The proposed approach overcome the disadvantages which the neural network need learning off - line before using as a controller and lack of real - time and can not guarantee stability of the system , hi order to eliminate the extern disturbance and approximation error of network , the controller design combine with robust control approach and the system possess robustness 基于lyapunov稳定性理论，推导出了神经网络权值在线学习规律，保证了系统的全局稳定性，同时，为了消除或减小外部干扰以及神经网络逼近误差，在控制器设计时结合了鲁棒控制方法，使得系统具有一定的鲁棒性。
The mrafc scheme employs a reference model to provide closed - loop performance feedback for generating or modifying a fuzzy controller ' s knowledge base . the adaptive compensation term of optimal approximation error is adopted . by theoretical analysis , the closed - loop fuzzy control system is proved to be globally stable , with tracking error converging to zero 该方案利用参考模型作为闭环系统的反馈信号来产生、调节模糊控制器的规则库，并通过引入最优逼近误差的自适应补偿项来消除建模误差的影响，不但能保证闭环系统稳定，而且可使跟踪误差收敛到零。
The relation of radius of curvature and error as well as formulas of increasing parameters on condition of constant error are diverted . the equation of the line on the center of approximate circular arc is obtained ， and it can avoids the trouble that numerical solution owns possibility of no convergence and simplifies node calculation of non - circular curve 导出了曲率半径与逼近误差之间的关系和等误差条件下的参数递推公式，建立了通过逼近圆弧圆心的直线方程和圆心坐标计算公式.按这种方法用圆弧逼近平面参数曲线，不需要求解非线性方程组，避免了计算可能不收敛的麻烦，简化了非圆曲线的节点计算过程
With energy method , we can conveniently control the precision of the objective surface and add boundary constraints for preserving the model ' s global geometric continuity , but this method is very time - consuming . stiffness adjustment is the easiest method to be implemented and the fairing result is always satisfying except that the acquired surface editing is awkward . based on wavelets decomposition , the surface model ' s data size can be compressed efficiently and this method is running fast , however , the error and boundary constraints are difficult to be considered 其中基于能量原理的光顺方法能够方便地控制目标曲面的精度和边界条件，从而能够实现曲面模型的全局连续性，但是能量法的运算速度还有待提高；刚度调整法实现简单，但是生成的曲面的可编辑性较差；小波分解方法计算速度很快，能够有效地实现数据压缩，但是其逼近误差和边界条件却难于控制。
Firstly , based on backstepping and the supervisory control strategy , a robust adaptive fuzzy controller is designed for a class of nonlinear systems . the first type fuzzy logic system is used to approximate the unknown part of the process . the adaptive compensation term of the optimal approximation error is adopted 本文首先针对一类不确定非线性系统，基于backstepping方法，利用监督控制，引入最优逼近误差的自适应补偿项，并利用型模糊逻辑系统逼近系统的未知部分，提出了一种鲁棒自适应模糊控制器设计方案，运用李亚普诺夫第二方法，先证明了闭环模糊控制系统全状态有界，再证明了跟踪误差收敛到零。
Because the extension of dynamic change in weak nonlinear system is not large , the robust reliable controller designed by ldi can make the whole controlled system stable when time lag and faults exit in the system , at the same time , satisfying robust performance index of the system . next , considered that the approximation error produced by ldi , the unmodeling error produced by system , the parameter uncertainties and the external disturbances can not be ignored , a dynamic neural network controller is designed to compensate their effect on line . adjusted by the state output error between the ideal model and the controlled system , the cooperation of on - line network compensator and linear h _ ( ) controller of ideal model makes the whole close - loop system guar antee robust stability and track the specified signal well 本文在基于线性微分包含( ldi )的技术基础上，提出了两种非线性系统的鲁棒控制方法，首先讨论了一类弱非线性时滞控制系统中的鲁棒可靠控制器设计问题，由于弱非线性系统本身的动态变化范围不大，在确保整个系统鲁棒性能指标的前提下，当系统存在时滞和故障时，通过ldi设计出的鲁棒可靠控制器可以镇定整个被控系统；其次，在考虑运用ldi技术产生的逼近误差、系统本身的未建模误差及参数不确定性以及外部扰动的影响不能被忽略的情况下，设计了在线补偿这部分影响的动态神经网络控制器，在理想模型和被控系统状念输出误差的调节作用下，在线神经网络补偿器与理想模型的线性h _控制器相互配合，使得整个闭环系统既可以保证鲁棒稳定性又能够跟踪给定的指令信号。
Adaptive bounding technique is used to deal with unknown boundedness of approximation errors . the arbitrary output tracking accuracy is achieved by tuning the design parameters . thirdly , based on the results in chapter 3 , two design approaches of adaptive iterative learning control ( ailc ) are proposed for two classes of parametric nonlinear time - delay systems 神经网络用于逼近未知的非线性时滞函数，当状态不可测时，采用时滞滤波器估计系统状态，利用backstepping技术设计权值自适应律和控制律，占优化方法处理时滞基函数，自适应界化技术处理逼近误差的未知上界，通过调节设计参数可以实现对目标轨线任意精度的跟踪。
In this approach , the neural network is used to learning the nonlinear function of the system . the network weights are derived using lyapunov - based design and are adapted on - line . due to the existence of neural network approximation error and external disturbance , the sliding mode control which is insensitive to disturbance and parameter pertabation is used to achieve robust tracking for the system 该方法利用神经网络学习系统中的非线性函数，神经网络的权值由lyapunov稳定性理论导出，并且在线调整；考虑到网络逼近误差和外部干扰的存在，文中利用滑动模态对参数和扰动不敏感的特点，实现了系统的鲁棒输出跟踪。
