摘要
十多年来,人们对不确定非线性下三角系统通过状态反馈的设计方法做了许多工作,并取得了大量的成果。对于系统仅有部分状态或输出可测的情况,如何设计一个能够实现非线性系统全局渐进稳定的控制器,仅通过状态反馈的方法显然是不可能的。这种情况,对于线性系统来说,利用分离原理可以通过状态反馈控制器结合状态观察器来解决。但是分离原理对于非线性系统不再适用。在许多实际问题中,系统的所有状态均可测量且可用于反馈的假设往往是不现实的,故难以应用状态反馈控制律来对系统进行控制。有时即使系统的状态可以直接测量,但考虑到实施控制的成本和系统的可靠性等因素,如果可以用系统输出反馈来达到闭环系统的性能要求,则更适合于选择输出反馈的控制方式。因此,不确定性非线性系统的输出反馈镇定研究及其控制器设计具有重要的理论意义和实际应用价值。
本文针对一些可以利用微分几何的方法转化为下三角系统的不确定性系统,运用基于非辨识自适应的通用控制的思想设计输出反馈控制器,实现了不确定非线性系统的全局镇定。这个自适应系统的直接思想是只要系统输出不为零调节器就增加控制器增益,最终,控制器增益达到足够大,直至系统稳定。控制器增益被确定为单调非减。数值只是决定控制器增益的增长速度。因此,这种基于非辨识的通用自适应控制,解决了基于辨识的自适应不能处理不确定项有非线性属性的难题。
论文按照以下结构组织:
第一章:介绍所研究课题的背景知识,国内外相关研究状况和本课题研究的理论意义和实际应用,并说明本文的主要工作。
第二章:介绍论文所涉及的基础理论,包括基本概念、主要引理和重要不等式。具体说来,着重介绍了通用控制和通用输出反馈自适应调节的概念以及设计方法,Barbalat引理,Young不等式,以及几个论文中多次用到的引理和不等式。
第三章:研究了一类由不可测状态相互关联的m个子系统组成的不确定非线性关联系统,其子系统是下三角系统,带有未知参数,增长速率未知,满足线性增长条件,采用分散控制策略,通过设计一种通用输出反馈控制器,引入由估计误差驱动的动态增益,实现了经由通用输出反馈的全局分散控制。
第四章:研究了一类不确定项由一个有界光滑函数乘以一个未知常数来主导的非完整系统,采用State-scaling技术,把系统转化为下三角结构,应用通用输出反馈自适应调节的思想,引入了动态增益来处理未知参数和光滑函数对系统全局镇定的影响,通过构建一个降阶自适应观测器和一个非辨识输出反馈控制器实现了不确定非完整系统的全局自适应镇定。
第五章:对论文内容进行总结,并提出进一步研究的方向。
Over the past decades,tremendous progress has been achieved to control a class of nonlinear lower triangular systems with uncertainties via state feedback through a systematic design way.When only a part of the state or the output of the system is measurable,how to design the controller to globally asymptotically stabilize nonlinear systems becomes more realistic.In the case of linear systems,the separation principle allows output feedback problems to be solved by combining state feedback controller with state observers.However,the separation principle does not hold for nonlinear systems~([46]).In many practical problems,the assumptions that all states of the nonlinear systems can be measured and can be used in feedback design are often unrealistic, such that it is difficult to apply state feedback control law here.Sometimes,even if the states of the nonlinear systems can be measured directly,but taking into account the costs of the implementation and other factors,the output feedback control approach are adopted more,if it can achieve the stabilization of the closed-loop system.
This dissertation studies a class of nonlinear systems which can be transformed into the lower triangular systems,with the aid of the differential geometric approach~([3]).The intuitive idea behind this adaptive system is the tuner increases the controller gain as long as the output of the system is not zero,then eventually,the controller gain becomes sufficiently large and the system is stabilized.Performs has partially been determined offiine.Partially in the sense that it has been decided that the controller gain will be monotonically nondecreasing.The data only determine how fast the controller gain will indeed increase.In such a case,the idea of universal control to design adaptive control for the systems with a nonidentifier based tuner will address the problem which is hard to identify these unknown parameters,as the unknown parameters occur nonlinearly.
In our thesis contents are organized as follows:
In chapter 1,introduce the background of this topic,internal and overseas research situations, theoretical and Practical significance,the main contributions of this dissertation.
In chapter 2,introduce thesis involved basic theory,including basic concepts,the main lemma and inequality important.Universal control,universal adaptive regulation control,Barbalat's lemma,Young's inequality,and so on.
In chapter 3,for a class of large-scale uncertain nonlinear systems interconnected by the uncertain states.Each sub-system is a lower triangular system under linear growth conditions, with unknown parameters and unknown rate.We show that under linear growth conditions,there is a decentralized universal output feedback controller rendering the closed-loop system globally stabilization.Use global decentralized control approach,the introduction of dynamic gain which will be driven by the estimation error.
In chapter 4,for a class of nonholonomic uncertain systems in chained form,with uncertainties was dominated by a smooth function multiplied by an unknown constant.Using of the state-scaling~([78][79]) technique,we transform it into a lower triangular system.Using the idea from universal control,in order to deal with the unknown constant and smooth function,dynamic gains are introduced.Then the universal output feedback domination design is applied to design a reduced-order adaptive observer and an universal output feedback controller,such that all the state of non system can be regulated to zero.
In chapter 5,we summarize the dissertation and discuss open problems for future research.
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