Razumikhin-Type Theorems on p-th Moment Stability for Stochastic Switching Nonlinear Systems with Delay

This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumik- hin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the results.

Solution of the Nucleon Structure Problem from a Field Theory of Fermions and Bosons and the Origin of the Proton Stability

A bound state formalism derived from a fermion-boson symmetric Lagrangian has been used to calculate the nucleon masses, the charge neutrality of the neutron, the magnetic moments and the electromagnetic form factor ratios μpGEp/GMpand μnGEn/GMn. A quantitative description is obtained, assuming a mixing of a scalar bound state of 3(f f¯)fstructure with its corresponding vector (f f¯)fstate (f indicating massless elementary fermions). Only a few parameters are needed, mainly fixed by energy and momentum conservation. The nucleon stability is explained by an extra binding in the confinement potential, negative for electric and positive for magnetic binding of the proton, and opposite for the neutron. The stronger electric extra binding of the proton allows a decay of the neutron to proton and electron.

pth-Moment Stabilization of Hybrid Stochastic Differential Equations by Discrete-Time Feedback Control

The given unstable hybrid stochastic differential equation is stabilized in the sense of p th-moment exponential stability.We achieve the results by feedback controls based on the discrete-time state and mode observations.The upper bound on the duration between two consecutive observations is obtained as well.Finally,a numerical example is given to verify the validity of the theoretical conclusions.

Moment stability for a predator–prey model with parametric dichotomous noises

In this paper, we investigate the solution moment stability for a Harrison-type predator-prey model with parametric dichotomous noises. Using the Shapiro-Loginov formula, the equations for the first-order and second-order moments are obtained and the corresponding stable conditions are given. It is found that the solution moment stability depends on the noise intensity and correlation time of noise. The first-order and second-order moments become unstable with the decrease of correlation time. That is, the dichotomous noise can improve the solution moment stability with respect to Gaussian white noise. Finally, some numerical results are presented to verify the theoretical analyses.

Asymptotical p-moment stability of stochastic impulsive differential system and its application to chaos synchronization

In this paper, the asymptotical p-moment stability of stochastic impulsive differential equations is studied and a comparison theory to ensure the asymptotical p-moment stability of the trivial solution is established, which is important for studying the impulsive control and synchronization in stochastic systems. As an application of this theory, we study the problem of chaos synchronization in the Chen system excited by parameter white-noise excitation, by using the impulsive method. Numerical simulations verify the feasibility of this method.

p-Moment Stability of Nonlinear Stochastic Difference Equations

In the paper, nonlinear ordinary stochastic difference equations are first studied. Then a few of sufficient conditions on (uniform, uniform and asymptotic, uniformly asymptotic) p-moment stability of these equations are established by Liapunov function.

Razumikhin-Type Theorems on General Decay Stability of Impulsive Stochastic Functional Differential Systems with Markovian Switching

In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.

Four Wheel Independent Drive Electric Vehicle Lateral Stability Control Strategy

In this paper,a kind of lateral stability control strategy is put forward about the four wheel independent drive electric vehicle.The design of control system adopts hierarchical structure.Unlike the previous control strategy,this paper introduces a method which is the combination of sliding mode control and optimal allocation algorithm.According to the driver’s operation commands(steering angle and speed),the steady state responses of the sideslip angle and yaw rate are obtained.Based on this,the reference model is built.Upper controller adopts the sliding mode control principle to obtain the desired yawing moment demand.Lower controller is designed to satisfy the desired yawing moment demand by optimal allocation of the tire longitudinal forces.Firstly,the optimization goal is built to minimize the actuator cost.Secondly,the weighted least-square method is used to design the tire longitudinal forces optimization distribution strategy under the constraint conditions of actuator and the friction oval.Beyond that,when the optimal allocation algorithm is not applied,a method of axial load ratio distribution is adopted.Finally,Car Sim associated with Simulink simulation experiments are designed under the conditions of different velocities and different pavements.The simulation results show that the control strategy designed in this paper has a good following effect comparing with the reference model and the sideslip angle is controlled within a small rang at the same time.Beyond that,based on the optimal distribution mode,the electromagnetic torque phase of each wheel can follow the trend of the vertical force of the tire,which shows the effectiveness of the optimal distribution algorithm.

Underactuated spacecraft angular velocity stabilization and three-axis attitude stabilization using two single gimbal control moment gyros

Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.

Stability of a delayed predator prey model in a random environment

The stability of the first-order and second-order solution moments for a Harrison-type predator-prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Ito interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.

Dynamic stability of quadruped robot walking on slope with trot gait

The dynamic stability of a quadruped robot trotting on slope was analyzed.Compared with crawl gait,trot gait can improve walking speed of quadruped robots.When a quadruped robot trots,each leg is in the alternate state of swing phase or supporting phase,and two legs in the diagonal line are in the same phase.The feet in the supporting phase form a supporting region on the ground.When a quadruped robot walks on slope,the vertical distance from zero moment point(ZMP) to the supporting diagonal line is defined as ZMP offset distance.Whether this distance is less than the maximum offset distance or not,the stability of robot trotting on slope can be judged.The foot trajectory was planned with the sinusoidal function.Based on the kinematic analysis,the ZMP offset distance of quadruped robot under different slope angles,step length and step height was calculated,then the reasonable slope angle,step length and step height for quadruped robot trotting on slope to keep dynamic stability can be determined.On the other hand,the posture angle of quadruped robot should be controlled within the desired range.Computer simulations were executed to verify the theoretical analysis.The study will provide reference for determining reasonable step parameters of the quadruped robot.

Map-based control method for vehicle stability enhancement

This work proposes a map-based control method to improve a vehicle's lateral stability, and the performance of the proposed method is compared with that of the conventional model-referenced control method. Model-referenced control uses the sliding mode method to determine the compensated yaw moment; in contrast, the proposed map-based control uses the compensated yaw moment map acquired by vehicle stability analysis. The vehicle stability region is calculated by a topological method based on the trajectory reversal method. A 2-DOF vehicle model and Pacejka's tire model are used to evaluate the proposed map-based control method. The properties of model-referenced control and map-based control are compared under various road conditions and driving inputs. Model-referenced control uses a control input to satisfy the linear reference model, and it generates unnecessary tire lateral forces that may lead to worse performance than an uncontrolled vehicle with step steering input on a road with a low friction coefficient. However, map-based control determines a compensated yaw moment to maintain the vehicle within the stability region,so the typical responses of vehicle enable to converge rapidly. The simulation results with sine and step steering show that map-based control provides better the tracking responsibility and control performance than model-referenced control.

Stability Analysis for Projectile with Wrap-Around Fins

Based on the stability theory, numerical simulations and theoretical calculations are performed for a projectile with wrap-around fins. Its stability is analyzed and the flow field is simulated with computational fluid dynamics method. Consequently, the pitching moment coefficient of the projectile is further investigated under the conditions of Mach number ranging from 0.3 to 0.8, attack angle from 0 to 8° and yaw angle from 0 to 4°. A trajectory equation is established and its trajectory characteristics are also explored. All the results of theoretical analysis, numerical simulation and trajectory equation agree well with each other, which indicates the projectile is flying steadily at the given conditions. These results provide an effective way for judging the stability of the projectile with wrap-around fins.

Stability of Neutral Stochastic Differential Equations with Multiple Variable Delays

This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of φ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.

Global Solutions and Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay

This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.

A multi-index coupling system of ice slope stability and its application

Based on the Simplified Bishop Method, the minimum safety factor of ice slope both with and without tension cracks is calculated in combination with triaxial compression tests. It is found that there exists a critical depth for each crack. Then, factors influencing ice slope stability such as slope ratio, slope height, ice cohesion, internal friction angle, unit weight and temperature were analyzed. Meanwhile, a regression equation between the aforementioned factors and safety factor is obtained, with which sensitivity analysis is carried out. The performance function is built in combination with random distribution of physical and mechanical parameters to analyze the reliability index. The Advanced First Order Second Moment Method is employed on the solution to the perfor- mance function. The one-way coupling system of ice slope stability is therefore formed based on safety factor and reliability index. Finally, an illustrated example of ice slope is provided, which shows that failure probability is relatively high, up to 6.18%, alt- hough safety factor is 2.77. Thus, it is objective and reasonable to apply the coupled system method to the slope stability rating.

Influence of Non-uniform Elevated Temperature on the Structural Stability and Strength of Gypsum-Sheathed Cold-Formed Steel Beam Channel Members

The objective of this paper is to computationally explore the structural stability and strength of gypsum-protected CFS(cold-formed steel)beam channel sections under non-uniform elevated temperatures when exposed to standard fire on one side of the panel and subjected to pure bending.When a CFS member is subjected to fire(or thermal gradients)its material properties change-but this change happens around the cross-section and along the length creating a member which is potentially non-uniform and unsymmetrical in its response even if the apparent geometry is uniform and symmetric.Computational finite element models were analyzed in ABAQUS to establish steady-state thermal gradients of interest.Existing test data were utilized to develop the temperature dependence of the stress-strain response.The time-dependent temperature distribution on the cross-sections obtained from heat transfer analysis was later used in the stability and collapse analyses.The stability of the models was explored to characterize how local,distortional,and global buckling of the member evolves under both uniform and non-uniform temperature distributions.Finally,collapse simulations were performed to characterize the strength under pure bending and explore directly the evolution of strength under the influence of non-uniform temperature.

面向光伏电站除尘作业的移动机械臂抗倾覆稳定性研究

对光伏电站移动机械臂倾覆稳定性的研究是其安全、高效作业的前提。采用重力法分析移动机械臂在水平路面和倾斜路面的静态稳定性,以倾覆力矩为标识对移动平台与机械臂耦合状态下的稳定性进行分析,并利用Matlab和Adams仿真验证移动机械臂的稳定性,结果表明移动机械臂在水平路面上进行作业运动时处于稳定状态;通过分析移动机械臂在倾斜路面上的稳定性,确定其可安全操作的最大路面倾斜角度。

鸭舵转速对双旋弹追随稳定性影响研究

发展了适合双旋弹虚拟飞行仿真的高保真计算流体力学和刚体动力学耦合平台,以此为基础研究了旋转鸭舵对双旋弹弹道追随稳定性的影响。为了准确刻画双旋弹前后体的差动旋转效应,将滑移网格算法引入自研非结构混合网格流场数值模拟程序HUND3D。通过对双旋弹进行定轴转动非定常模拟,考察了不同鸭舵转速下双旋弹的流动特征与气动特性。通过耦合求解非定常雷诺平均NS方程和七自由度刚体动力学方程,实现了双旋弹不同弯度弹道的虚拟飞行仿真,分析了弹道追随过程的动力学机理,并结合气动特性分析结果研究了控制鸭舵转速改善弹道追随稳定性的策略。研究结果表明:鸭舵旋转所产生的气动干扰,能够显著影响弹体的侧向力与偏航力矩。通过控制前体鸭舵转速以产生有利于弹道追随的偏航力矩,能够在一定程度上改善弹道追随稳定性。

中国南海神狐海域水合物储层井壁稳定可靠度分析

天然气水合物具有巨大的潜在经济和环境价值,其开发利用对国家能源安全和实现国家碳达峰碳中和的“双碳目标”具有战略意义。我国天然气水合物资源主要分布于南海海域,海洋环境的复杂性和隐蔽性使工程测量数据具有较大不确定性,影响钻井安全。目前未见有水合物储层井壁稳定可靠度研究。为定量评估在我国南海神狐海域水合物储层钻井风险,基于水合物储层钻井井壁稳定解析理论和南海神狐海域具体地质条件,结合可靠度分析方法中的改进一次二阶矩法和响应面法,研究南海神狐海域水合物储层钻井井壁失稳概率分布特征,分析该海域井壁失稳概率及安全钻井液压力窗口对主要参数均值和不确定性的敏感性,结果表明:(1)若测量数据足够精确,在我国南海神狐海域水合物储层进行钻井活动的安全性较高,安全钻井液压力窗口也较大。测量数据的不确定性增大将使井壁失稳概率显著升高,缩窄安全钻井液压力窗口。(2)较低的钻井液温度对降低井壁失稳概率略有帮助,且能明显地扩大安全钻井液压力窗口。(3)5个主要参数的均值和不确定性对井壁失稳概率的影响次序相同,均为初始地应力>初始内摩擦角>弹性模量比>初始黏聚力>初始弹性模量。实际工程中对初始地应力数据精确测量,能够显著提高水合物储层钻井井壁稳定性。