误差律

After analyzing the shortage of classical track following control rule, the abscissa error of track position of the robot is introduced in the method to fasten the track approaching speed, as well as the combined function of manual field and position error is applied to control the orientation of the robot.

在分析经典轨迹跟踪控制律缺点的基础上，方法中引入了机器人跟踪位姿误差的横坐标误差以加速机器人的轨迹逼近速度，并采用人工场和位姿误差协同作用来共同完成机器人的导向控制。

By using the interpolation mechanism of fuzzy system, an approach of building the series of fuzzy systems, which can uniformly approximate any continuous function on a compact domain to any accuracy, is given, and then the universal approximation theorem is generally proved.

利用模糊系统的插值模型来代替被控对象的真实模型，设计了一个自适应模糊控制策略；为保证系统的全局稳定性，增加了一个补偿控制律，它是根据模糊系统的逼近误差估计量来设计的，因此这里系统跟踪误差的收敛性不依赖于模型最小误差的平方可积性[70，71]。

When the errors meet certain requirements, the adaptive law based on the Lyapunov stability further adjusts the weights of networks to ensure the asymptotic convergence of the tracking error to be zero.

当误差满足一定要求时，根据Lyapunov稳定性理论的自适应律进一步调整网络权值，以保证机械手位置误差和速度跟踪误差渐近收敛于零。

According to the Lyapunov stability theory, the weight update law of neural network, the adaptive law of error bound and the feedback control are obtained, thus the stability of closed-loop control system is ensured.

基于Lyapunov稳定性理论，得到了神经网络的权值更新律、误差界自适应律及反馈控制律，确保了闭环控制系统的稳定性。

According to the Lyapunov stability theory, the weight update law of neural network, the adaptive law of error bound, the stabilizing function and the control are obtained, thus the stability of closed-loop control system is ensured.

基于Lyapunov稳定性理论，得到了神经网络的权值更新律、误差界自适应律、稳定函数及控制律，确保了闭环控制系统的稳定性。

By applying the concept of "dominant input",the existence of both the approximation error and external disturbance which are supposed to have unknown boundaries is considered.What's more,the adaptive law utilizes two types of errors in the adaptive fuzzy systems,the tracking error and approximation error.

该方法应用"主导输入"的概念，同时考虑了函数逼近误差和系统外扰的存在，假设了该系统逼近误差和系统外扰有界但界未知的情况；并探讨了自适应模糊控制器的参数自适应律由跟踪误差和逼近误差共同进行调节。

It is proved that the"feedback linearization" certainty equivalence control law with"regressor vector-based"update law can guarantee the real output to track reference output in relative degree one case.

当控制对象的相对阶为1时，我们证明了采用"反馈线性化型"确定性等价控制律，和"基于回归向量"的自适应律，可以保证实际输出有界跟踪参考输出；当控制对象的相对阶大于1时，控制律和自适应律的结构保持不变，但是构造自适应律的信号采用了由跟踪误差得来的"增广误差"。

A new switching scheme to the gain of variable structure control signals is proposed. The following important open problems in standard VS-MRAC and MRAC are solved by using the scheme: 1 . a prespecified transient and steady-state performance index for tracking error can be achieved without requiring any information about the plant high frequency gain sign when relative degree of modelled part of plant is one, and 2 . it is shown that as long as the performance indexes are guaranteed for the auxiliary errors, each of which in dynamics is a sub-system with relative degree one, the tracing error will converge to a small residual set in a prespecified transient time when relative degree of modelled part of plant is greater than one.

提出了一种控制增益可切换的变结构自适应律，解决了如下变结构模型参考自适应控制（包括基于调参律的模型参考自适应控制）理论研究中长期没有解决的问题：当对象建模部分相对阶为1、高频增益符号未知且存在非线性输入扰动和未建模动态等情况下，系统跟踪误差可满足预先给定的动态和稳态性能指标；当对象建模部分相对阶大于1且存在非线性输入扰动和未建模动态时，可保证系统跟踪误差在预先给定的过渡过程时间内收敛到一个残差集中； 5。

First, we consider nonholonomic chained systems with modeling error, in this section,based on back-stepping , using the so-called adding a integrator , state-scaling technique , we design discontinuous feedback law,such that the trival solution of the closed-loop systems global strong stable; Second,we consider high-order nonholonomic chained systems with modeling errors and external disturbances, in this section,using input/state-scaling and integrator backstepping methods , we design discontinuous feedback law and give out the switching strategy, such that the closed-loop systems global /C-exponential stable; Finally, we consider a class of more general power chained form systems with particular drift-terms, in this section , using Lyapunov method, we design time-varying feedback law , such that the closed -loop systems p—exponential stable.

第一部分考虑的模型为带有模型误差的高阶非完整链系统，我们运用加幂积分器、State-scaling技巧以及基于Back-stepping方法构造出不连续反馈律，从而使得所讨论系统的闭环系统的平凡解全局强稳定；第二部分考虑的模型为带有模型误差的不确定高阶非完整链系统，这一部分我们运用input／state scaling和integrator backstepping方法构造出不连续反馈律，并给出切换策略，使得所对应的闭环系统全局κ-指数稳定；第三部分考虑的系统是形式更为一般的且带有特殊形式漂移项的幂链系统，利用Lyapunov函数方法，设计出时变反馈律，从而使得相应的闭环系统ρ-指数稳定。

First, according to the tracking error dynamics and kinematics described by unit quaternion error and angular velocity error, a sliding mode controller is derived based on Lyapunov theory.

首先根据由误差四元数和误差角速度描述的跟踪误差动力学和运动学方程，设计了基于李亚普诺夫方法的滑模变结构控制律。

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。