查询词典 nonlinear optimization

By introducing the parameter , construct a new kind of weighted implicit difference scheme for (1+1)-dimension nonlinear Sine-Gordon equation and the generalized nonlinear Sine-Gordon equation respectively. Give out an ADI scheme for (2+1)-dimension nonlinear Sine-Gordon equation.

通过引进参数，分别为（1+1）维的非线性Sine-Gordon方程和广义的非线性Sine-Gordon方程建立了它们的加权隐式差分格式，给出了（2+1）维的非线性Sine-Gordon方程的ADI格式。

Presents the design of longitudinal control for ASTOVL lift-fan aircraft, a multi-variable, strong-coupling, complicated nonlinear system to make the system nonlinear offset and decouple, and the method used for linear system in designing the system to gain expectant flying qualities and the combination of aerodynamic control surfaces with thrust vectors to delay the control surfaces getting into saturation, and the minimum N-norm generalized inverse theorem of weighted generalized inverse adopted to apportion the moments commands, which make the control surfaces gain appropriate deflection and the simulation results to verify the dynamic inverse control laws designed really make the system nonlinear offset and decouple; when one command is given, only this output will response, and others do not response; when all commands are given together, the responses will be just the linear superpose of the response of each command, therefore the operation of the pilot will be simplified greatly.

摘 要： ASTOVL升力风扇飞机是多变量、强耦合、复杂的非线性系统，采用非线性动态逆理论设计控制律以实现系统的非线性对消及解耦，然后，采用线性系统的设计方法对系统进行设计，以使系统获得期望的飞行品质。同时，考虑到ASTOVL升力风扇飞机是由气动舵面和推力矢量融合作用的，为了延缓各舵面进入饱和的时间，采用加权广义逆中的极小N-范数广义逆定理分配力矩指令，从而使各舵面达到适当的偏转角。并将所设计的控制律进行了仿真，结果验证了所设计的动态逆控制律使系统实现了非线性对消和解耦，单个指令作用时，只有该项响应，其余不受影响；所有指令作用时，其结果就等于单个指令作用时的线性叠加，这样使驾驶员的操纵大大简化而易于控制，从而大大降低了飞行事故率。

At first, this paper surveys nonlinear control and the applications of neural networks in control respectively. Then it studies definitions, mathematical descriptions and conditions of invertibility for nonlinear systems, which are used to analyze the feasibility of inverse system control method. Conclusions about the feasibility of inverse control and the realizability of αth-order inverse systems in engineering are achieved. Furthermore, this paper discusses the feasibility, structure and identification of neural network αth-order inverse system for general single-input single-output continuous or discrete nonlinear systems and various composite control methods based on the αth-order inverse. At last, as a part work of an actual project, this paper focuses on the design of neural network αth-order inverse control method for thyristor controlled series compensation in power systems and its effect in improving the stability of power systems.

本文首先分别概述非线性系统的控制与人工神经网络在控制中的应用；然后研究非线性系统各种可逆性的定义、数学描述及可逆性条件，并用于分析逆系统控制方法的可行性，得出有关逆系统控制方法可行性的结论，阐明一般情况下α阶逆系统才工程可实现；接着本文针对一般单输入单输出连续、离散非线性系统，研究神经网络α阶逆系统的可行性、结构与辨识以及基于神经网络α阶逆系统的各种复合控制方法，并给出应用例子；最后本文结合实际项目，针对采用可控串补的电力系统，设计神经网络α阶逆系统控制方法，研究其对提高电力系统稳定性的作用。

Base vectors are selected for formulating the nonlinear mapping. An approximate explicit expression is formed by using the Nystrm method for nonlinear mapping which is not available originally. The data in the nonlinear input space is mapped into some linear feature subspace and fisher linear discriminant analysis is computed for the mapped data.

首先提取基向量；然后采用Nystrm方法，以基向量为训练样本，将形式未知的非线性映射近似表达为已知形式的非线性映射，这种近似的非线性映射将变量由非线性的输入空间转换到线性的特征子空间；最后对映射数据进行线性Fisher判别分析。

Nonlinear functional analysis has become an important direction of research in modern mathematics,nonlinear operator theory is also an important part of nonlinear functional analysis.

非线性泛函分析已成为现代数学中的重要研究方向之一，而非线性算子理论又是非线性泛函分析的重要内容。

Nonlinear functional analysis is not only profound theory but also widelyused research discipline in mathematics, in the context of nonlinear problemsof mathematics and natural sciences, a number of theories and methods of dil-ing with nonlinear problems have been established.

非线性泛函分析是数学中既有深刻理论又有广泛应用的研究学科，以数学和自然科学中出现的非线性问题为背景，建立了处理非线性问题的若干理论和方法。

Due to the complexity of the nonlinear system,it is classified as five kinds of discrete nonlinear multi-variable system according to nonlinear operator.

鉴于非线性多变量系统的极端复杂性，将离散的非线性多变量系统按非线性算子的不同分为五类。

The joint effect of active and reactive power on the voltage stability of a typical power system was considered by analysing the two parameter bifurcation problem related to nonlinear oscillation phenomena. Numerically, as the active power P1 increases, the Hopf points get closer and eventually coincide at P1=1.455 43 the cyclic fold curve gets closer and closer to the Hopf curve and finally intersects the Hopf curve at a singular point the period-doubling points also get closer and finally coincide at P1≈0.65. The stability behaviour is pre-determined using the normal form approach near the limit point of the Hopf curve. Hence, in the power system attention should be paid to both the consumption of active power and the decrease in the reactive power to prevent nonlinear oscillations. A controller can be designed to absorb some active power and to avoid the nonlinear oscillations that damage the system components.

针对一个典型的单机无穷大电力系统，通过分析系统的双参数分岔的非线性振荡现象，综合考虑有功和无功功率对电压稳定性的影响数值分析表明，随着有功功率的增加，电力系统的Hopf点越来越靠近，最终合为一点在P1=1.455 43处同时圈折cyclic fold 曲线也越来越靠近Hopf曲线，并在Hopf曲线的稳定与不稳定临界点处与Hopf曲线相交倍周期分岔点也随着越来越靠近，最终在P1≈0.65 合为一点应用正规形理论方法，初步确定了Hopf曲线极限点附近的稳定性态因而，电力系统应注意让负荷利用有功功率，减少无功功率的产生以防止非线性振荡另外，可以设计一个稍微吸收网络的有功功率的控制器，以避免因周期振荡而造成电力系统仪器的损坏或电压崩溃

Combustion instability in liquid rocket engine is investigated with theoretical analyses, numerical simulations and experiments. Nonlinear science, such as Nonlinear Dynamics, Non- equilibrium Thermodynamics, and Wavelets, is introduced in the studies.Nonlinear oscillation equation of chamber pressure is established.

本文结合非平衡热力学、小波分析、非线性动力学等非线性学科，建立燃烧稳定性理论模型，发展两相喷雾燃烧非定常数值模拟程序，利用激光测粒系统，发动机高频热试系统等测试手段，重点围绕液体推进剂的化学动力学过程，对燃烧不稳定进行了较为系统的理论、仿真和实验研究。

Also the response amplitude will be changed with the initial conditions due to the nonlinear properties of the cables.Taking the bending stiffness, cable sag and cable inclination into consideration, the space vibration control of the cables using the visco-elastic dampers in cable-stayed bridges is investigated by joining the center difference method and the state space strategy. Both the maximum modal damping ration and the optimal damper size are obtained, then the practical suggestions are proposed for the design of the dampers. The space nonlinear vibration equations of the cable-damper system are derived, and anew hybrid method for solving the cable-damper system is presented by combing the Newmark method and Pseudo-force technology. According to the known properties of the cable-damper system, the nonlinear transient responses are analyzed under all kinds of excitations. Based on the transient response, the control effectiveness of the visco-elastic dampers is further demonstrated.

综合考虑了拉索抗弯刚度、垂度的影响，研究了粘弹性阻尼器对斜拉桥拉索的空间振动控制，联合中心差分方法及状态空间法，得出了拉索面内、外振动各阶模态可能达到的最大阻尼比及相应的最优阻尼器系数，并对斜拉桥拉索的阻尼器设计提出了参考建议：考虑拉索抗弯刚度、垂度及几何非线性，导出了索-阻尼器系统的空间振动非线性方程组，结合Newmark方法及伪力(Pseudo-Force)方法，创新地提出了求解非线性方程组的杂交方法，根据拉索-阻尼器系统的阻尼特性，在各种荷载作用下，对索-阻尼器系统的非线性瞬态振动响应进行了研究，从系统响应的角度更加直接地验证了阻尼器的控制效果。

Salt is good, but if the salt becomes flat and tasteless, with what do you season it?

14：33 盐本是好的，盐若失了味，可用什么叫它再咸呢？

He reiterated that the PLA is an army of the people under the leadership of the Communist Party of China.

他重申，人民解放军是在中国共产党领导下的人民军队。