Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.

ASYMPTOTIC BEHAVIOR NEAR THE BOUNDARY OF A LARGE SOLUTION TO SEMILINEAR POISSON EQUATION WITH DOUBLE-POWER NONLINEARITY

We deal with a large solution to the semilinear Poisson equation with doublepower nonlinearityΔ^(u)=u^(p)+αu^(q)in a bounded smooth domain D■R^(n),where p>1,-1<q<p andα∈R.We obtain the asymptotic behavior of a solution u near the boundary OD up to the third or higher term.

Effect of Wave Nonlinearity on the Instantaneous Seabed Liquefaction

The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.

Quasi-anti-parity–time-symmetric single-resonator micro-optical gyroscope with Kerr nonlinearity

Parity–time(PT) and quasi-anti-parity–time(quasi-APT) symmetric optical gyroscopes have been proposed recently which enhance Sagnac frequency splitting. However, the operation of gyroscopes at the exceptional point(EP) is challenging due to strict fabrication requirements and experimental uncertainties. We propose a new quasi-APT-symmetric micro-optical gyroscope which can be operated at the EP by easily shifting the Kerr nonlinearity. A single resonator is used as the core sensitive component of the quasi-APT-symmetric optical gyroscope to reduce the size, overcome the strict structural requirements and detect small rotation rates. Moreover, the proposed scheme also has an easy readout method for the frequency splitting. As a result, the device achieves a frequency splitting 10~5 times higher than that of a classical resonant optical gyroscope with the Earth's rotation. This proposal paves the way for a new and valuable method for the engineering of micro-optical gyroscopes.

Bright soliton dynamics for resonant nonlinear Schrödinger equation with generalized cubic-quintic nonlinearity

For systems modeled by the resonant nonlinear Schrödinger equation(RNLSE)with generalized cubic-quintic nonlinearity,we derive the bright soliton solution of the equation in(1+1)dimensions,using the modified F-expansion method along with the novel ansatz of F-base function.Furthermore,we extend the analytical study of soliton dynamics to higher(2+1)and(3+1)dimensions by using the self-similar method,and demonstrate the soliton behavior via graphical illustration.Moreover,we investigate the effect of the resonance term on bright soliton solution in(1+1)dimensions.Additionally,we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional(1D)to three-dimensional(3D)cases.The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model.

Selective Impact of Dispersion and Nonlinearity on Waves and Solitary Wave in a Strongly Nonlinear and Flattened Waveguide

The waveguide which is at the center of our concerns in this work is a strongly flattened waveguide, that is to say characterized by a strong dispersion and in addition is strongly nonlinear. As this type of waveguide contains multiple dispersion coefficients according to the degrees of spatial variation within it, our work in this article is to see how these dispersions and nonlinearities each influence the wave or the signal that can propagate in the waveguide. Since the partial differential equation which governs the dynamics of propagation in such transmission medium presents several dispersion and nonlinear coefficients, we check how they contribute to the choices of the solutions that we want them to verify this nonlinear partial differential equation. This effectively requires an adequate choice of the form of solution to be constructed. Thus, this article is based on three main pillars, namely: first of all, making a good choice of the solution function to be constructed, secondly, determining the exact solutions and, if necessary, remodeling the main equation such that it is possible;then check the impact of the dispersion and nonlinear coefficients on the solutions. Finally, the reliability of the solutions obtained is tested by a study of the propagation. Another very important aspect is the use of notions of probability to select the predominant solutions.

一类非线性互联系统鲁棒控制问题的求解方法

含扰动的非线性互联系统的鲁棒控制问题一直是研究的热点。针对此问题,构建了一种非线性互联系统状态观测器,并基于观测器的状态估计值设计了一种状态反馈控制器。对状态估计误差与状态反馈闭环互联系统进行增广联合设计,构造了一种增广李雅普诺夫函数,给出了增广系统渐近稳定的充分条件,保证了状态估计误差趋于零,状态反馈闭环互联系统鲁棒镇定。最后,选取两类互联系统算例对所提控制方法进行仿真验证,仿真结果验证了所构建的状态观测器的可行性和基于估计状态的状态反馈控制器的有效性,所提控制方法为含扰动的非线性互联系统的鲁棒控制问题求解提供了一种参考。

未知环境中基于控制障碍函数的机器人安全控制研究综述

随着机器人系统工作环境的复杂程度日益增加,以及对实时性需求的逐步提升,机器人的安全避障能力将面临新的挑战,控制障碍函数作为一种基于控制器的安全方法在机器人安全控制系统中迎来新的发展契机。调研分析了控制障碍函数及基于二次规划的优化控制器,总结了机器人在已知和未知环境中的避障问题,综述了高斯过程和强化学习两种理论合成控制障碍函数的策略。最后,讨论了未来基于控制障碍函数的空地协同机器人安全控制需要重点关注的问题,为未来控制障碍函数的理论研究和技术应用提供了参考。

岩石非线性黏弹塑性损伤蠕变模型研究

准确描述岩石蠕变行为的各阶段特征对岩石力学与岩体工程的研究具有重要的意义。由于经典元件组合模型不能较好地描述岩石蠕变过程中的非线性特征,基于损伤力学理论及Kachanov蠕变损伤演化规律,通过改进传统的Kelvin模型和村山体模型,建立起能够描述岩石衰减蠕变阶段和加速蠕变阶段的非线性函数。将弹性体、线性Kelvin体、非线性Kelvin体、损伤黏弹塑性体进行串联,建立能够同时描述岩石瞬时弹性应变、非线性黏弹性应变、非线性黏塑性应变和黏性应变的非线性黏弹塑性损伤蠕变模型,采用Origin软件的Levenberg-Marquardt算法对模型参数进行了辨识,最后通过用不同应力水平下的砂岩单以及三轴压缩蠕变试验,验证该模型的合理性。结果表明:试验曲线和理论曲线的吻合度较高,所建模型不仅能够准确地描述岩石的瞬时弹性应变阶段、等速蠕变阶段的蠕变曲线特征,而且能够较好地描述衰减蠕变阶段和加速蠕变阶段蠕变曲线的非线性特征,验证了该模型的合理性与准确性。

利用匹配滤波的调频连续波激光测距技术研究

基于差频解算的调频连续波激光测距技术存在测量距离短、易受噪声干扰、受非线性调频影响大的问题。为了在相同机制条件下解决此问题,提出了基于匹配滤波的调频连续波激光测距方法,改进相干探测光路,加入信号反转单元和信号共轭单元,将混频器换成卷积器,同时满足系统响应与发射波形匹配,并进行了相关仿真实验。结果表明,相比差频解算方法,匹配滤波方法可实现两倍于差频解算方法的测距范围,信噪比提高了9.5 dB,在非线性调频误差为19.8 MHz、198 MHz和396 MHz条件下均能得到较高分辨率的距离谱,表现出较好的抵抗非线性调频的能力。此研究可为该领域的科研工作者提供技术指导和新的思路。

基于正系统分析的不确定非线性系统性能驱动控制方法

针对一类不确定非线性系统,提出一种保证系统状态满足预设边界性能函数的新型性能驱动控制(Performancedriven control,PDC)方法.不同于传统预设性能控制(Prescribed performance control,PPC)方法中对误差与边界性能函数的比值进行非线性变换的思路,本文基于保证状态量与上下边界的两个误差量均始终非负这一思想,引入基于Metzler矩阵的正系统分析理论,并结合切换控制技术,以最终保证系统状态始终在预设性能函数之内.系统的稳定性取决于边界性能函数的选取,而不改变控制器的形式.给出针对一类不确定非线性系统的控制设计、稳定性分析和方法讨论,数值仿真例子验证了所提出方法的有效性.

船冰多次碰撞下极地航行船舶舷侧结构动态响应研究

近年来全球变暖的加剧使得北极航道的开放更具可行性,为分析极地船舶航行过程中的冰载荷及船体结构响应特性,本文针对船体舷侧结构与浮冰场多次碰撞的场景开展数值仿真研究。参考现阶段浮冰观测统计经验,建立船体舷侧结构-浮冰场相互作用有限元数值模型,在不同碰撞角度与不同浮冰密集度下开展仿真计算,分析船冰连续多次碰撞过程中碰撞力、能量及响应数据,研究碰撞角度和浮冰场密集度对浮冰载荷及船体舷侧结构响应特性的影响规律。结果表明,船冰多次相互作用下的结构响应规律与船冰单次作用存在一定差异,碰撞角度与浮冰场密集度参数对船冰碰撞力与船体舷侧结构响应特征影响呈现出一定的规律。本文研究内容对极地航行船舶舷侧结构的安全性设计具有参考价值。

基于非线性动力学稀疏辨识的涡致振动系统建模

以二维和三维圆柱涡致振动(VIV)系统为研究对象,通过非线性动力学稀疏辨识(SINDy)的方法,识别VIV系统的结构响应模型和尾流振荡模型.对模型进行验证和分析,得到VIV系统的流固耦合模型,实现不同缩减速度下圆柱VIV位移和速度响应的预测.结果表明,采用SINDy算法,识别了带有附加阻尼的二维VIV系统的结构响应模型.该模型与流固耦合系统的动力学特征表现出明显的规律:当涡致振动系统处于锁定(lock-in)区域时,附加阻尼随缩减速度变大而基本保持不变,结构的无量纲最大振幅保持在较高水平;当涡致振动系统处于非锁定区域时,附加阻尼随缩减速度变大而呈现线性下降的特征,结构的无量纲振幅保持在较低水平.基于SINDy方法识别的二维VIV系统流固耦合模型和三维VIV系统结构响应模型有较好的预测能力,其中二维VIV系统流固耦合模型有一定的泛化能力.模型预测值能够表征原系统的运动特征,对二维VIV系统结构位移响应预测的相对误差小于6%,结构速度响应预测的相对误差小于5%,对三维VIV系统结构位移和速度响应预测的相对误差小于4%.

电动汽车无线充电系统PBC-NDO复合控制器设计与参数优化

针对电动汽车无线充电系统在变电压间歇快速充电过程中由原副边线圈偏移和负载波动引起充电电压不稳定的问题,以及控制器参数大多依靠经验值和试凑法选取的问题,提出一种基于粒子群优化算法的无源控制器(passivity based controller,PBC)与非线性干扰观测器(nonlinear disturbance observer,NDO)相结合的复合控制策略。针对无线电能传输(wireless power transfer,WPT)系统副边DC-DC变换器设计考虑干扰补偿的无源控制器,通过引入非线性干扰观测器对干扰量进行估计,将干扰估计值与无源控制器结合,设计适合电动汽车变电压间歇无线充电系统的PBC-NDO复合控制器,采用粒子群多目标优化算法对复合控制器进行参数寻优,进一步提高控制器的抗干扰性能以及动态响应性能,通过仿真和实验验证该策略的有效性。实验结果表明:复合控制器具有强抗干扰性和动态响应性,充电阶段最大稳态误差偏移率为2%,动态响应时间控制在0.6 ms内。

时滞反馈对超磁致伸缩换能器输出的影响分析

为研究时滞反馈对超磁致伸缩换能器输出的影响规律,扩大超磁致伸缩伸缩换能器的使用范围。通过分析换能器工作原理,建立时滞反馈控制下的系统动力学模型,采用多尺度法求解得到系统在位移、速度和加速度时滞反馈控制下的输出响应。仿真分析得知:无时滞反馈控制系统的输出呈硬式非线性特性;与无时滞反馈系统相比,位移和速度时滞反馈控制的换能器通过调整控制增益或时滞可有效降低系统的振动幅值、提高系统的稳定性;加速度时滞反馈控制下的换能器能够在不改变系统振幅的条件下改变系统的谐振频率,将加速度时滞反馈控制的换能器应用于能量回收系统中,仿真发现:调整控制增益不仅能够改变能量回收系统的有效频带范围,也可以调整系统的感应电压幅值。

一种X构型的负刚度NES抗震性能研究

为拓宽非线性能量阱(NES)的控制频率范围,提出一种引入负刚度的NES,由附加质量通过X型环绕弹簧产生非线性恢复力,增加准零刚度特性,同时调整控制动力参数,降低系统固有频率,能够有效提高NES的非线性和鲁棒性。采用拟静力试验方法,对所提出的负刚度NES模型进行低周往复加载,同时采用ABAQUS有限元软件完成负刚度NES的数值模拟,系统分析弹簧运动行程长宽比、预压缩量和刚度3种参数对负刚度NES抗震性能的影响。研究结果表明:这种X构型负刚度NES比常规NES表现出更宽的频率范围;调整弹簧刚度、长宽比和弹簧预压缩量都能拓宽NES的负刚度和频率变化范围,提高NES的耗能能力和抗震性能,有助于推广非线性结构控制技术在工程中的应用。

考虑相关性的配电网分布式光伏承载能力提升方法

配电网中分布式光伏渗透率的不断提升对其充分消纳提出了更高的要求。针对配电网分布式光伏承载能力提升的问题,提出一种考虑相关性的分布式光伏承载能力提升方法。首先,利用Frank-Copula函数描述分布式光伏出力与负荷间的相关性,基于Nataf变换得到各随机变量的相关性样本矩阵,并进行概率潮流计算。然后,以分布式光伏接入容量最大为目标,电网运行安全指标为约束,建立分布式光伏承载能力提升模型。最后,提出采用非线性反向学习鲸鱼算法对模型进行求解,以IEEE 33节点系统为算例进行仿真分析。结果表明,所提方法能够有效提升配电网分布式光伏承载能力。

基于改进差分进化算法的水下恒定电流元定位方法随电极数量的变化

针对水下非合作军事目标的远程被动电场定位需求,提出利用非规则布放的测量电极获得水下电位数据,并采用边界变异自适应差分进化算法可以实现对半无限大海水中恒定电流元的准确定位。从半无限大海域中恒定电流元所产生的标量电位表达式出发,通过建立目标函数,将电流元的定位问题转化为目标函数最小值优化问题;然后引入参数自适应策略和边界变异处理机制,以解决基本差分进化算法存在的易陷入局部最优解、收敛性差、抗噪能力弱等问题。仿真分析和实验室定位结果表明:所提出的边界变异自适应差分进化算法在解决水下恒定电流元定位问题时,具有不依赖初值、搜索范围大、抗噪性能好等优点,具有较强的实用性。

高阶非线性不确定系统的复合有限时间控制

本文针对一类带有外界干扰的高阶非线性不确定系统,提出基于有限时间干扰观测器的复合有限时间控制策略,为了解决终端滑模的奇异性问题,设计改进的非奇异终端滑模面.同时,双曲正切函数和指数型函数相结合,构造新型复合趋近律.为了处理外界干扰,设计非奇异终端滑模观测器,将观测到的干扰值前馈到滑模控制中,进一步提高系统的抗干扰性.最后,将设计的复合趋近律与其他5种趋近律进行仿真对比,验证复合趋近律的收敛速度和削弱抖振能力,并通过非线性系统的数值仿真验证所提出控制策略的有效性和优越性.

风浪联合作用下驳船型海上浮式风机的非线性耦合模型与TMD振动控制研究

海上浮式风机是捕获深远海风能的重要装置,是风能开发的主要研究方向之一。驳船型风机多采用二维低阶简化动力学模型和非线性最小二乘参数识别方法,建立高阶耦合动力模型能更准确地反映其动力特性。本文关注驳船型海上浮式风机的多体系统,建立风浪联合作用下的16自由度耦合动力学模型,通过数值仿真验证模型的准确性。其中,利用修正的叶素动量理论计算叶片气动荷载,利用线性势流理论计算波浪荷载,采用准静态法计算系泊张力。此外,为减小驳船型海上浮式风机的结构振动,在考虑发电机转矩控制和叶片集体变桨控制的基础上,提出将双向碰撞调谐质量阻尼器置于机舱中,并引入限位装置控制振子行程。随后,通过穷举法和遗传算法进行控制参数优化。仿真分析表明,本文所建模型可准确计算驳船型海上浮式风机的动力响应;双向碰撞调谐质量阻尼器对结构振动有较好的控制效果。