一类非线性摄动微分方程的振荡定理

本文讨论了非线性摄动微分方程(1)的解的振荡问题,给出了几个判定方程(1)具有振荡解的充分性定理。     

有界扰动滞环非线性系统的自适应控制

对存在有界扰动下的滞环非线性系统，建立了适合于最小相位和非最小相位情况的自适应控制算法，证明了闭环系统的稳定性，同时给出了控制误差上界。仿真实验表明了这种算法的有效性。     

强关联体系中的自旋与电荷密度涨落的共存性

对于具有晶格结构的固体、利用在相对论狄喇克方程的非相对论极限下得到的电子自旋－轨道相互作用，推导出自旋涨落一声子相互作用。利用此相互作用推导出自旋磁化率、电荷极化率、声子格林函数的一组自洽方程。然后，又讨论了自旋和电荷密度涨落的共存性及其对高温超导的影响。     

钢丝绳弹性组合元件中滞后力的数学建模

钢丝绳弹性元件具有滞后非线性，其恢复力可表示为“非线性无滞后力”和“纯滞后力”之和．由于实际系统中阻尼力的描述比较困难，文中引入了新的参数，描述同时具有干摩擦和线性阻尼特性的混合型阻尼．参数辨识的结果表明，这个模型能够合理反映兼有不同性质阻尼的滞后非线性特性．     

General Characteristic Equations of Four Fundamental Electronic Elements From Linearity to Nonlinearity

The approximate equations for self- and mutual-inductance can be further investigated. In addition, the general characteristic equations for the four fundamental elements in three situations are basically completed. This new development not only reveals theoretically the characteristics of the four fundamental electronic elements, but also practically deals with all the media from linearity to nonlinearity. This will meet all the purposes of application. Hence, it is very important and significant to the development of the science of electronic elements.     

基于遗传算法的非线性模式识别

文章设计了一种人工神经网络模型结构,以一种遗传算法进行该模型参数的组合优化建模,将其用于非线性模式识别.该方法不仅对线性问题有效,对非线性问题同样有效;该法简洁易行,优于多段线性分类器设计方法与BP误差回传网络算法.实例表明,遗传算法仅繁殖40代就能达到理想结果,其识别率达100%.     

Nonlinearity degree of short-term heart rate variability signal

A nonlinear autoregressive (NAR) model is built to model the heartbeat interval time series and the optimum model degree is proposed to be taken to evaluate the nonlinearity degree of heart rate variability (HRV). A group of healthy persons are studied and the results indicate that this method can effectively get nonlinear information from short (6—7 min) heartbeat series and consequently reflect the degree of heart rate variability, which supplies convenience in clinical application. Finally, a comparison with the traditional time domain method shows that the NAR model method can reflect the complexity of the whole signal and lessen the influence of noise and instability, in the signal.     

扑翼微型飞行器自适应鲁棒姿态控制

给出了扑翼微型飞行器姿态控制系统的数学模型,并提出了一种自适应鲁棒控制的新方法。飞行过程的复杂性使得姿态控制器的设计极具挑战性,主要困难是系统表现为非线性、不确定性、多变量参数耦合以及各种干扰。由于自适应鲁棒控制不依赖系统的精确数学模型,所以将系统分为名义模型、结构不确定性和非结构不确定性,对其分别设计直接反馈控制器、自适应控制器和鲁棒控制器,并用李亚普诺夫定理分析了系统的稳定性。仿真结果证实了所提方法的有效性。     

Adaptive control method for nonlinear time-delay processes

Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.     

栖息地与种群灭绝的生态系统耦合模型的近似解

研究了一类栖息地与种群生态环境问题,描述了动力学模型.利用广义泛函-变分迭代理论和方法,得到了相应模型的近似解,从而可以进一步进行预测和控制.