【作者】 岳红云；

【导师】 李俊民；

【作者基本信息】 西安电子科技大学 ， 应用数学， 2014， 博士

【摘要】 近些年来,由于被控对象和控制目标越来越复杂,逐渐建立起来很多新的控制理论.对于复杂非线性系统的控制问题现在比较有效的控制方法仍然是模糊控制方法.另外,由于该控制理论的不断发展,人们越来越关注其在实际生活生产中的应用.在现有的模糊控制理论中,模糊逻辑系统(FLS)控制方法越来越多的受到诸多学者的关注.而对于该类控制方法而言其主要优点在于可以运用专家学者的先验知识来研究非线性系统的稳定性以及控制器设计问题.但是运用该方法的劣势在于由于模糊逻辑系统本身的特点造成了没有系统的稳定性理论分析方法,这也是使用模糊逻辑系统控制方法的挑战性所在.另一方面,在控制器设计过程中随着模糊规则数的增加使得在线调节的参数也不断的增大,所以对于实际的工业系统而言在控制器的设计过程中减小调节参数个数也是极其有必要的.另外,在实际系统中时间延时是造成系统不稳定的主要因素之一,在本文中针对具有离散或者分布时变时延的非线性系统,设计出有效的模糊自适应控制器.同时为了减小系统的运算负担所提控制器含有较少自适应参数.具体来说我们取得了以下研究成果：1.基于合理的假设,采用合适的Lyapunov-Krasovskii泛函处理系统中的未知时变时滞项,同时运用FLS逼近系统中的未知非线性连续函数,另外采用Nussbaum类型的函数探测系统的控制方向,最后基于backstepping技术分别对具有离散时间延时和未知控制方向的非线性系统以及具有分布时间延时和未知控制方向的非线性系统设计状态反馈模糊自适应跟踪控制器.同时,控制器中含有较少的自适应参数,从而使得控制器的运用更加方便有效.2.基于合理的假设和线性状态观测器,运用适当的Lyapunov-Krasovskii泛函, Nuss-baum类型的函数,最小学习参数(MLP)算法, FLS以及backstepping技术分别对具有未知控制方向的时变时延系统和具有未知控制方向以及输入时延的非线性系统设计出有效的模糊自适应输出反馈控制器.值得一提的是,在控制器设计之前通过一个线性变换将分散在系统中的未知控制系数整合到一个系数中去,从而变为对比较常见的只有一个未知控制方向的系统的输出反馈控制问题的研究,且值得注意的是控制器中含有较少待估参数.3.运用恰当的Lyapunov-Krasovskii泛函,动态面控制(DSC)技术, MLP算法, FLS以及backstepping技术分别针对具有未知死区的时变时延非线性系统和具有输入时延的MIMO非线性系统设计出含有较少待估参数的模糊自适应控制器.值得指出的是DSC技术的选用有效的避免了采用backstepping技术产生的“参数爆炸”问题,从而有效地简化了控制器设计过程.另外控制器中含有非常少的自适应参数(1个或2个)极大地减少了在线运算量.4.现有研究随机非线性系统跟踪控制器结果大多是利用四次Lyapunov函数或者是结合传统的二次Lyapunov函数和风险灵敏度准则处理问题.而在本文中作者引进双曲正切函数处理Ito微分产生的高阶Hessian项,再结合传统的二次Lyapunov函数、backstepping技术以及FLS为具有时变时滞的随机非线性系统设计出有效的模糊自适应跟踪控制器.更多还原

【Abstract】 In recent years, many new control theories have been gradually established because ofthe controlled plants and the control objectives becoming more and more complex. For thecontrol problem of the complex nonlinear systems, the much more effective control methodis the fuzzy control technology. Moreover, the applications of the fuzzy control theory in theactual production and daily life has been concerned with its development. In the existing fuzzycontrol theory, the fuzzy logic systems(FLS) control method receives more and more attentionfrom the scholars. The main advantage of the method is that it can combine some experienceand knowledge from designers or experts to investigate the stability and the controller designproblem of the nonlinear systems. However, the main disadvantage of the method is that due tothe characteristic of the FLS such that there is no systematic stability theory analysis method,and this also is the challenging of the use of the FLS control method. On the other hand, duringthe controller design process, the number of the adjusted parameters depends on the number ofthe fuzzy rule bases. With an increase of fuzzy rules, the number of parameters to be estimatedwill increase significantly, therefore, for the actual industrial systems, during the controllerdesign process, it is extremely necessary to design the controller containing much less adjustedparameters. In addition, in the practical systems, the time delay is one of the main factorswhich make the system unstable. In this dissertation, the effective adaptive fuzzy controllersare proposed for the nonlinear systems with discrete or distributed time-varying delays. And inorder to reduce the online computation burden of the systems, the proposed controllers containmuch less adjusted parameters. Specifically, we obtain the following research results.1. Based on the reasonable assumptions, by utilizing the appropriate Lyapunov-Krasovskiifunctional, the FLS and the Nussbaum-type functions to deal with the unknown time-varyingdelay terms, approximate the unknown nonlinear continuous functions and detect the controldirections of the systems, respectively, finally, for the nonlinear systems with discrete timedelays and unknown control directions and the nonlinear systems with distributed time delaysand unknown control directions, the adaptive fuzzy tracking controllers are designed by usingthe backstepping technique. Moreover, the proposed controllers contain much less adjustedparameters such that the use of the controllers are much more convenient and effective.2. Based on the reasonable assumptions and the linear state observer, for the time-varyingdelay nonlinear systems with unknown control directions and the nonlinear systems with inputdelay, the output feedback adaptive fuzzy controllers are proposed by combining the properLyapunov-Krasovskii functional, the Nussbaum-type functions, the minimal learning parame-ters (MLP) algorithm, the FLS and the backstepping technique. It is should be pointed out thatbefore the controllers are designed, we introduce a linear state transformation, through which the unknown control coefficients distributed in the system can be lumped together, then, theproblem is become that how to design the output feedback controllers for the relatively com-mon systems with only one unknown direction, and it is worth noting that the controllers containmuch less adjusted parameters.3. For the nonlinear time-varying delay systems with unknown dead zone and the MIMOnonlinear system with input delays, the adaptive fuzzy controllers which contain much lessadjusted parameters are constructed by combining the proper Lyapunov-Krasovskii functional,the dynamic surface control (DSC) technique, the MLP algorithm, the FLS and the backsteppingtechnique. It is should be pointed out that the use of the DSC technique effectively overcomethe“explosion of complexity” cased by the use of the backstepping technique, therefore, thecontroller design process is simplified effectively. Moreover, the controllers contain very fewadaptive parameters (one or two) such that the online computation burden is reduced greatly.4. Most of the existing results investigating the tracking control problem of the stochasticnonlinear systems are obtained by using the quartic Lyapunov functions or by combining theclassical quadratic functions with the risk-sensitive cost criterion. However, in this dissertation,the hyperbolic tangent functions are introduced to deal with the Hessian terms which comefrom the Ito differential, and then, by applying the classical quadratic functions, the backstep-ping technique and the FLS, the effective fuzzy adaptive tracking controller is designed for thestochastic nonlinear time-varying delay system.更多还原