Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.

THE UNCONDITIONAL STABILITY OF PARALLEL DIFFERENCE SCHEMES WITH SECOND ORDER CONVERGENCE FOR NONLINEAR PARABOLIC SYSTEM

For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the （Dirichlet） boundary condition for solving the sub-domain problems. Then the values in the sub-domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.

Discretization of Nonlinear Non-affine Time Delay Systems Based on Second-order Hold

When calculating the sampled-date representation of nonlinear systems second-order hold(SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input.Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method.The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems.The comparison between SOH assumption with first-order hold(FOH) and zero-order hold(ZOH) assumptions is given to show the advantages of the proposed method.

A Second Order Difference Scheme with Nonuniform Rectangular Meshes for Nonlinear Parabolic System

In this paper, a difference scheme with nonuniform meshes is proposed for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in both space and time.

STABILITY OF DIFFERENCE SCHEMES FOR NONLINEAR PARABOLIC SYSTEMS WITH THREE DIMENSIONS

In this paper the existence of discrete vector solutions with bounded second order quotientsfor the difference systems of nonlinear parabolic system is established by the fixed point technique,and then the absolute and relative stability for the general difference schemes is justified in thesense of continuous dependence of the discrete vector solution of the difference schemes on thediscrete data of the original problems.

基于积分滑模的二阶系统任意预设时间编队控制

在通信过程中,智能体受各种未知干扰信号的影响,导致系统性能降低。针对二阶非线性多智能体系统,研究了在有向通信拓扑结构下实现任意预设时间编队期望的问题。首先,结合预设时间机制与积分滑模控制策略,设计一种新的编队控制协议,该控制协议能够确保二阶多智能体系统在任意预设时间内实现到达段和滑动段2个阶段的收敛,引入的积分滑模控制项有效降低了系统的稳态误差,并提高其在预设时间控制下的鲁棒稳定性;其次,利用李雅普诺夫方法与代数图论知识,分析得出二阶系统在该控制方法下达到预设时间编队期望的充分条件,并证明了包含预设时变函数控制协议的有界性。仿真实验结果验证所设计控制方法的有效性与可行性,即给定任意初值,带干扰项的二阶系统均可在任意预设时间内快速准确地达到稳定状态。

大失准角条件下制导炮弹组合导航方法研究

制导炮弹多采用发射后上电空中对准的方式实现导航初始信息的获取,初始姿态信息中滚转角的获取难度远高于俯仰角和偏航角。针对空中对准中滚转角信息获取难度较高的问题,提出了一种适用于大初始滚转角误差的组合导航方法,旨在省略滚转角对准过程和压缩空中对准时间。通过在组合导航状态向量中引入四元数误差,将状态方程的强非线性误差模型转换为了二阶非线性模型,降低了系统的复杂度。在此基础上,采用二阶扩展卡尔曼滤波方法实现惯性导航系统各项误差的估计,并基于四元数模1约束设计了优化的量测更新方法。各量级初始滚转角误差下的半实物仿真结果表明:所设计方法可适应大初始滚转角误差情况,7 s内滚转角误差可由180°收敛至10°内;各量级初始滚转角误差下收敛位置稳定一致,有效的提升了组合导航的适应性。

多传感器非线性系统序贯观测融合二阶扩展卡尔曼滤波器

对多传感器非线性系统提出了一种序贯观测融合二阶扩展卡尔曼滤波(Second-order Extended Kalman Filter,SOEKF)算法。该算法的中心思想是根据传感器观测数据到达融合中心的先后次序依次进行处理。研究表明,提出的序贯观测融合SOEKF算法比集中式观测融合EKF算法具有更高的精度;与集中式观测融合SOEKF算法精度相当,且具有更低的计算复杂度。目标跟踪系统的仿真验证了算法的有效性。

交直流电力系统与供热系统联合经济调度

随着热电联产等技术的广泛应用,电力系统和供热系统耦合日益紧密,电热联合调度得到了广泛的关注,但现有电热联合调度忽略了热网供电来源的多样性,由此提出了交直流电力系统与供热系统联合经济调度方法。首先,建立交直流电力系统模型,并提出一种线性近似方法对电压源变换器模型所带来的强非线性进行处理;然后,以运行成本最低为目标,建立考虑热网热惯性的交直流电力系统与供热系统联合调度模型,该模型中供热系统通过热电联产机组和交流电锅炉与交流电网耦合,通过直流电锅炉与直流电网耦合;最后,通过算例仿真验证了所提方法的有效性并说明了在电热联合调度中考虑交直流电源的必要性。

施加电场的半抛物量子阱中的二阶非线性光学极化率(英文)

利用量子力学中的紧致密度矩阵方法 ,研究了施加电场的半抛物量子阱中的二阶非线性光学极化率 (光整流系数 ) ,得到了此系统的光整流系数的解析表达式 数值计算的结果表明 ,随着电场强度的增加 ,光整流系数几乎线性随之增加 ,而且在同样的电场强度及抛物束缚势频率作用下 ,半抛物量子阱模型中的光整流系数比抛物量子阱模型中的值大一个数量级 。

飞航导弹纵向控制系统的二阶滑模控制设计

在介绍了高阶滑模控制的基础上,提出了一种简单有效的二阶滑模控制器,并应用到飞航导弹纵向控制系统中。仿真结果说明:它对参数不确定的系统具有良好的鲁棒性,并能有效的消弱系统的振颤。

一类不确定非线性系统的全局鲁棒有限时间镇定

对一类不确定非线性系统提出了一种连续的全局鲁棒有限时间控制律.首先,针对标称系统设计出了一种状态反馈控制律,应用Lyapunov直接稳定性理论和LaSalle不变性原理证明了闭环标称系统的全局渐近稳定性,同时具有负的齐次度,其次,引入辅助变量和采用有限时间收敛的二阶滑模Super-twisting算法,设计出了对不确定性和干扰进行抑制的补偿控制项,并根据有限时间Lyapunov函数给出了补偿控制项参数的取值范围;最后,综合得到一种连续的使实际闭环系统有限时间收敛到平衡点的鲁棒镇定控制律.仿真结果表明了所提控制律的有效性.

二阶非线性系统三点边值问题的可控性

研究一类二阶非线性系统三点边值问题的可控性 .利用 Green函数将此可控性问题转化为证明一个算子具有不动点问题 ,进而利用 Schauder不动点定理得到一个精细的可控性结果 .

基于干扰观测器的一类不确定非线性系统自适应二阶动态terminal滑模控制

针对一类不确定非线性系统的跟踪控制问题,在考虑建模误差、参数不确定和外部干扰情况下,以其拥有良好的跟踪性能以及强鲁棒性为目标,提出基于回归扰动模糊神经网络干扰观测器(recurrent perturbation fuzzy neural networks disturbance observer,RPFNNDO)的鲁棒自适应二阶动态terminal滑模控制策略.将回归网络、模糊神经网络和sine-cosine扰动函数各自优势相结合,给出一种回归扰动模糊神经网络结构,提出RPFNNDO设计方法,保证干扰估计准确性;构造基于带有指数函数滑模面的二阶快速terminal滑模面,给出其控制器设计过程,避免了滑模到达阶段、传统滑模的抖振问题,采用具有指数收敛的鲁棒项抑制干扰估计误差对系统跟踪性能的影响,利用Lyapunov理论证明闭环系统的稳定性;将该方法应用于混沌陀螺系统同步控制仿真实验,结果表明所提方法的有效性.

弱非线性斯托克斯波在非平整海底上传播的新型抛物型方程

由于缓坡方程计算量大和其本身的缓坡假定而在实际应用中受到了限制，故对斯托克斯波在非平整海底（适用于缓坡和陡坡地形）上传播的Liu和Dingemans的三阶演化方程进行抛物逼近，得到一个新的非线性抛物型方程，它能够包含同类方程未曾考虑的二阶长波效应．通过数值计算结果与Berkhoff等人的经典实验数据的比较，证明所提出的抛物型模型理论具有较高的精度。

香豆素衍生物分子二阶非线性光学效应理论研究

用ＣＮＤＯ／Ｓ－ＣＩ程序，计算了一系列香豆素衍生物的分子二阶极化率。从微观上探讨了该类化合物的取代基的电子性质，取代基位置及取代基数目对分子二阶极化率的影响。认为取代基的电子性质和取代方式对非线性光学系数有明显的影响。

LM算法在二阶过阻尼系统参数估计中的应用

针对二阶过阻尼系统传递函数的参数辨识问题,提出一种根据二阶过阻尼系统阶跃响应估计系统传递函数未知参数的新方法。该方法首先求解出二阶过阻尼系统的阶跃响应表达式,然后定义模型输出与观测数据的差值作为代价函数,将参数估计问题转换为非线性最小二乘问题。通过采用Levenberg-Marquarat算法极小化代价函数,估计出系统未知参数。为确定参数估计的初值,给出采用两点法的参数初值估计方法。仿真结果表明,在含有观测噪声的情况下,提出的方法能有效解决过阻尼二阶系统未知参数的估计问题。

神经网络建模在热膨胀螺栓形变测量中的应用

基于神经网络建立热膨胀螺栓形变的非线性数学模型。神经网络的辨识采用变尺度二阶快速学习算法 ,利用二阶插值法来优化搜索学习速率。新方法具有很快的收敛速度和良好的收敛精度 ,克服了 BP算法在神经网络的权值训练中收敛速度过慢的缺点。热膨胀螺栓的受热形变测量结果表明 。

二阶输出反馈滑模极值搜索控制方法

针对一类单输入单输出(single-input-single-output,SISO)非线性极值系统的控制问题,提出了一种二阶输出反馈滑模极值搜索控制方法。考虑到此系统的状态量不可测,利用斜坡函数作为输出量的参考跟踪信号,以系统的输出跟踪误差及其微分信号构建切换函数,设计出二阶滑模极值搜索控制律。稳定性分析证明了在任意初始条件下,该方法可使系统的输出量全局收敛至其期望极值的任意小邻域内且所有状态量均是一致范数有界。仿真结果验证了该方法的有效性。

非线性二阶微分系统正解的存在性

考虑二阶微分系统边值问题x″( t) +λ f( t,x( t) ,y( t) ) =0 ,y″( t) +μ g( t,x( t) ,y( t) ) =0 , 0 <t<1 ,x( 0 ) =x( 1 ) =y( 0 ) =y( 1 ) =0 .其中 λ,μ>0 ,f,g:[0 ,1 ]× [0 ,∞ )× [0 ,∞ )→R连续 .突破了以往文献要求非线性项 f,g非负的限制 ,运用锥上的一个不动点定理 。