Response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control

We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.     

Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints

The suboptimal reliable guaranteed cost control （RGCC） with multi-criterion constraints is investigated for a class of uncertain continuous-time systems with sensor faults. A fauk model in sensors, which considers outage or partial degradation of sensors, is adopted. The influence of the disturbance on the quadratic stability of the closed-loop systems is analyzed. The reliable state-feedback controller is developed by a linear matrix inequalities （LMIs） approach, to minimize the upper bound of a quadratic cost fimction under the conditions that all the closed-loop poles be placed in a specified disk, and that the prescribed level of H∞ disturbance attenuation and the upper bound constraints of control inputs＇ magnitudes be guaranteed. Thus, with the above muki-criterion constraints, the resulting closed-loop system can provide satisfactory stability, transient property, a disturbance rejection level and minimized quadratic cost performance despite possible sensor faults.     

两参数马氏过程，鞅及平稳过程之间的关系

本文给出了两参数随机过程均马氏过程的定义,证明了两参数马氏过程和鞅都是均马氏过程,但均马氏过程不一定是马氏过程也不一定是鞅．另外．本文还研究了两参数均马氏过程,马氏过程,鞅及平稳过程之间的关系．     

连续时间线性时不变系统的能控性判据研究

研究了连续时间线性时不变系统的能控性判据,给出格拉姆判据更精确的表达及证明.并给出秩判据及PBH判据的另外证明.     

Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input

This paper presents a sliding mode (SM) based identifier to deal with the parameter identification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier. Project supported by the National Natural Science Foundation of China(No. 69974035) and Zhejiang Provincial Natural Science Key Foundation of China (ZD9905)     

Regular-singular crossings on nonlinear systems with turning point

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具有转向点的非线性系统的奇异摄动

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Vibration response analysis of 2-DOF locally nonlinear systems based on the theory of modal superposition

1 Introduction ? Low frequency vibration has an important effect on body comfort and on the fatigue of a vibrating system. Nearly all actual vibrating systems are nonlinear. However, nonlinear behaviors are not always observed in the system dynamics. Thus…     

非线性广义系统的Lagrange稳定性

研究非线性广义系统的Lagrange稳定性问题.类似于正常非线性系统的Lagrange稳定性概念,给出非线性广义系统相应的Lagrange稳定性定义.利用K∞类函数和Dini导数,分别得到非线性广义系统Lagrange稳定、等度La-grange稳定或一致Lagrange稳定的充分条件.     

Passive control of a class of chaotic dynamical systems with nonlinear observer

A passive control strategy with nonlinear observer is proposed, which can be used to control a class of chaotic dynamical systems to stabilize at different equilibrium points. If the nonlinear function of chaotic system satisfies Lipschitz condition, the nonlinear observer can observe the state variables of the chaotic systems. An important property of passive system is studied to control chaotic systems, that is passive system can be asymptotically stabilized by state feedback controller whose state variables are presented by nonlinear observer. Simulation results indicated that the proposed chaos control method is very effective in a class of chaotic systems.     

非线性时滞动力系统的研究进展

现如今,随着我国经济的发展,各个工程的不断完善与壮大,在工程中所运用到的理论以及系统等要素也逐渐的丰富了起来。尤其是具有时滞的非线性动力系统,作为一个非常重要的元素,更是被广泛的运用到了许多的工程中去。随着其自身特点的变化以及我们研究范围、研究角度的变化,时滞动力系统也有其自身的演化趋势。时滞动力系统的演化趋势并不是独立、单一存在的。它既要依存于系统当前的状态,而且还要依存于系统过去某时刻的状态。其运动方程的描述方式要依靠泛函微分方程这样的方式来描述。因此,对非线性时滞动力系统进行研究有着重要的现实意义。本论文将围绕时滞动力系统的特点、研究方法等问题对非线性时滞动力系统的研究进展展开论述。     

Adaptive backstepping sliding mode control for nonlinear systems with input saturation

An adaptive backstepping sliding mode control is proposed for a class of uncertain nonlinear systems with input saturation.A command filtered approach is used to prevent input saturation from destroying the adaptive capabilities of neural networks (NNs).The control law and adaptive updating laws of NNs are derived in the sense of Lyapunov function,so the stability can be guaranteed even under the input saturation.The proposed control law is robust against the disturbance,and it can also eliminate the impact of input saturation.Simulation results indicate that the proposed controller has a good performance.     

Decomposing apparent power and losses in distribution systems with nonlinear loads

The definition of reactive power for non-sinusoidal conditions is a controversial issue. The mathematical treatment of nonlinear loads in power systems is also unsettled. This paper starts with the decomposing of apparent power in,the cases of linear and nonlinear loads. When harmonics are present, apparent power is composed of active power, reactive power, and disturbed reactive power. Linear element can be defined as the element without disturbed reactive power. This definition is based on a practical engineering concept which can separate the contribution from the apparent power into utility-duty part and custom-duty part. The field investigation of home-used facilities was conducted. Also the data acquisition in the 0.4 kV distribution systems was completed. Moreover, the loss increase due to the nonlinear loads was estimated. Nonlinear loads can be a dominant effect with respect to reactive power and power factor. Field data from a number of nonlinear load types indicate that the disturbed reactive power can cause significant losses in utility supply systems.     

Exact failure probability formula for strict consecutive-k-out-of-n:F systems with homogeneous Markov dependence

An exact formula is presented for calculating the failure probability of strict consecutive-k-out-of-n:F systems with homogeneous Markov dependence Project supported by the National Natural Science Foundation of China (19271084)     

一类带有非线性阻尼项的二阶周期系统的Lagrangian稳定性

用KAM迭代方法研究了下列二阶微分方程:(φP(x′))′+F(x,x′,f)+ωpφP(x′)+α∣x∣ ′+e(x,t)=0,其中,φP(s)=∣s ∣P-2s,p＞l,α＞0,ω＞0为正常数,f满足-1＜ω＜p +2.当F(x,x ′,t)与e(x,t)的导数满足一定条件时,利用可逆映射的小扭转定理得到拟周期解的...     

一类非线性系统的广义预测控制

对于时延的非线性系统,将其等价为含有纯滞后的时变线性系统,利用三次样条函数逼近时变参数,利用渐消记忆递推最小二乘法在线辨识多项式的参数以实现时变参数估计,将基于Hammerstein模型的非线性系统线性化.最后运用广义预测控制策略实现对该系统的仿真,结果表明被控对象在广义预测控制算法的控制下系统闭环稳定性好、稳态误差小.     

Proportional-integral-derivative control of nonlinear half-car electro-hydraulic suspension systems

This paper presents the development of a proportional-integral-derivative (PID)-based control method for application to active vehicle suspension systems (AVSS). This method uses an inner PID hydraulic actuator force control loop, in combination with an outer PID suspension travel control loop, to control a nonlinear half-car AVSS. Robustness to model uncertainty in the form of variation in suspension damping is tested, comparing performance of the AVSS with a passive vehicle suspension system (PVSS), with similar model parameters. Spectral analysis of suspension system model output data, obtained by performing a road input disturbance frequency sweep, provides frequency response plots for both nonlinear vehicle suspension systems and time domain vehicle responses to a sinusoidal road input disturbance on a smooth road. The results show the greater robustness of the AVSS over the PVSS to parametric uncertainty in the frequency and time domains.     

一类非线性系统的有限时间控制问题

讨论了一类带有动态不确定项的非线性系统的鲁棒有限时间控制问题.通过利用“加幂积分器”的方法构造出了一个部分状态反馈控制律，解决了这类不确定非线性系统的有限时间镇定问题.     

一类具有小扰动参数的非线性拟周期系统在平衡点附近的可约化性(英文)

考虑一类有重特征值的非线性拟周期系统在小扰动下平衡点附近的可约化性问题,也就是研究x=(A+εQ(t))x+εg(t)+h(x,t),其中A可以是具有重特征值的常数矩阵;h=O(x2)(x→0);h(x,t),Q(t)和g(t)关于t是解析拟周期的,且有相同的频率.在某些非共振条件及非退化条件下,对充分小的大多数ε,通过仿线性拟周期变换,系统可约化为具有平衡点的非线性拟周期系统.     

Robust adaptive controller design for a class of nonlinear systems with unknown high frequency gains

INTRODUCTIONMany researchers have devoted their energy to the development of nonlinear system with unknown control directions during the past few years. The class of nonlinear system has been developed greatly since Mudgett and Morse (1985) relaxed the assumption that the unknown multiplicative terms are not only sign-invariant but also have known signs. A method called correction vector approach was proposed in (Lozano et al., 1990) and has been applied to design adaptive controller of …