具时滞反馈非线性系统差分系统的稳定周期解(英文)

本文考虑一类具McCulloch pitts型信号函数的描述两个相同神经元动力作用的时滞差分系统 .所得结论推广了文 [2 ]的相应结果 ,同时对参数 (β ,σ)的某些范围得到了一个渐近稳定的 2k + 1周期解 .

一种非线性系统差的样条约束EMBET方法

在靶场弹道解算和卫星轨道解算中,通过样条约束的EMBET方法对测元的系统误差的估计,大大提高了测量系统的解算精度.针对EMBET方法中通常只能估计常数、线性系统差的问题,提出了使用B样条描述非线性系统差,并可采用Gauss-Newton迭代方法对参数进行求解.经仿真验证,此方法可以较为准确地估计非线性系统差、线性系统差,适用于系统差函数不易描述的情形.

带有时滞的非线性随机差分系统的均方指数稳定性

针对具有时变时滞的非线性随机差分系统,通过非负矩阵的比较原理和谱性质,提出了解的均方指数稳定性的判别准则和时滞无关的稳定性判据、时滞相关的稳定性判据,讨论并举例说明了理论结果的有效性。

具有连续变量非线性差分系统的稳定及振动性

以微积分为工具讨论了具有连续变量的非线性差分系统的稳定性和振动性，给出了系统稳定的新判据和系统振动的充分必要条件及线性系统存在非振动解的充分必要条件。

非线性差分系统稳定性概述

随着工程理论的发展 ,在控制系统中 ,稳定性非常重要。人们对近期发展起来的非线性差分系统稳定性进行了大量的研究。介绍了有关非线性差分系统稳定性的近期研究情况 ,并总结了一些判定非线性差分系统稳定性的重要方法 。

周期系数非线性差分系统的稳定性

本文讨论了周期系数非线性差分系统的稳定性 ,在文 [1 ]的基础上得到判定系统解的稳定性的充分条件 ,推广了文 [1

非线性二阶差分系统周期解的多重性

变分方法是研究非线性差分方程周期解存在性的一种新的并且行之有效的方法.运用乘积空间上的环绕定理[1]证明二阶非线性差分系统{-Δ2un-1=μ1uαn1+f1(n,un)+λh1(n,un,vn),n∈M-Δ2vn-1=μ2vαn2+f2(n,vn)+λh2(n,un,vn),n∈M其中αi∈(0,1),i=1,2,至少存在3个非平凡的周期解.

离散等级种群系统的能控性与最优控制

建立具有离散个体等级差异的种群模型,它是一类高维非线性差分方程组.证明了系统的近似能控性;分析了种群资源的最优收获策略,对几种特殊情形获得了最优策略的具体形式,并用数值方法考察了参数变化对最优策略及最优收益的影响.

Robust adaptive control for a class of uncertain non-affine nonlinear systems using neural state feedback compensation

A robust adaptive control is proposed for a class of uncertain nonlinear non-affine SISO systems. In order to approximate the unknown nonlinear function, an affine type neural network(ATNN) and neural state feedback compensation are used, and then to compensate the approximation error and external disturbance, a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proven that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method. Finally, two simulation examples show that the proposed method exhibits strong robustness, fast response and small tracking error, even for the non-affine nonlinear system with external disturbance, which confirms the effectiveness of the proposed approach.

Multi-sensor federated unscented Kalman filtering algorithm in intermittent observations

Aiming at the adverse effect caused by limited detecting probability of sensors on filtering preci- sion of a nonlinear system state, a novel muhi-sensor federated unscented Kalman filtering algorithm is proposed. Firstly, combined with the residual detection strategy, effective observations are cor- rectly identified. Secondly, according to the missing characteristic of observations and the structural feature of unscented Kalman filter, the iterative process of the single-sensor unscented Kalman filter in intermittent observations is given. The key idea is that the state estimation and its error covariance matrix are replaced by the state one-step prediction and its error covariance matrix, when the phe- nomenon of observations missing occurs. Finally, based on the realization mechanism of federated filter, a new fusion framework of state estimation from each local node is designed. And the filtering precision of system state is improved further by the effective management of observations missing and the rational utilization of redundancy and complementary information among multi-sensor observa- tions. The theory analysis and simulation results show the feasibility and effectiveness of the pro- posed algorithm.

Gross Error Detection and Identification Based on Parameter Estimation for Dynamic Systems

The detection and identification of gross errors, especially measurement bias, plays a vital role in data reconciliation for nonlinear dynamic systems. Although parameter estimation method has been proved to be a pow-erful tool for bias identification, without a reliable and efficient bias detection strategy, the method is limited in ef-ficiency and cannot be applied widely. In this paper, a new bias detection strategy is constructed to detect the pres-ence of measurement bias and its occurrence time. With the help of this strategy, the number of parameters to be es-timated is greatly reduced, and sequential detections and iterations are also avoided. In addition, the number of de-cision variables of the optimization model is reduced, through which the influence of the parameters estimated is reduced. By incorporating the strategy into the parameter estimation model, a new methodology named IPEBD (Improved Parameter Estimation method with Bias Detection strategy) is constructed. Simulation studies on a con-tinuous stirred tank reactor (CSTR) and the Tennessee Eastman (TE) problem show that IPEBD is efficient for eliminating random errors, measurement biases and outliers contained in dynamic process data.

Nonlinear Control of Magnetic Bearings

In this paper, recent results controling nonlinear systems with output tracking error constmints are applied to the design of new tracking controllers for magnetic bearings. The proposed controllers can force the rotor to track a bounded and sufficiently smooth reference trajectory asymptotically and guarantee non-contactedness betweea the rotor and the stator of the magnetic beadngs. Simulation results are included to illustrate the effectiveness of the propsed controllers.

The Almost Exponential Asymptotic Stability of a Type Nonlinear Differential Difference System

A type nonlinear differential difference system ·↑x(i)(t)=n↑∑↑j=1[αijfij(xj(t))+bijgij(xj(t-τj))](i=1,2,…,n) is studied.We give some theorems which decide the almost exponential asymptotic stability of the zero so-lution.

Control of Nonlinear Systems with Output Tracking Error Constraints

A oanstructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficient smooth reference trajectory asymptotically. Under suitable condition with the initial output tracking error, the proposed controllers guarantee the output tracking error within a symmtric or an asymmetric pre-specified limit range, and boundedness of all signals of the closed loop system. A transformation is inmxuced to take care of the output tracking error constraint. Smooth and/or p -times differentiable step functions are propsed and incor- porated in the output tracking error transformation to overcome difficulties due to the asynxnetric limit range on the output tracking error. As a result, there are no switchings in the proposed controllers despite of the asymmnetric limit range.

Solving position-posture deviation problem of multi-legged walking robots with semi-round rigid feet by closed-loop control

The semi-round rigid feet would cause position-posture deviation problem because the actual foothold position is hardly known due to the rolling effect of the semi-round rigid feet during the robot walking. The position-posture deviation problem may harm to the stability and the harmony of the robot, or even makes the robot tip over and fail to walk forward. Focused on the position-posture deviation problem of multi-legged walking robots with semi-round rigid feet, a new method of position-posture closed-loop control is proposed to solve the position-posture deviation problem caused by semi-round rigid feet, based on the inverse velocity kinematics of the multi-legged walking robots. The position-posture closed-loop control is divided into two parts: the position closed-loop control and the posture closed-loop control. Thus, the position-posture control for the robot which is a tight coupling and nonlinear system is decoupled. Co-simulations of position-posture open-loop control and position-posture closed-loop control by MATLAB and ADAMS are implemented, respectively. The co-simulation results verify that the position-posture closed-loop control performs well in solving the position-posture deviation problem caused by semi-round rigid feet.

Fuzzy Modeling, Tracking Control and Synchronization of the Rossler's Chaotic System

In this paper, a novel method to model, track control and synchronize the Rossler’s chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coefficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler’s system is used in this paper. We represent the Rossler’s chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.

改进的微分-差分特征列方法

基于高小山,J.Van der Hoeven等人2009年提出的微分-差分(DD)特征列方法理论,针对微分-差分系统的一些特性,在原有理论方法的基础上进行改进与补充,对升列,导元,约化等概念重新定义.提出了一则新算法(Seesaw),用来对多项式系统中的变量的类重新确定,目的是为在比较升列序的过程中重新对变量排序,在实际计算中可以降低系统求解的难度.另外对DD-伪余算法也进行了改进.

Information theory in nonlinear error growth dynamics and its application to predictability:Taking the Lorenz system as an example

In nonlinear error growth dynamics,the initial error cannot be accurately determined,and the forecast error,which is also uncertain,can be considered to be a random variable.Entropy in information theory is a natural measure of the uncertainty of a random variable associated with a probability distribution.This paper effectively combines statistical information theory and nonlinear error growth dynamics,and introduces some fundamental concepts of entropy in information theory for nonlinear error growth dynamics.Entropy based on nonlinear error can be divided into time entropy and space entropy,which are used to estimate the predictabilities of the whole dynamical system and each of its variables.This is not only applicable for investigating the dependence between any two variables of a multivariable system,but also for measuring the influence of each variable on the predictability of the whole system.Taking the Lorenz system as an example,the entropy of nonlinear error is applied to estimate predictability.The time and space entropies are used to investigate the spatial distribution of predictability of the whole Lorenz system.The results show that when moving around two chaotic attractors or near the edge of system space,a Lorenz system with lower sensitivity to the initial field behaves with higher predictability and a longer predictability limit.The example analysis of predictability of the Lorenz system demonstrates that the predictability estimated by the entropy of nonlinear error is feasible and effective,especially for estimation of predictability of the whole system.This provides a theoretical foundation for further work in estimating real atmospheric multivariable joint predictability.

Estimation of atmospheric predictability for multivariable system using information theory in nonlinear error growth dynamics

To estimate atmospheric predictability for multivariable system, based on information theory in nonlinear error growth dynamics, a quantitative method is introduced in this paper using multivariable joint predictability limit(MJPL) and corresponding single variable predictability limit(SVPL). The predictability limit, obtained from the evolutions of nonlinear error entropy and climatological state entropy, is not only used to measure the predictability of dynamical system with the constant climatological state entropy, but also appropriate to the case of climatological state entropy changed with time. With the help of daily NCEP-NCAR reanalysis data, by using a method of local dynamical analog, the nonlinear error entropy, climatological state entropy, and predictability limit are obtained, and the SVPLs and MJPL of the winter 500-hPa temperature field, zonal wind field and meridional wind field are also investigated. The results show that atmospheric predictability is well associated with the analytical variable. For single variable predictability, there exists a big difference for the three variables, with the higher predictability found for the temperature field and zonal wind field and the lower predictability for the meridional wind field. As seen from their spatial distributions, the SVPLs of the three variables appear to have a property of zonal distribution, especially for the meridional wind field, which has three zonal belts with low predictability and four zonal belts with high predictability. For multivariable joint predictability, the MJPL of multivariable system with the three variables is not a simple mean or linear combination of its SVPLs. It presents an obvious regional difference characteristic. Different regions have different results. In some regions, the MJPL is among its SVPLs. However, in other regions, the MJPL is less than its all SVPLs.

Hadamard precoding for PAPR reduction in optical direct detection OFDM systems

The high peak-to-average power ration (PAPR) values of optical orthogond frequency division multiplexing (OFDM) signal limit the system nonlinear tolerance (NLT). In this paper, a novel method based on Hadamard precoding is proposed to reduce the peak-to-average power ratio in optical direct detection OFDM system. The proposed scheme is successfully applied to an experimental system of optical direct-detection OFDM signal transmission through fiber. In this experiment, the 2.5 Gbit/s binary phase shift keying (BPSK) optical OFDM signals with Hadamard precoding are generated and transmitted though a single mode fiber. The experimental results show that the proposed scheme can reduce PAPR by almost 1.5 dB. Meantime the received sensitivity is improved by 2 dB with 100 km fiber transmission compared with that of an ordinary optical direct detection OFDM system.