Mean-Square Exponential Input-to-State Stability of Numerical Solutions for Stochastic Control Systems

这份报纸处理随机的控制系统(SCS ) 的数字解决方案的吝啬平方的指数的 input-to-state 稳定性(expbe ) 。第一，一个有限时间的强壮的集中条件成立为，这被显示出随机 ? SCS 上的方法。那么，如果并且仅当，我们能看到 SCS 的吝啬平方的 expbe 成立的随机 ? 方法(为足够地小的步尺寸) 在有限时间的强壮的集中条件下面被保存。为有片面 Lipschitz 飘移的 SCS 的一个班，第二，它被证明那二含蓄的 Euler 方法(为任何步尺寸) 能继承 SCS 的吝啬平方的 expbe 性质。最后，数字例子证实在这研究介绍的定理的正确性。

Asymptotical mean square stability of cellular neural networks with random delay

In this paper,the asymptotical mean-square stability analysis problem is considered for a class of cellular neural networks (CNNs) with random delay. Compared with the previous work,the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed cellular neural network is asymptotic mean-square stability. By using some stochastic analysis techniques and Lyapunov-Krasovskii functional,some conditions are derived to ensure that the cellular neural networks with random delay is asymptotical mean-square stability. A numerical example is exploited to show the vadlidness of the established results.

Random Crank-Nicolson Scheme for Random Heat Equation in Mean Square Sense

The goal of computational science is to develop models that predict phenomena observed in nature. However, these models are often based on parameters that are uncertain. In recent decades, main numerical methods for solving SPDEs have been used such as, finite difference and finite element schemes [1]-[5]. Also, some practical techniques like the method of lines for boundary value problems have been applied to the linear stochastic partial differential equations, and the outcomes of these approaches have been experimented numerically [7]. In [8]-[10], the author discussed mean square convergent finite difference method for solving some random partial differential equations. Random numerical techniques for both ordinary and partial random differential equations are treated in [4] [10]. As regards applications using explicit analytic solutions or numerical methods, a few results may be found in [5] [6] [11]. This article focuses on solving random heat equation by using Crank-Nicol- son technique under mean square sense and it is organized as follows. In Section 2, the mean square calculus preliminaries that will be required throughout the paper are presented. In Section 3, the Crank-Nicolson scheme for solving the random heat equation is presented. In Section 4, some case studies are showed. Short conclusions are cleared in the end section.

Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.

NONLINEAR RANDOM STABILITY OF VISCOELASTIC CABLE WITH SMALL CURVATURE

The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.

ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS

Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.

Stability and output feedback stabilization for systems with Markovian switching and impulse effects

We investigate the exponential stability in the mean square sense for the systems with Markovian switching and impulse effects.Based on the statistic property of the Markov process,a stability criterion is established.Then,by the parameterizations via a family of auxiliary matrices,the dynamical output feedback controller can be solved via an LMI approach,which makes the closed-loop system exponentially stable.A numerical example is given to demonstrate the method.

Effect of Exercise with Rhythmic Auditory Stimulation on Muscle Coordination and Gait Stability in Patients with Diabetic Peripheral Neuropathy: A Randomized Controlled Trial

Background: Diabetic peripheral neuropathy (DPN) changes leg muscle coordination during walking and reduces stability. The aim of this study was to determine whether rhythmic auditory stimulation (RAS) affected the gait performance of patients with DPN. Methods: Forty DPN patients (mean age, 59.1 ± 9.4 y) were randomly allocated to RAS and control groups in equal numbers. The participants in each group underwent 2 weeks of supervised rehabilitative treatment (40 min/day) as inpatients. This included walking twice a day, during which the RAS group participants walked in time with a metronome set at a self-chosen, comfortable rate. We compared gait function, lower limb muscle co-contraction, and gait stability before and after the intervention for both groups, calculated the change in score for each parameter, and assessed differences between the groups with unpaired t-tests and ANCOVA. Results: RAS was associated with significant improvement in all parameters. In the control group, there was no improvement in cadence, co-contraction, or gait stability (vertical). Compared with the control group, the RAS group showed improvement in co-contraction and gait stability. Conclusion: RAS may be helpful for improving the lower limb muscle coordination and gait function of DPN patients.

Novel delay-distribution-dependent stability analysis for continuous-time recurrent neural networks with stochastic delay

In this paper, the problem of delay-distribution-dependent stability is investigated for continuous-time recurrent neural networks （CRNNs） with stochastic delay. Different from the common assumptions on time delays, it is assumed that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delay and by using a tighter bounding technique （the reciprocally convex combination method）, less conservative asymptotic mean-square stable sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. Two numerical examples show that our results are better than the existing ones.

A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS

A type of complex systems under both random influence and memory effects is considered. The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations. A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough. Numerical simulations are presented to illustrate the theoretical result.

LAGRANGE STABILITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION EQUATIONS

This work is devoted to the discussion of stochastic reaction diffusion equations and some new theorems on Lagrange stability in mean square of the solution are established via Lyapunov method which is nothing to be done in the past.

基于BaGa_(4)Se_(7)晶体的中红外辐射源稳定性实验研究

在实际应用中,光源的输出能量稳定性影响着光源在各种应用中的可靠性和性能,如激光治疗、光谱分析、光电对抗以及光成像等领域。本文首先对光学参量振荡器(OPO)系统从激光泵浦源、谐振腔结构和非线性晶体三个方面对输出能量稳定性进行分析。实验方面,使用BaGa_(4)Se_(7)(BGSe)晶体搭建脉冲激光泵浦的3~8μm中红外OPO辐射源,从激光泵浦源和OPO系统两部分对输出能量波动性进行了详细的测量和分析。当输入泵浦能量为30 mJ,正入射输出4.5μm波长时,平均能量为2.151 mJ,标准差为56.49μJ,计算RMS波动为2.62%。根据分析得出,随着激光增益的提高和腔损耗的减小,输出脉冲的波动减小。该研究为不同应用场景下BGSe晶体的红外辐射源的工作参数的选择提供了有益的指导。

Mean-square Stability of Stochastic Age-dependent Delay Population Systems with Jumps

In this paper, we present the compensated stochastic θ method for stochastic age-dependent delay population systems（SADDPSs） with Poisson jumps. The definition of mean-square stability of the numerical solution is given and a sufficient condition for mean-square stability of the numerical solution is derived. It is shown that the compensated stochastic θ method inherits stability property of the numerical solutions. Finally,the theoretical results are also confirmed by a numerical experiment.

基于DDS-PLL技术的MEMS陀螺仪闭环驱动系统设计

为了提高科氏振动陀螺仪驱动模态的控制精度与稳定性,设计了基于DDS-PLL技术的MEMS陀螺仪闭环驱动系统。利用基于直接数字频率合成器(DDS)算法的数字锁相环实现对陀螺谐振频率和相位的跟踪,采用数字自动增益模块(AGC)实现驱动幅值的稳定控制。实验结果表明,通过DDS算法实现的闭环驱动系统具有更高的控制精度,驱动幅值变化的均方差缩小到0.0011 mV,幅度稳定性为183 ppm,谐振频率变化的均方差缩减至0.07 Hz,频率稳定性为3.48 ppm,陀螺仪驱动模态的幅值和频率控制精度得到了提高。

离散时间平均场随机系统的滚动时域控制

研究了一类离散时间平均场随机时变系统的滚动时域控制(RHC)镇定问题。定义一个新的条件期望型的性能指标;通过利用随机极值原理,得到RHC控制器。基于最优性能指标的单调非增性,得到了使平均场随机系统在RHC控制器下均方镇定的条件,即当2个耦合的Lyapunov型不等式被满足时,由RHC策略控制的系统是均方镇定的。通过数值算例得到在RHC控制器下,其状态轨迹满足渐近均方镇定的条件,即平均场随机系统是渐近均方镇定的,验证了该结论的有效性。

分数布朗运动驱动的随机微分方程的稳定性

考虑如下形式的由分数布朗运动驱动的随机微分方程的均方指数稳定性,{dX(t)=(AX(t)+f(t,X(t))dt+g(t)dB^(H)(t)X(t)=φ(t),t∈[0,T]式中Hurst参数H∈(0,1/2)。通过对该方程中分数布朗运动的维纳积分进行估计,得到矩估计不等式。在一些特定条件下,采用积分不等式讨论了温和解的稳定性,给出相应的例子,验证了结论的准确性。

一类随机SIR传染病模型的非标准数值离散化

研究一个具有饱和发生率和疫苗接种率的随机离散SIR传染病模型的稳定性.首先,引入一个具有饱和发生率和疫苗接种率的确定性SIR模型,考虑到随机噪声对疾病传播有很大影响,应用非标准有限差分(NSFD)方法将模型离散化,最终得到一个随机离散的SIR传染病模型.这种离散方法是对系统的右侧进行局部离散,得出离散模型,然后系统左侧用广义前向差分法对一阶导数进行逼近,并且要选取恰当的分母函数.其次,应用Lyapunov函数和矩阵方法给出了系统平衡解稳定的充分条件,并且得到了非线性差分方程概率稳定的充分条件和线性差分方程渐近均方稳定的充分条件.最后,通过数值仿真对理论分析结论进行验证.

Robust stabilization of stochastic systems based on the LQ controller

The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.