误差律

The overall control scheme and the weight update laws based on Lyapunov stability theory can guarantee the system stability and asymptotic convergence of the tracking error to zero, and attenuate the effect of the disturbance on system to a prescribed level.

总体控制方案及基于李亚普诺夫稳定性理论的权值更新律保证了系统的稳定性及跟踪误差渐近收敛于零，并使干扰对系统的影响衰减到指定的性能指标。

A differential difference type adaptive law and an adaptive iterative learning controller are constructed to ensure the asymptotic convergence of tracking errors in the sense of square error norm on the finite interval, by introducing a Lyapunov-like function, a sufficient condition of the convergence of the method is given.

通过引入微分－差分自适应学习律，设计了一种自适应控制策略，使得跟踪误差在一个有限区间上的积分渐近收敛于零；通过构造Lyapunov-like函数，给出了闭环系统收敛的一个充分条件。

Furthermore, a changeable update rule was introduced to accelerate the convergence speed, a forget factor and a predefined error bound were used to enhance the robustness of the algorithm.

同时还提出可变学习增益的方法来加快算法收敛速度；应用遗忘因子和学习律误差容限控制的方法来提高学习算法的鲁棒性。

The controller's parameters were identified directly without solving the Diophantine equation or the inverse of matrices, and the online computing time was shortened, which makes the approach be very suitable for the fast rolling process.

采用对模型要求宽松的广义预测控制方法，基于广义误差估计值对控制器参数进行自适应调整，直接辨识控制律参数，省略Diophantine方程的求解、矩阵的求逆，缩短在线计算的时间，适用于快速的轧钢过程。

In order to avoid introducing errors existing in full state observer, for flexible structure with immeasurable states a equivalent system is constructed which only takes the past inputs and outputs of the original system as the states. Multi-step predictive optimal method is required to solve the convergence law of sliding surface.

针对模态不可测的挠性结构，为了避免设计状态观测器以及引入观测器误差，从原系统构造了仅利用过去的输入和输出信息作为状态的等价系统，用多步预测滚动最优的方法求解滑动平面的趋近律。

Precision estimation is made more reliable using error calculation by the law of covariance propagation.

采用协方差传播律进行误差计算，使精度评定的结果更加准确。

An optimal control law is obtained by minimizing the average performance through spectral factorization and a practical control method for integrator and dead time plant is presented in the presence of plant uncertainty and control energy constraint.

首先基于一类随机模型误差的描述，定义了一个平均意义上的包含跟踪误差和控制能量在内的性能指标；然后通过谱分解极小化该性能指标，导出一个最优的控制律，从而为模型不确定性和控制能量约束并存条件下一类非自衡对象的最优控制问题提供了一种实用的控制方法。

Firstly, applying spectral factorization to minimize an integral square performance criterion containing tracking error and control energy, an optimal control law for the nominal model is derived on condition of control energy constraint. Then, for model uncertainty, using spectral factorization to minimize the variance of the actual system performance from the nominal performance over all frequency range, a robust controller design method is abtained, which has optimal robustness of the system nominal performance to model errors.

首先针对控制对象的标称模型应用谱分解最小化一个包含跟踪误差和控制能量在内的积分平方性能指标，导出一个控制能量约束条件下的最优控制律；然后再针对模型不确定性应用谱分解最小化实际系统性能和标称性能在整个频段上的方差，得到一个鲁棒控制器的设计方法，可使系统的标称性能对模型误差具有最优的鲁棒性。

The forgetting factor was optimized by reducing the trace of the input error covariance matrix. This factor is able to modify the iterative learning law of control input. The error signal of the feed-forward learning controller was filtered by a zero-phase FIR digital filter.

通过减小系统输入误差协方差矩阵迹的方式得到优化的遗忘因子，来修正控制输入的迭代学习律，同时采用零相位FIR数字滤波器对前馈学习控制器中的误差信号进行滤波处理。

This paper discusses some application cases of the error propagation law by the examples of trigonometrical survey, and presents that not only sum function and numeral multipling function in which there is only one independent observed value but also more complex functions which are equal in mathematics are not opposite in the process of error propagation according to the error propagation law.

1引言本文以三角测量为例，对误差传播定律一些应用问题进行了讨论，指出当只有一个独立的观测值时，和函数与倍数函数运用误差传播定律不会出现悖论；如果在测量工作中有多余的直接观测值，就需用平差后的间接观测值按协方差传播律来计算，这样数学中相等的函数关系才能得到同样的函

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。