高会军博士论文.pdf

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文摘

英文文摘

论文说明：符号与缩写

第1章绪论

1.1不确定系统研究的背景及意义

1.2不确定系统研究的主要方法

1.2.1多项式代数方法

1.2.2μ理论方法

1.2.3基于状态空间的时域方法

1.3参数依赖Lyapunov稳定性研究的意义

1.4参数依赖Lyapunov稳定理论的发展及研究现状

1.5本论文的主要研究内容

1.5.1基于参数依赖Lyapunov函数的鲁棒稳定及性能分析

1.5.2基于参数依赖Lyapunov函数的状态反馈镇定及H∞控制

1.5.3基于参数依赖Lyapunov函数的鲁棒滤波问题研究

1.5.4基于参数依赖Lyapunov函数的模型降阶理论

1.5.5基于参数依赖Lyapunov函数的汽车主动悬架的多目标控制

1.6论文涉及的系统和控制中几个重要问题的研究背景

1.6.1鲁棒滤波研究

1.6.2时滞系统研究

1.6.3 2D系统研究

1.6.4模型降阶研究

第2章参数依赖Lyapunov稳定条件及性能准则

2.1有代表性的研究成果

2.2新的参数依赖Lyapunov稳定条件

2.2.1连续系统的参数依赖Lyapunov稳定条件

2.2.2离散系统的参数依赖Lyapunov稳定条件

2.2.3数值算例

2.3参数依赖有界实引理

2.3.1基本问题描述

2.3.2连续系统的参数依赖有界实引理

2.3.3离散系统的参数依赖有界实引理

2.3.4数值算例

2.4本章小结

第3章时滞系统的参数依赖Lyapunov稳定条件

3.1不确定连续时滞系统的参数依赖鲁棒稳定条件

3.1.1问题描述

3.1.2主要结果

3.1.3讨论

3.1.4数值算例

3.2不确定离散时滞系统的参数依赖鲁棒稳定条件

3.2.1问题描述

3.2.2主要结果

3.2.3与已有结果的关系

3.2.4数值算例

3.3本章小结

第4章不确定系统的镇定及H∞控制

4.1鲁棒状态反馈控制器设计

4.1.1鲁棒镇定状态反馈控制器设计

4.1.2鲁棒H∞状态反馈控制器设计

4.2参数依赖状态反馈控制器设计

4.2.1参数依赖镇定控制器设计

4.2.2参数依赖H∞控制器设计

4.3本章小结

第5章不确定系统的Kalman滤波

5.1问题描述

5.2连续系统的Kalman滤波

5.2.1主要引理

5.2.2参数依赖Kalman滤波

5.2.3鲁棒Kalman滤波

5.3离散系统的Kalman滤波

5.3.1主要引理

5.3.2参数依赖Kalman滤波

5.3.3鲁棒Kalman滤波

5.4应用算例

5.5本章小结

第6章时滞不确定系统的鲁棒H∞滤波

6.1连续时滞不确定系统的鲁棒H∞滤波

6.1.1问题描述

6.1.2滤波误差分析

6.1.3滤波器设计

6.2离散时滞不确定系统的鲁棒H∞滤波

6.2.1问题描述

6.2.2滤波误差分析

6.2.3滤波器设计

6.3多时滞不确定系统的鲁棒H∞滤波

6.3.1连续情形

6.3.2离散情形

6.4应用算例

6.5本章小结

第7章不确定2D离散系统的鲁棒H∞滤波

7.1基于FM模型的2D离散系统的鲁棒H∞滤波

7.1.1问题描述

7.1.2滤波器设计

7.1.3应用实例

7.2基于Roesser模型的2D离散系统的鲁棒H∞滤波

7.2.1问题描述

7.2.2滤波器设计

7.2.3应用实例

7.3本章小结

第8章不确定系统的H∞模型降阶

8.1问题描述

8.2主要结果

8.2.1连续系统

8.2.2离散系统

8.3不确定2D离散系统的H∞模型降阶

8.3.1问题描述

8.3.2主要结果

8.4应用实例

8.5本章小结

第9章汽车主动悬架的多目标控制

9.1引言

9.2主动悬架控制的数学描述

9.3多目标问题的求解

9.4设计实例

9.5本章小结

结论

参考文献

攻读博士学位期间所发表的学术论文

哈尔滨工业大学博士学位论文原创性声明及哈尔滨工业大学博士学位论文使用授权书

致谢

个人简历

摘要......曰口........巨........曰日.....口.口......摘要在航空、航天以及工业生产过程等领域，被控对象的动态特性一般都难以用精确的数学模型来描述，使得用于描述被控对象的数学模型和实际对象之间总是不可避免地存在着误差。因此，不确定系统的研究长时间以来一直受系统和控制领域广大学者的普遍关注。发展了近三十年的鲁棒控制理论在解决参数不确定系统的分析与综合问题时大多建立在二次稳定概念基础之上。因其对于整个不确定区域，使用一个公共的Lyapunov函数，因而不可避免地具有较大的保守性，在很大程度上限制了普棒控制理论的进一步发展及其在实际工程中的应用。参数依赖Lyapunov稳定性及在此基础之上的分析与综合问题是近年来替棒控制领域的前沿研究课题。本论文在总结前人工作的基础上，系统、深入地研究了基于参数依赖Lyapunov函数的凸多面体不确定连续和离散时间系统的稳定性及性能分析、状态反馈控制器综合、滤波器设计以及模型降阶等问题，以一个统一的框架提出了不确定动态系统基于参数依赖Lyapunov函数的分析与综合方法，并将部分理论研究成果应用于汽车主动悬架的多目标控制。第1一章首先系统地分析和总结了参数依赖Lyapunov稳定性这一前沿研究领域的主要成果，指出目前以在不确定区域内固定所引入的附加松驰矩阵变量为代价，从而获得参数依赖Lyapunov函数的方法在降低保守性和处理复杂系统及复杂问题方面的局限性。在此基础上，提出了获得参数依赖幼apunov函数的新思路和新的处理手段，给出了凸多面体不确定连续和离散时间系统新的鲁棒稳定条件及H性能准则。并将这一思想进一步推广，研究了以网络控制系统为典型背景的时变时滞不确定连续和离散时间系统的鲁棒稳定性问题，提出了荃于参数依赖Lyapunov函数的时滞相关鲁棒稳定条件。所提出的稳定条件及性能准则与目前这一领域的主要研究成果相比，因其不再要求对于整个不确定区域存在公共的矩阵变量，因而在降低保守性方面具有较大的潜力. 第4章研究了凸多面体系统墓于参数依赖Lyapunov函数的状态反馈镇定及H.控制问题。根据系统的不确定参数是否可以在线获得，分别提出了鲁棒和参数依赖状态反馈控制两种解决方案。首先给出了基于参数依赖Lyapunov函数的不确定连续和离散时间系统的鲁棒和参数依赖状态反馈镇定控制器的-I-

哈尔滨工业大学工学博士学位论文设计方法，将控制器的存在条件转化为一组线性矩阵不等式的可解性问题。在此基础上，解决了具有闭环H,性能指标约束时的控制器设计问题。在问题的解决中充分融入了参数依赖稳定思想，保证了所提出的设计方法具有较低的保守性。第5-7章基于参数依赖功apunov稳定思想，研究了在导航等领域具有较强工程背景的、与控制相对偶的滤波问题。首先针对经典的Kalman滤波理论无法应用于不确定系统这一问题，提出了基于参数依赖Lyapunov函数的不确定连续和离散时间系统的Kalman滤波器设计方法。根据不确定参数是否可以在线获得，分别提出了鲁棒和参数依赖滤波两种解决方案。在此基础上，研究了时变时滞不确定连续和离散时间系统的鲁棒H滤波问题。所设计的髻棒H滤波器能够保证对于所有允许的不确定参数及状态时滞，滤波误差系统稳定且具有一定的H.扰动衰减性能。所提出的滤波器设计方法即融入了参数依赖稳定思想，又与系统中时滞的信息相关;不仅适用于具有固有时滞的系统，还适用于具有测全信号传输延时的系统。此外，第7章研究了在信号处理、热能工程等领域具有较强应用背景的2D离散系统的鲁棒几滤波问题。分别基于不确定2D FM和Roesser模型，提出了基于参数依赖Lyapunov函数的鲁棒H浦波器设计方法。本论文在滤波方面的研究成果就设计的保守性而言明显优于Geromel. Tuan及Me等国际知名学者所取得的最新研究成果。第8章研究了不确定动态系统的模型降阶问题。基于参数依赖Lyapunov稳定思想，提出了多面体系统满足H误差性能要求的低阶多面体模型的构造方法。首先基于矩阵的全等变换及变量替换，将多面体连续时间系统的模型降阶问题转化为基于线性矩阵不等式的凸优化求解问题。其次针对1D和2D离散时间系统，采用锥补线性化思想将H.模型降阶问题转化为受线性矩阵不等式约束的序列最小化问题。在问题的求解中充分融入了参数依赖稳定思想，这是首次尝试将参数依赖Lyapunov稳定思想扩展应用到不确定系统的模型降阶问题的解决中。第9章将第4章提出的参数依赖状态反馈控制器设计方法应用于汽车主动悬架的振动控制。首先在分析汽车主动悬架的基本功能的荃础上，将主动悬架的振动控制在数学上表述为一个凸多面体系统的多目标控制问题。鉴于系统模型中的车身质It参数可以实时测>t，提出了参数依赖状态反馈控制策略。将主动悬架的多目标控制器的设计转化为受线性矩阵不等式约束的凸优化问题。仿真实例验证了所提出的控制策略的可行性及在改善乘坐舒适度方面的优越性。这一部分是参数依赖切apunov稳定思想向实际工程问短的尝试-n-

摘要...........目.曰口巴性应用，进一步拓展了参数依赖Lyapunov稳定理论，同时又为工程实际研究人员提供了可以借鉴的设计思想。关健词参数依赖Lyapunov稳定;鲁棒控制和滤波:模型降阶;主动悬架的振动控制:线性矩阵不等式-m-

哈尔滨工业大学工学博士学位论文Abstract In aerospace, astronautics and industrial process, it is usually difficult tocharacterize the dynamics of the controlled object exactly by a mathematicalmodel, which renders inevitable error to exist between the derived mathematicalmodel and the practical object. Thus, study on uncertain systems has long drawnmuch attention from researchers working in systems and control areas. Robustcontrol theory, originating from 1970s, generally solves analysis and synthesisproblems for parameter uncertain systems based on the notion of quadratic sta-bility. Due to its utilization of a common切apunov function for the entire uncer-tainty domain, quadratic stability has been well recognized to be conservative,which prevents robust control theory from further development and limits its ap-plications in practical engineering to a great extent. Parameter-dependent切apunov stability and its related analysis and synthesis problems are researchfrontiers in robust control theory. This thesis, based on previous works of others,systematically and deeply investigates the problems of stability and performanceanalysis, state-feedback controller synthesis, filter design and model reductionfor polytopic uncertain systems in both continuous- and discrete-time cases basedon parameter-dependent切apunov functions, and presents analysis and synthesismethodologies for uncertain dynamic systems in the unified parameter-dependentframework. Part of the developed theories is applied to the multi-objective con-trol of vehicle active suspension systems. Chapters 1-3 first summarize and analyze the main results in the frontiers ofparameter-dependent切apunov stability, and point out that the method com-monly used for achieving parameter-dependent Lyapunov functions at the ex-pense of setting additionally introduced slack matrices to be constant for the en-tire uncertainty domain has limitations in reducing conservativeness and dealingwith complex systems and complicated problems. Based on this, new idea andmethodology are proposed for achieving parameter-dependent Lyapunov func-tions, with new stability and H. performance conditions presented for polytopicuncertain systems in both continuous- and discrete-time cases. This idea is fur-一W一

Abstractther extended to investigate the stability of uncertain time-varying delay con-tinuous- and discrete-time systems typified by networked control systems, withnew delay-dependent stability conditions derived based on the parame-ter-dependent stability idea. Compared with the main results in this area,山e sta-bility and performance conditions proposed in these chapters are significantlyless conservative due to their avoidance of setting any matrix to be constant forthe entire uncertainty domain. Chapter 4 investigates the problems of stabilization and H control forpolytopic uncertain systems based on parameter-dependent Lyapunov functions.According to the online availability of uncertain parameters, two control strate-gies, namely robust and parameter-dependent state-feedback controls, are pro-posed to solve these problems. A method is first proposed for designing stabiliz-ing controllers of both strategies, which converts the existence condition of ad-missible controllers into the feasibility of convex problems subject to linear ma-trix inequalities (LMls). Based on this, the controller design problem withclosed-loop几performance constraint is also solved. The parameter-dependentstability idea is fully utilized in solving these problems, guaranteeing the lessconservativeness of the proposed controller designs. Chapters 5-7 are concerned with the filtering problem which is dual to con-trol and has strong application backgrounds in the areas like navigation. Aimingat the non-applicability of the classical Kalman filtering theory to uncertain sys-tems, Chapter 5 proposes Kalman filter design methods for uncertain continuous-and discrete-time systems on the basis of parameter-dependent Lyapunov func-tions. Similar to the control problem considered in Chapter 4, according to theonline availability of uncertain parameters, two filtering strategies, namely robustand parameter-dependent filtering, are proposed. Based on this, Chapter 5 studiesthe problem of designing robust H filters for uncertain time-varying delay sys-tems in both continuous- and discrete-time cases. The designed H} filter canguarantee the filtering error system to be asymptotically stable and have a pre-scribed H disturbance attenuation performance for all admissible uncertain pa-rameters and state delays. The proposed filter design methods are not only de-pendent of the uncertain parameters in the sense of utilizing parameter-dependentLyapunov functionais, but also dependent of the a priori information of delays.-v-

哈尔滨工业大学工学博士学位论文They are not only applicable to systems with inherent delays, but also applicableto systems with signal transmission delays. Moreover, Chapter 7 considers therobust H. filtering problem for 2D discrete systems which have strong applica-tion backgrounds in signal processing and heat energy engineering etc. Proce-dures for designing robust几filters are proposed for both uncertain 2D FM andRoesser models based on parameter-dependent Lyapunov functions. The filteringresults presented in this thesis have surpassed the most recent works by Geromel,Tuan and Xie et al, the world renowned scholars in this specific area, concerningconservativeness. Ch叩ter 8 focuses on the problem of model reduction for uncertain勿namicsystems. Based on the parameter-dependent Lyapunov stability idea, this chapterproposes methods for constructing a reduced-order polytopic system to approxi-mate a given polytopic one with guaranteed H. error performance. For the con-tinuous-time case, this problem is converted into a convex optimization problemsubject to LMls based on congruence transformations and matrix variableschanges. Moreover, the cone complementarity linearization idea is utilized to castthe model reduction problems for both 1D and 2D discrete-time systems intoLMI-based sequential minimization problems. Solving these problems have madefull use of the parameter-dependent stability idea, which represents the first at-tempt to extend the parameter-dependent stability idea to model reduction prob-lems for uncertain systems. The last chapter applies the idea of designing parameter-dependent control-lers developed in Chapter 4 to vibration control of vehicle active suspension sys-tems. By analyzing the basic functions of vehicle active suspensions, the vibra-tion control for these systems is mathematically translated into a multi-objectivecontrol problem for polytopic uncertain systems. Considering that the parameterof body mass can be measured online, we propose state-feedback control strategyvia parameter-dependent controllers. The multi-objective controller design prob-lem is then cast into a convex optimization problem with LMI constraints. Asimulation design verifies the validity of the control strategy and its advantage inimproving ride comfort. This part constitutes an attempt of applying the parame-ter-dependent Lyapunov stability idea to practical engineering problems, whichextends the parameter-dependent Lyapunov stability theory and provides a design_VI_

人七3廿日Ctexample forengineers，reference as well.Key words Parameter-dependent Lyapunov stability; Robust control and filter- ing; Model reduction; Vibration control for active suspensions; Linear matrix inequality-vu-

哈尔滨工业大学工学博士学位论文符号与缩写1D2DLMICCL8x(t)传递函数T(约兄Erdiag{从，从，…，戈}sym(A)IRhR月民加XTX-'Xu2X>_0X>0XlXR(1D连续)一维(One Dimensional)二维(Two Dimensional)线性矩阵不等式(Linear Matrix Inequality)锥补线性化(Cone Complementarity Linearization)对于连续系统指-(t)对于离散系统指x(t十1)对于连续系统指T(s)对于离散系统指T(a)指向量又全以，一，A)属于集合r,r---0{(^，一、:,t, =1, .ii·。}由NNZ,...,N组成的块对角矩阵A十AT单位阵N维实Euclidean空间nxm矩阵集合矩阵X的转置矩阵X的逆对于矩阵X二XT >_ 0，矛1z丫12=X对称半正定矩阵对称正定矩阵矩阵X的直交补:对于秩为k的矩阵XER",Xl定义为秩为(m一k)且满足XlX二0的矩阵矩阵X的Moore-Penrose逆矩阵X的满秩因子，即戈瓜二X向量x的Euclidean范数信号{·(，)，的、范数，。p(f}·(t)}’，)inRA (8x(1)12 dt)X+x’，lxl风

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