摘要
时滞是工程实际系统中普遍存在的现象,且是导致系统不稳定的一个主要因素,从而成为控制理论界广泛关注和近年来研究的重点之一。特别地,中立型时滞系统已逐渐成为控制领域的一个热点,并且日益受到人们的关注;此类时滞系统不但包含过去的运动状态,还包含过去运动状态的微分信息。然而对中立型系统的研究相对滞后,这主要是由于中立型泛函微分方程中差分算子较难处理,致使此类方程解的形式十分复杂。鉴于中立型系统是一类广泛存在于工程实践中的时滞系统,因此对其研究具有重要的理论需求和应用价值。本文着重探讨了不确定中立型系统的反馈控制与滤波问题;同时也研究了不确定离散时滞系统鲁棒控制问题。
本文主要利用Lyapunov第二方法及协方差控制理论,基于运用Matlab中LMI工具箱求解线性矩阵不等式,针对不同类型的时滞系统,考虑其方差约束控制及其滤波问题,最终给出了控制器和滤波器的存在条件。全文主要分为两个部分,具体内容如下:
第一部分主要研究不同类型时滞系统的鲁棒方差约束控制问题。首先,研究了线性中立型具有参数不确定性时滞系统的鲁棒方差约束控制问题,得到了一个时滞无关的充分条件,满足这一条件的反馈控制器将保证闭环系统是一致渐进稳定的,同时满足给定的方差约束;在此基础上,基于线性矩阵不等式给出了控制器的设计方法,同时给出一个数值算例以验证所提出算法的有效性。其次,研究了非线性中立型时滞系统的方差约束控制问题。该系统中的非线性是以扰动的形式出现的,最终得到的反馈控制器将保证系统是一致渐进稳定的,同时满足给定的方差约束。最后,研究了非线性离散具有参数不确定性时滞系统的鲁棒方差约束控制问题,得到了一个时滞无关的充分条件,满足这一条件的反馈控制器将保证系统是一致渐进稳定的,同时满足给定的方差约束。
第二部分主要研究中立型时滞系统的鲁棒滤波问题。针对不确定中立型时滞系统的Kalman滤波问题,所得的Kalman滤波器,将保证增广系统是一致渐进稳定的,同时满足给定的方差约束。在此基础上,基于线性矩阵不等式,给出了滤波器的设计方法,同时给出了一个数值算例,来验证该算法的有效性。
Time-delays are frequently encountered in the behavior of many physical processes and very often are the main cause for poor performance and instability of control systems. In view of this, the control issue of time-delay systems is a topic of great practical importance which has attracted a great deal of interest for recent years. Specially, neutral delay systems have come to a hotspot of control field and are increasingly highlighted for special attention, which concern not only previous dynamic states but also their differential states. However, the development of neutral systems is relatively slow and the references are fewer. The main reason is that difference operator of the neutral system is so difficult to deal with that the properties of the solutions to neutral systems are more complicated than those normal delay systems. Neutral delay systems extensively exist in practical engineering, so the relative investigation is quite necessary for theoretical requirement and application. And this thesis mainly investigates feedback control and filtering problem of neutral delay systems and discrete delay systems.
The thesis principally applies Liapunov's second method and the variance control theory on the base of LMI in Matlab to a variety of delay-time systems, taking variance constrained and filtering into account and finally derives the existence conditions of such controllers and filters. The whole thesis mostly consists of two parts and details as follows:
The first part mainly investigates robust variance constrained control for various delay-time systems. On the one hand, the problem of robust variance control for neutral systems, taking parameter uncertainties and time-delay into account, is researched. The delay-independent sufficient condition that guarantees the system to meet the variance-constrained and asymptotically stable is obtained. Based on it, linear matrix inequality technology is adopted to obtained controller. Furthermore, a numerical example is given to illustrate the effectiveness of the proposed approach. On the other hand, this thesis works over the problem of robust variance control for neutral systems, taking parameter uncertainties and nonlinearities into account. The purpose of this considered problem is to design a static state feedback controller, such that not only the steady-state variance of each state is not more than the individual pre-specified value but also the resulting closed-loop system is asymptotically stable simultaneously. And also, this thesis studies the problem of robust variance control for discrete systems, taking parameter uncertainties and nonlinearities into account. The purpose of this considered problem is to design a static state feedback controller, such that not only the steady-state variance of each state is not more than the individual pre-specified value but also the resulting closed-loop system is asymptotically stable simultaneously.
The second part primarily focuses on robust filtering for neutral delay systems with norm-bounded parameter uncertainty. The addressed problem is to design a Kalman filter such that the resultant error system is asymptotically stable and the effect of the noise on the estimation error is attenuated to a prescribed level. Sufficient conditions for the solvability of the robust Kalman filtering problem are obtained in terms of LMIs. Furthermore, a numerical example is given to illustrate effectiveness of the proposed algorithm.
引文
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