THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS

We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.     

一类混沌系统观测器

对Rssler系统、Chua系统等一类混沌系统讨论了混沌观测器的设计问题,对该类系统利用一个非线性标量信号实施反馈就可以使得观测器的状态变量与被观测系统的状态变量达到同步. 关键词： 混沌系统 状态观测器 同步     

CANONICAL FORMULATION OF NONHOLONOMIC CONSTRAINED SYSTEMS

Based on the Ehresmann connection theory and symplectic geometry, the canonical formulation of nonholonomic constrained mechanical systems is described. Following the Lagrangian formulation of the constrained system, the Hamiltonian formulation is given by Legendre transformation. The Poisson bracket defined by an anti-symmetric tensor does not satisfy the Jacobi identity for the nonintegrability of nonholonomic constraints. The constraint manifold can admit symplectic submanifold for some cases, in which the Lie algebraic structure exists.     

SYMMETRIES OF MECHANICAL SYSTEMS WITH NONLINEAR NONHOLONOMIC CONSTRAINTS

The dynamical symmetries and adjoint symmetries of nonlinear nonholonomic constrained mechanical systems are analysed in two kinds of geometrical frameworks whose evolution equations are Routh's equations and generalized Chaplygin's equations, respectively. The Lagrangian inverse problem and the interrelation between Noether's symmetries and dynamical symmetries are briefly concerned with. Finally an illustrative example is analysed.     

NOETHER'S THEOREM OF NONHOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS

In this paper, we present Noether's theorem and its inverse theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints. We present first the principle of Jourdain for the system and, on the basis of the invariance of the differential variational principle under the infinitesimal transformations of groups, we have established Noether's theory for the above systems. An example is given to illustrate the application of the result.     

包含伺服约束的非完整系统的Lie对称性与守恒量

利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式. 关键词： 非完整系统 伺服约束 Lie对称性 守恒量     

EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS

After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain.     

A NEW SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY CHAOTIC SYSTEMS

We propose a new sliding mode control scheme for a class of uncertain time-delay chaotic systems. It is shown that a linear time invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. A sliding mode controller is then designed to drive the output of the time-delay chaotic system to track the desired linear system. On the sliding mode, the output of the controlled time-delay chaotic system can behave like the desired linear system. A simulation example is given in support of the proposed control scheme.     

半导体激光系统的特殊设计

根据半导体激光器远场光束呈椭圆斑,输出功率、光谱特性、寿命、温度以及输出具有偏振性等光学特性,本文讨论了半导体激光系统的特殊设计问题。着重研讨半导体激光器输出功率的稳定,椭圆光束的准直和整圆等。     

混沌Lur’e系统的线性输出反馈同步

针对一类特殊的混沌Lur’e系统,以系统最后一状态变量作为驱动信号进行误差的线性输出反馈,提出一个同步的全局控制规律,并证明了同步的渐近稳定性.最后以蔡氏振子为例进行仿真,验证该同步方法的有效性. 关键词： 混沌同步 输出反馈 Lur’e系统 蔡氏振子     

A STOCHASTIC NEWMARK METHOD FOR ENGINEERING DYNAMICAL SYSTEMS

The purpose of this study is to develop a stochastic Newmark integration principle based on an implicit stochastic Taylor (Ito-Taylor or Stratonovich-Taylor) expansion of the vector field. As in the deterministic case, implicitness in stochastic Taylor expansions for the displacement and velocity vectors is achieved by introducing a couple of non-unique integration parameters, α and β. A rigorous error analysis is performed to put bounds on the local and global errors in computing displacements and velocities. The stochastic Newmark method is elegantly adaptable for obtaining strong sample-path solutions of linear and non-linear multi-degree-of freedom (m.d.o.f.) stochastic engineering systems with continuous and Lipschitz-bounded vector fields under (filtered) white-noise inputs. The method has presently been numerically illustrated, to a limited extent, for sample-path integration of a hardening Duffing oscillator under additive and multiplicative white-noise excitations. The results are indicative of consistency, convergence and stochastic numerical stability of the stochastic Newmark method (SNM).     

SYNCHRONIZATION FOR A CLASS OF CHAOTIC SYSTEMS BASED UPON OBSERVER THEORY

A new synchronization theorem for a class of chaotic systems is presented based on nonlinear observer theory. We take the first state variable of the drive system as the driving scalar signal. Its linear feedback gain is a function of a free parameter. It is proven that global synchronization can be attained through simple linear output error feedback. This approach is illustrated by the WGY hyperchaotic system and Chua's oscillator.     

一类含参数不确定性混沌系统的自适应控制

基于Lyaponov函数,对一类含参数不确定性混沌系统,当系统的不确定性参数具有未知界时,给出了自适应控制器的设计方法和构造控制器的解析式.构造混沌控制器直接代入控制器的参数化公式即可.方法简单,无需拼凑,能够使系统消除混沌并渐近稳定到任何期望的光滑轨道上.而整个设计过程无需预先知道未知参数的估计值和精确值.仿真验证了其有效性 关键词： 混沌系统 自适应混沌控制 Lyaponov函数 参数不确定性     

一类时滞竞争系统的定性分析

本文考虑具有连续时滞的Lotka-Volterra竞争系统。给出了该系统的稳定性分析。利用Hopf分支定理,我们证明了由时滞引起的不稳定性可以导致系统产生稳定的极限环。利用Birkhoff定理证明了系统可能出现循环解。最后,我们给出数值实例,验证了上述结果。     

求解一阶电路对任意信号响应的一种方法

提出一种求解任意信号作用下的一阶电路响应的方法．利用三要素法求其阶跃响应和零输入响应，再利用卷积得出结果．方法简洁方便．     

GENERAL SOLUTIONS OF A CLASS OF DISSIPATIVE SYSTEMS AND THEIR APPLICATIONS

General solutions are obtained for a class of quantum dissipative systems. This is achieved by calculating the characteristic function in the Heisenberg picture. The irreversible behavior of these systems is nalyzed. The general formalism is applied to some typical examples and the influence of noise on these systems is gained.     

SENSITIVITY ANALYSIS AS A METHOD OF ABSORBER TUNING FOR REDUCTION OF STEADY STATE RESPONSE OF LINEAR PARAMETRIC SYSTEMS

The aim of this paper is to determine whether one dynamic absorber can reduce the amplitude of the steady state vibration of a parametric system for natural and parametric resonance frequencies simultaneously. The efficiency of both the conventional dynamic absorber and the parametric absorber is analyzed. The first order sensitivity analysis of parametric periodic systems in the time domain is applied to obtain logarithmic sensitivity functions in the frequency domain. The first order sensitivity logarithmic functions are used to tune the conventional absorber and the parametric absorber.     

A MECHANISM FOR ENERGY TRANSFER IN MECHANICAL SYSTEMS

We propose a general mechanism for the transfer of energy within and between mechanical systems. The proposal is borne out by the analytical solution of a model system.     

用直接模拟法分析量子阱半导体激光器瞬态响应

根据光增益与载流子密度的对数关系 ,通过适应于多量子阱激光器的速率方程的直接模拟分析 ,得到了注入电流、阱数和腔长对多量子阱激光器的激射阈值、开关延迟时间、弛豫振荡频率和光输出等参量之间的依赖关系 .运用相图确立了在瞬态过程中 ,载流子数密度和光子数密度之间的转化过程 .从而为改善量子阱激光器的高频调制特性以及优化设计器件结构参数提供了理论依据     

用直接模拟法分析量子阱半导体激光器瞬态响应

根据光增益与载流子密度的对数关系,通过适应于多量子阱激光器的速率方程的直接模拟分析,得到了注入电流、阱数和腔长对多量子阱激光器的激射阈值、开关延迟时间、弛豫振荡频率和光输出等参量之间的依赖关系.运用相图确立了在瞬态过程中,载流子数密度和光子数密度之间的转化过程.从而为改善量子阱激光器的高频调制特性以及优化设计器件结构参数提供了理论依据.