逐步加速交通流模型的渐近稳态行为

提出一种新的一维交通流元胞自动机模型，该模型采用NS模型中的车辆逐步有限加速方式和FI模型中的仅最大速车辆可随机慢化的方式．证明了新模型的基本图平均场方程，即渐近稳态中车辆平均速度＜V（t→∞）＞与车辆密度ρ之间的函数关系，与一般FI模型完全相同．这说明：在车辆随机延迟方式确定后，交通流渐迈德态的行为并不依赖于车辆的加速方式．不管是逐步有限加速方式（如NS模型），还是在同一个时步内从零直接增加到速限或前方间距所允许的最大速度的突然加速方式（如FI模型），车辆之间的自组织相互作用将产生完全相同的渐近稳态行为．

Stability of second order Hopfield neural networks with time delays

Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.

Lurie系统的输出反馈H_∞滑模控制

研究了不确定Lurie系统的输出反馈滑模控制与Lurie系统的输出反馈H∞滑模控制问题,并证明了设计的切换面的可达性,基于Lyapunov稳定性理论给出了系统渐稳的充分条件.

一类不确定Lurie系统的输出反馈H_∞滑模控制问题

研究了一类不确定Lurie系统的输出反馈H∞滑模控制问题,并证明了设计的切换面的可达性,基于Lyapunov稳定性理论给出了系统渐稳的充分条件.

决定论性逐步加速交通流模型的渐近稳态行为

研究ＮａｇｅｌＳｃｈｒｅｃｋｅｎｂｅｒｇ（ＮＳ）交通流元胞自动机模型在不考虑车辆随机延迟情况下的决定论性模型的基本图，即渐近稳态的车流平均速度作为车辆密度的函数关系．证明决定论性ＮＳ模型，在车流的自组织作用下，其渐近稳态的基本图，与决定论性ＦｕｋｕｉＩｓｈｉｂａｓｈｉ（ＦＩ）交通流模型的基本图完全相同．这个结果表明，若把ＦＩ交通流模型中的车辆突然加速方式（即车辆速度可以在仅仅一个时步内加速到其最高速限Ｍ或前方空距所允许的最大速度），改变为车辆逐步加速方式（车辆速度在每一时步中最多仅能增加一个速度单位），则车辆的自组织相互作用，并不会改变其车流的长时间渐近稳态行为．

Robust adaptive dynamic surface control for nonlinear uncertain systems

We propose a new method for robust adaptive backstepping control of nonlinear systems with parametric uncertainties and disturbances in the strict feedback form. The method is called dynamic surface control. Traditional backstepping algorithms require repeated differentiations of the modelled nonlinearities. The addition of n first order low pass filters allows the algorithm to be implemented without differentiating any model nonlinearities, thus ending the complexity arising due to the 'explosion of terms' that makes other methods difficult to implement in practice. The combined robust adaptive backstepping/first order filter system is proved to be semiglobally asymptotically stable for sufficiently fast filters by a singular perturbation approach. The simulation results demonstrate the feasibility and effectiveness of the controller designed by the method.

Asymptotic Stability in the Large of Zero Solution of Second Order Nonlinear Differential Equation

There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.

Stability of Difference Systems with Finite Delay

In this paper, the authors establish some theorems that can ascertain the zero solutions of systemsx(n+1)=f(n,x n)(1)are uniformly stable,asymptotically stable or uniformly asymptotically stable. In the obtained theorems, ΔV is not required to be always negative, where ΔV(n,x n)≡V(n+1,x(n+1)) -V(n,x(n))=V(n+1,f(n,x n))-V(n,x(n)), especially, in Theorem 1, ΔV may be even positive, which greatly improve the known results and are more convenient to use.

Note on a diffusive ratio-dependent predator-prey model

Subject to the homogeneous Neumann boundary condition, a ratio-dependent predator-prey reaction diffusion model is discussed. An improved result for the model is derived, that is, the unique positive constant steady state is the global stability. This is done using the comparison principle and establishing iteration schemes involving positive solutions supremum and infimum. The result indicates that the two species will ultimately distribute homogeneously in space. In fact, the comparison argument and iteration technique to be used in this paper can be applied to some other models. This method deals with the not-existence of a non-constant positive steady state for some reaction diffusion systems, which is rather simple but sufficiently effective.

The Asymptotic Stability for a Class of Nonlinear Large Sceale System

This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.

Analysis of an Epidemic Model with Age of Vaccination

A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.

Dynamic Behavior of a Predator-prey System with Stage-structure for Prey

In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.

Adaptive friction compensation for large diameter electro-hydraulic proportional valve cores based on LuGre

This paper presents an adaptive friction compensation method based on LuGre model for large diameter electric-hydraulic proportional valves in which the valve core contains friction.A mathematic model of the electric-hydraulic proportional valve is established,and the friction characteristics are described based on the LuGre model.The global asymptotic stability of the control system with the adaptive friction compensation controller is guaranteed over Lyapunov theorem.The adaptive compensation of the friction on LuGre friction model is verified by simulation and experiment.The steady-state error is about [-4.23 × 10^(-5)m,5.91 × 10^(-5)m]and[-2.5 × 10^(-4)m,2.6 ×10^(-4) m] on simulation and experiment,the position tracking accuracy is higher,and the lag time of the main valve through the dead zone is shorter.The result proves that the adaptive friction compensation method can effectively compensate for the negative effects of nonlinear friction.

On Stability of Solutions of a Certain Fourth-Order Functional Differential Equations

Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptotic stability of the zero solution of a certain fourth order functional differential equations.The result generalizes the well known results.

Permanence and Periodic Solution of an Impulsive Delay Two-prey One-predator System with Variable Coefficients

two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.

Adaptive output feedback control for uncertain nonholonomic chained systems

An adaptive output feedback control was proposed to deal with a class of nonholonomic systems in chained form with strong nonlinear disturbances and drift terms. The objective was to design adaptive nonlinear output feedback laws such that the closed-loop systems were globally asymptotically stable, while the estimated parameters remained bounded. The proposed systematic strategy combined input-state-scaling with backstepping technique. The adaptive output feedback controller was designed for a general case of uncertain chained system. Furthermore, one special case was considered. Simulation results demonstrate the effectiveness of the proposed controllers.

Adaptive trajectory tracking control of two-wheeled self-balance robot

Wheeled mobile robot is one of the well-known nonholonomic systems. A two-wheeled sell-balance robot is taken as the research objective. This paper carried out a detailed force analysis of the robot and established a non-linear dynamics model. An adaptive tracking controller for the kinematic model of a nonhotonomic mobile robot with unknown parameters is also proposed. Using control Lyapunov function （CLF）, the controller＇s global asymptotic stability has been proven. The adaptive trajectory tracking controller decreases the disturbance in the course of tracking control and enhances the real-time control characteristics. The simulation result indicated that the wheeled mobile robot tracking can be effectively controlled.

Interval standard neural network models for nonlinear systems

A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.

Global Asymptotic Stability for a Class of Nonlinear Populations Model

This paper discussed the stability of model of an age structured population systems,proved that the equilibrium solution systems is globally asymptotically stable.

Stability of Second Order Differential Equation Disturbed with Delays

In this paper, stability problems for the second order nonlinear differential equations disturbed with delays are studied. By means of the new stability theorems and Liapunov functional, the authors obtain some results of the zero solution of the equations, some well-known results are extended.