【作者】 赵友刚；

【导师】 唐功友；

【作者基本信息】 中国海洋大学 ， 海洋信息探测与处理， 2008， 博士

【摘要】 在多数实际的控制系统中,由于或多或少的存在不确定的因素,建立系统被控对象的准确数学模型通常是不可能的。在控制系统中引入不确定性的数学模型可以更真实地描述实际控制过程和反映系统的参数摄动和外部扰动。因此,研究不确定系统的鲁棒稳定性和鲁棒控制问题无论在理论上还是在实际应用中,都有很重要的意义。本文研究不确定性系统的鲁棒稳定性及鲁棒控制问题。其中包括概括不确定性系统的模型分类及适用的研究方法;研究区间系统的鲁棒稳定性和鲁棒镇定,不确定时滞系统的保成本控制、不确定非线性时滞系统的非脆弱保成本控制以及非线性网络控制系统的保成本控制问题。主要研究内容和创新点概括如下:1.研究不确定系统的模型分类问题。首先描述了可参数化和非参数化不确定性模型及建模方法。然后给出了不确定性系统模型的分类方法和概括了不同类型的不确定性系统模型的表达形式,并分析了各类不确定系统的模型所适应的研究方法。2.研究区间系统的鲁棒稳定性问题。首先研究乘性区间线性系统的鲁棒稳定性,给出了若干单乘性区间线性系统鲁棒稳定性的充分必要条件和一个多乘性区间线性系统鲁棒稳定性的充分必要条件的猜想。然后研究多乘性和加性区间线性系统鲁棒稳定性,提出了多乘性和加性区间线性系统的鲁棒稳定性充分性判据。最后研究一类区间非线性系统的鲁棒稳定性,提出了鲁棒稳定性判据。3.研究区间系统鲁棒镇定问题。首先研究乘性区间线性系统的能稳性,给出了若干单乘性区间系统能稳的充分必要条件和多乘性及加性区间系统能稳的充分性判据。然后研究区间线性与非线性系统的鲁棒镇定控制器设计问题,提出了几类区间线性与非线性系统的鲁棒镇定控制器设计方法。4.研究不确定性系统的保成本控制问题。首先研究不确定性时滞非线性系统的保成本控制问题,给出了保成本控制律存在的充分条件和控制律的设计方法。然后对一类不确定非线性时滞系统,在控制器参数存在摄动的情况下,研究非脆弱保成本控制问题,给出了非脆弱保成本控制律的存在条件和非脆弱保成本控制器的设计方法。5.研究网络控制系统的保成本控制问题。首先对具有随机时滞的网络控制系统模型进行简化,导出了具有不确定系数的时滞离散时间系统模型。然后,针对导出了不确定时滞离散时间系统模型,给出了保成本控制律的存在条件和保成本控制器的设计方法。更多还原

【Abstract】 In most real engineering systems, it is almost impossible that the accurate mathematics model for the controlled plant is obtained since the uncertainty of the system is existent more or less. The uncertainty mathematics model may more factually describe the real control system and depict parameter perturbation and external disturbance of the system. Therefore, the research on robust stability and robust control for uncertain systems is significant in both theory and practice.This dissertation considers the problems of robust stability and robust control for uncertain systems. It is summarized that the model classification and suitable research methods of uncertain systems, robust stability and robust stabilization for interval systems, the guaranteed cost control of uncertain systems with time-delay, nonfragile guaranteed cost control for a class of uncertain nonlinear systems with time-delay, and the guaranteed cost control for nonlinear networked control system. The main contents and innovations in this paper are as follows:1. The model classification of uncertain systems is considered. We first describe the parameterized and non-parameterized uncertain modeles respectively, and sum up the modeling methods. Then the model classification method of uncertain systems is given and expressions are presented for different uncertain systems. And the research methods for different uncertain systems are analysed.2. The robust stability for interval systems is considered. We first study the robust stability for multiplicative interval systems. Some necessary and sufficient conditions of single-multiplicative interval systems are given, and a supposition necessary and sufficient condition of multi-multiplicative interval systems is presented. Then we consider the robust stability for interval systems. Some robust stability sufficient criteria are presented respectively. At last, we present a robust stability criterion of nonlinear interval systems.3. The robust stabilization for interval systems is considered. We first study the stabilizability for multiplicative interval linear systems. Some necessary and sufficient conditions of single-multiplicative interval systems are given, and some stabilizability sufficient criteria of multi-multiplicative and additive interval systems are presented. Then we consider the design problem of robust stabilization controller for interval linear and nonlinear systems. Some design algorithm of robust stabilization controller for interval systems are proposed.4. The guaranteed cost control problem for uncertain systems is considered. We first study the guaranteed cost control problem for uncertain time-delay nonlinear systems. Some existence sufficient conditions and design algorithm of guaranteed cost control law are given. For a class of uncertain nonlinear systems with time delay, with respect to perturbations in the controller coefficients, the nonfragile guaranteed cost control problem is considered, and the existence conditions and the design approach of nonfragile guaranteed cost control law are presented.5. The guaranteed cost control problem for networked control systems is considered. Firstly, the networked control system model with random time-delay is simplified and transformed into a discrete-time system model with uncertain parameters. Then the existence conditions and the design approach of guaranteed cost control law are presented based on the model educed.更多还原