【作者】 张宪福；

【导师】 程兆林；

【作者基本信息】 山东大学 ， 运筹学与控制论， 2005， 博士

【摘要】 本文研究了三角(下三角和上三角)结构非线性时滞系统镇定控制器的设计方法。在过去的十多年里,对于不带时滞的具有三角结构的非线性系统的状态反馈和输出反馈镇定问题的研究已经深入广泛地展开。但对于带时滞的具有三角结构的非线性系统的反馈镇定问题的研究仅是起步。熟知,对于不带时滞的具有三角结构的非线性系统,反步设计方法和前推方法是设计镇定控制器的有力工具。但是用这两种方法设计带时滞的具有三角结构的非线性系统的控制器则并非易事。此外,非线性系统的输出反馈控制研究的难点在于:1.缺乏比较系统的构造非线性状态观测器的方法,2.分离性设计原则不再适用。本文将首次给出一种有别于反步设计方法和前推方法的构造性方法,以设计带时滞的三角结构系统的镇定控制器,同时本文还给出了带时滞的三角结构系统的输出反馈控制器的非分离性设计方法。 本论文包括以下三章。 第一章回顾了时滞系统的基本理论、研究近况及未解决的问题,介绍了两种控制器的构造性设计方法:反步设计方法(backstepping)和前推方法(forwarding),这两种设计方法在三角(下三角和上三角)结构无时滞非线性系统的控制器设计中已得到广泛应用。 第二章研究了状态带有时滞的级联大规模下三角结构系统的递阶全局渐近镇定问题,构造性地给出了状态反馈和输出反馈控制器。本章构造的所有镇定控制器都是与时滞长度无关的。大规模系统是由若干个相互关联的子系统组成的一个整体系统。控制大规模复杂系统的基本方法是分散控制和动态递阶控制。总的思想是把大规模系统的控制分解为若干个独立子系统的控制,每个子系统的控制只使用子系统本身的信息或来自另外一个上层系统的信息。基于分散控制和反步设计方法,文献[1][2]给出了大规模下三角系统的状态反馈控制器。本文用到的方法与广泛应用于下三角系统设计的反步设计方法有很大的区别。对于下三角系统,早期文献[1][2][3][4][5]设计的镇定控制器的增益一般是比较高的,而过高的增益必然使系统瞬态响应的品质变坏。把本文给出的设计方法与传统的反步设计方法相比较,本文得到的控制器的增益是比较低的,设计程序更加简单有效,这主要是因为,本文的设计避开了反步设计算法中随着迭代步数增加,控制增益快速增加的反步迭代过程。 2.1节与2.2节分别研究了大规模级联非线性时滞下三角系统的动态递阶状态反馈镇定问题与输出反馈镇定问题。系统的非线性项不仅含有输出的多项式函数,而且更多还原

【Abstract】 In this dissertation, the controller design of triangular (lower triangular and upper triangular) structural nonlinear time-delay systems is researched. Asymptotic stabilization by state and output feedback of triangular structural nonlinear systems in the absence of delay has been studied by many researchers during the last decade. While the progress of asymptotic stabilization by state or output feedback of triangular structural nonlinear time-delay systems seems less significant. It is well known that the backingstepping method and the forwarding method are powerful tools to design the stability controllers for triangular system without delay. But, it is not easy to apply them designing stability controllers for triangular system with delay. It is also well known that output feedback control is a hard problem for nonlinear systems because of the lack of systematic approach for designing nonlinear observers and the failure of separation principle which may make observers not applicable for output feedback design. For the first time, this dissertation provides systematically alternative constructive control techniques instead of the backingstepping method or the forwarding method to design stability controllers for triangular system with delay, and proposes nonseparation principle paradigms in designing output feedback control for triangular systems with delay.There are three chapters in this dissertation.In Chapter 1, we review some fundamental theories of time-delay systems and the background of time-delay systems, point out some open problems in this field, and introduce two constructive methods (backstepping and forwarding) which have been widely applied in designing controller for the triangular (lower-triangular and upper-triangular) structural nonlinear systems without delay.In Chapter 2, we study the problem of global stabilization for large-scale lower-triangular systems with delays in the state. It is provided constructively state feedback controller and output feedback controller for such systems. All controllers given in Chapter 2 are delay-independent. Large-scale systems are comprised of several interconnected subsystems. The fundamental approaches for the control of large-scale complex systems are decentralized control and dynamical hierarchial control. They decompose the control of large-scale systemsas a set of independent control of subsystems, which can only access the local information or the information of a high-level auxiliary system. Based on the decentralized control and the backstepping method, it was constructed the state feedback controller for large-scale lower-triangular systems in [1][2]. While the method used here is quite deferent from the backstepping method, which is widely used in dealing with lower triangular system. For lower triangular systems, the gains of stabilizing controller given by many people (see[1][2][3][4][5]) are very high, and the high gains may make the system cause a undesirable transient behavior. Comparing our design schemes proposed here with the backstepping method, the gains of our controllers are lower and the design procedures are much simpler and more efficient because no recursive computation is involved here.In section 2.1 and section 2.2. constructive control techniques have been proposed for controlling large-scale nonlinear lower triangular systems with delayed state interconnections using state feedback and output feedback, respectively. The uncertain nonlinearities are assumed to be bounded not only by polynomial functions of the outputs, but also by polynomial functions of the states or delayed states. The nonlinear systems considered in section 2.1 are more general than conventional lower triangular systems (see[3][4][5][6][7]), and they could be viewed as generalized lower triangular systems. Based on the use of a memoryless hierarchial high gain controller (or, the use of a memoryless hierarchial high gain observer in combination with a memoryless hierarchial high gain controller) and choosing appropriate Lyapunov-Krasovskii functionals (LKF), the delay-independent hierarchial state (or output) feedback controller achieving global asymptotic stabilization of the large-scale nonlinear time delay systems is explicitly constructed. The hierarchial state (or output) feedback controller includes a high-level subsystem with all states (or outputs) of the large-scale systems as its input and a low-level subsystem whose gains are from high-level subsystem. For the first time, the approaches are proposed to design the stabilizing controller for large-scale nonlinear lower-triangular systems with delays in the state. Simulation examples are given in every section of Chapter 2 to demonstrate the effectiveness of the proposed design procedure.In Chapter 3, we study the problem of global stabilization for a class of nonlinear systems with delays in the input or output. All controllers given in Chapter 3 are delay-dependent. The nonlinear systems considered here are more general than the upper-triangular systems widely considered in many papers (see [8] [9] [10] [11]). Hence our nonlinear systems could be viewed as generalized upper triangular systems. Asymptotic stabilization by state feedback of upper triangular system in the absence of delay has been studied by many researchers (see [12][13][14][15]). However, the stabilization of upper triangular systems with delays in the input or output has not been fully investigated, and few paper has considered the problem of the output feedback stabilization for such systems. In this paper, Based on the constructingappropriate LKF and applying the model transformation of time-delay systems, we shall propose constructive control techniques for controlling upper triangular nonlinear systems with delays in the input or output. The designed controllers have a very simple structure and do not involve any saturation or recursive computation, which are widely applied in designing control of upper triangular systems. By using the transformation of coordinates and the property of Hurwitz polynomial, the problem of designing controller can be converted into the problem of finding a parameter, which can be solved by solving optimization problem with linear matrix inequalities (LMIs) constraints. This is the main idea of the proposed design methods. All LMIs in this chapter always have solutions. Hence, the proposed design approach is quite different from the existed LMIs design method (see [14][16][17][18][19]). in which the sufficient condition for the existence of controller is always given in terms of LMIs. Therefore, the methods proposed here are all constructive methods.In section 3.1. section 3.2 and section 3.3, it is considered the state feedback stabilization of upper triangular nonlinear systems with delays in the input, output feedback stabilization of upper triangular nonlinear systems with delays in the input, and output feedback stabilization of upper triangular nonlinear systems with delays in the output, respectively. Examples are given in every section of Chapter 3 to illustrate the effectiveness of the proposed method.更多还原