y T,ZHONG S M,et al.Extended dissipative state estimation for memristive neural networks with time-varying delay[J].ISA Transactions,2016,64:113-128.
[12]WANG Z S,WANG J D,WU Y M.State estimation for recurrent neural networks with unknown delays:a robust analysis approach[J].Neurocomputing,2017,227:29-36.
[13]ZHONG M Y,HAN Q L.Fault-tolerant master-slave synchronization for Lur’e systems using timedelay feedback control[J].IEEE Transactions on Circuits and Systems,2009,56(7):1391-1404.
[14]LU J Q,CAO J D,HO D W C.Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay[J].IEEE Transactions on Circuits and Systems,2008,55(5):1347-1356.
[15]LIU Y J,LEE S M.Synchronization criteria of chaotic Lur’e systems with delayed feedback PD control[J].Neurocomputing,2016,189(37):66-71.
[16]LIU Y J,GUO B Z,PARK J H,et al.Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control[J].IEEE Transactions on Neural Networks and Learning Systems,2018,29(1):118-128.
[17]LI Q,SHEN B,WANG Z D,et al.A sampled-data approach to distributed H∞resilient state estimation for a class of nonlinear time-delay systems over sensor networks[J].Journal of The Franklin Institute,2017,354(15):7139-7157.
[18]RAKKIYAPPAN R,SAKTHIVEL N,PARK J H,et al.Sampled-data state estimation for Markovian jumping fuzzy cellular neural networks with mode-dependent probabilistic time-varying delays[J].Applied Mathematics and Computation,2013,221(9):741-769.
[19]ZHANG R M,ZENG D Q,ZHONG S M,et al.Event-triggered sampling control for stability and stabilization of memristive neural networks with communication delays[J].Applied Mathematics and Computation,2017,310:57-74.
[20]ANBUVITHYA R,MATHIYALAGAN K,SAKTHIVEL R,et al.Sampled-data state estimation for genetic regulatory networks with time-varying delays[J].Neurocomputing,2015,151:737-744.
[21]ALI M S,GUNASEKARAN N,ZHU Q.State estimation of T-S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control[J].Fuz z y Sets&Systems,2017,306:87-104.
[22]LIU Y J,LEE S M.Sampled-data synchronization of chaotic Lur’e systems with stochastic sampling[J].Circuits,Systems,and Signal Processing,2015,34(12):3725-3739.
[23]SHI K B,LIU X Z,ZHU H,et al.On designing stochastic sampled-data controller for master-slave synchronization of chaotic Lur’e system via a noel integral inequality[J].Communications in Nonlinear Science and Numerical Simulation,2016,34:165-184.
[24]GAO H,WU J,SHI P.Robust sampled-data H∞control with stochastic sampling[J].Automatica,2009,45(7):1729-1736.
[25]SHEN B,WANG Z D,LIU X H.Sampled-data synchronization control of dynamical networks with stochastic sampling[J].IEEE Transactions on Automatic Control,2012,57(10):2644-2650.
[26]RAKKIYAPPAN R,DHARANI S,ZHU Q X.Synchronization of reaction-diffusion neural networks with time-varying delays via stochastic sampled-data controller[J].Nonlinear Dynamics,2015,79(1):485-500.
[27]LEE T H,PARK J H,LEE S M,et al.Robust synchronization of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control[J].International Journal of Control,2013,86(1):107-119.
[28]WU Z G,SHI P,SU H,et al.Stochastic synchronization of Markovian jump neural networks with time-varying delay using sampled data[J].IEEE Transactions on Cybernetics,2013,43(6):1796-1806.
[29]YANG F S,ZHANG H G,WANG Y C.An enhanced input-delay approach to sampled-data stabilization of T-S fuzzy systems via mixed convex combination[J].Nonlinear Dynamics,2014,75(3):501-512.
[30]BOYD S,GHAOUI L E,FERON E,et al.Linear Matrix Inequalities in System and Control Theory[M].USA:Society for Industrial and Applied Mathematics,1994.