非线性时滞系统的保性能控制研究
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摘要
在大量的自然和社会现象中不可避免地存在时滞现象,亦即事物的发展趋势不仅依赖于当前的状态,而且还依赖于事物过去的情况。时滞系统的控制是控制理论应用的一个重要领域。时滞往往导致系统品质恶化,甚至于不稳定,也很有可能极大地破坏控制系统的性能。时滞的存在常常可以使系统的性能指标下降,甚至可能导致系统的不稳定。如伺抑制时滞造成的系统性能下降、降低系统的保守性就成为控制界的一个热点和难点问题。因此,研究时滞系统的保性能控制具有重要的理论和实际价值。本文主要研究几种不确定非线性时滞系统的稳定性及其保性能控制器或滤波器设计方法。
研究了具有时滞相关和非线性扰动的不确定广义系统的保性能控制问题。目的是设计一个有记忆的状态反馈控制器,不仅使得闭环系统渐进稳定且相应的性能指标不超过某个确定的上界。基于Lyapunov函数方法和线性矩阵不等式(LMI)方法,得到闭环系统渐进稳定的充分条件和保性能控制器的表达形式。最后,通过数值仿真说明了所给方法的可行性和有效性。
研究了具有分布时滞的奇异随机神经网络的H2保性能控制。目的是当参数不确定性在允许范围内,证明该神经网络是均方渐进稳定的和和性能函数值不超过规定上限界。基于Lyapunov稳定性理论和LMI方法,得到时滞相关的稳定的充分条件。最后,通过数值仿真说明所给方法的可行性和有效性。
研究了具有分布时滞的非线性随机中立系统的非脆弱H∞保性能控制问题。基于Lyapunov稳定性理论和LMI方法,得到闭环系统稳定的充分条件。通过线LMI方法,得到该保性能控制器的表达式和相应的性能指标的上界。最后,通过数值仿真来说明所给方法的可行性和有效性。
研究了非线性时滞随机系统的鲁棒H∞保性能滤波问题。设计鲁棒H∞保性能滤波器,对所有的不确定性,随机系统是鲁棒渐进稳定的且保证了一定的性能函数的上限。根据Lyapunov稳定性理论和LMI方法,得出了该系统的稳定的充分条件和鲁棒H∞保性能滤波器的参数。最后,通过数值仿真来说明所给方法的可行性和有效性。
There are inevitable time delays in a large number of natural and social phenomena. Namely, the development trend of things not only depends on the current state, but also relies on the past of things. The control of time delay systems is an important field of control theory. Time delay cause deterioration of system, and even unstable, will greatly damage performance of control system. The existence of time-delay system can often reduce performance index, and even can cause stability of the system. How to suppress the delay caused the system performance and to reduce the system conservative became a hot and difficult problem in control field. Therefore, the study on the guaranteed cost control for time delay systems have a important theoretical and practical value. This paper studies stability and guaranteed cost controller or filter design for several uncertain nonlinear systems with time delay. The organization of this dissertation is as follows:
In chapter two, the problem of the guaranteed cost control for a delay-dependent nonlinear singular system is studied. The purpose is to design a memory state feedback controller, the closed-loop system is asymptotically stable and the corresponding performance index is not more than a certain bound. Based on Lyapunov function method and the linear matrix inequality (LMI) technique, a sufficient stabilization condition of closed-loop system and explicit expressions of guaranteed cost control are obtained. Finally, the effectiveness of the proposed method is proved by a numerical example.
In chapter three, the problem of H2 guaranteed cost control for singular stochastic neural networks with distributed delays is saved. The aim of this paper is to prove neural networks are stochastically asymptotically stable in the means quare for all admissible parameter uncertainties and the cost function value is not more than a specified upper bound. Based on Lyapunov stability theory and LMI techniques, a sufficient stabilization condition is derived. Finally. a numerical example has shown the feasibility and effectiveness of the mentioned results.
In chapter four, the non-fragile H∞guaranteed cost control problem of uncertain non-linear stochastic neutral systems is considered. A sufficient stabilization condition is proposed based on Lyapunov stability theory combined with LMI technique. Furthermore. a sufficient condition for the existence of the controller is presented and the cost function value is not more than a specified upper bound by LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed techniques.
Last but not the least, the robust H∞guaranteed cost filter problem of a class of uncertain nonlinear time-delay stochastic systems is considered. A robust H∞guaranteed cost filter is designed such that for all uncertainties, the resulting augmented system is robustly asymptotically stable and satisfies the proposed guaranteed cost performance. In terms of Lyapunov stability theory and LMI technique. a sufficient stabilization condition is derived and robust H∞guaranteed cost filter is designed. Finally, a numerical example is shown to demonstrate the usefulness of the proposed techniques.
研究了具有时滞相关和非线性扰动的不确定广义系统的保性能控制问题。目的是设计一个有记忆的状态反馈控制器,不仅使得闭环系统渐进稳定且相应的性能指标不超过某个确定的上界。基于Lyapunov函数方法和线性矩阵不等式(LMI)方法,得到闭环系统渐进稳定的充分条件和保性能控制器的表达形式。最后,通过数值仿真说明了所给方法的可行性和有效性。
研究了具有分布时滞的奇异随机神经网络的H2保性能控制。目的是当参数不确定性在允许范围内,证明该神经网络是均方渐进稳定的和和性能函数值不超过规定上限界。基于Lyapunov稳定性理论和LMI方法,得到时滞相关的稳定的充分条件。最后,通过数值仿真说明所给方法的可行性和有效性。
研究了具有分布时滞的非线性随机中立系统的非脆弱H∞保性能控制问题。基于Lyapunov稳定性理论和LMI方法,得到闭环系统稳定的充分条件。通过线LMI方法,得到该保性能控制器的表达式和相应的性能指标的上界。最后,通过数值仿真来说明所给方法的可行性和有效性。
研究了非线性时滞随机系统的鲁棒H∞保性能滤波问题。设计鲁棒H∞保性能滤波器,对所有的不确定性,随机系统是鲁棒渐进稳定的且保证了一定的性能函数的上限。根据Lyapunov稳定性理论和LMI方法,得出了该系统的稳定的充分条件和鲁棒H∞保性能滤波器的参数。最后,通过数值仿真来说明所给方法的可行性和有效性。
There are inevitable time delays in a large number of natural and social phenomena. Namely, the development trend of things not only depends on the current state, but also relies on the past of things. The control of time delay systems is an important field of control theory. Time delay cause deterioration of system, and even unstable, will greatly damage performance of control system. The existence of time-delay system can often reduce performance index, and even can cause stability of the system. How to suppress the delay caused the system performance and to reduce the system conservative became a hot and difficult problem in control field. Therefore, the study on the guaranteed cost control for time delay systems have a important theoretical and practical value. This paper studies stability and guaranteed cost controller or filter design for several uncertain nonlinear systems with time delay. The organization of this dissertation is as follows:
In chapter two, the problem of the guaranteed cost control for a delay-dependent nonlinear singular system is studied. The purpose is to design a memory state feedback controller, the closed-loop system is asymptotically stable and the corresponding performance index is not more than a certain bound. Based on Lyapunov function method and the linear matrix inequality (LMI) technique, a sufficient stabilization condition of closed-loop system and explicit expressions of guaranteed cost control are obtained. Finally, the effectiveness of the proposed method is proved by a numerical example.
In chapter three, the problem of H2 guaranteed cost control for singular stochastic neural networks with distributed delays is saved. The aim of this paper is to prove neural networks are stochastically asymptotically stable in the means quare for all admissible parameter uncertainties and the cost function value is not more than a specified upper bound. Based on Lyapunov stability theory and LMI techniques, a sufficient stabilization condition is derived. Finally. a numerical example has shown the feasibility and effectiveness of the mentioned results.
In chapter four, the non-fragile H∞guaranteed cost control problem of uncertain non-linear stochastic neutral systems is considered. A sufficient stabilization condition is proposed based on Lyapunov stability theory combined with LMI technique. Furthermore. a sufficient condition for the existence of the controller is presented and the cost function value is not more than a specified upper bound by LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed techniques.
Last but not the least, the robust H∞guaranteed cost filter problem of a class of uncertain nonlinear time-delay stochastic systems is considered. A robust H∞guaranteed cost filter is designed such that for all uncertainties, the resulting augmented system is robustly asymptotically stable and satisfies the proposed guaranteed cost performance. In terms of Lyapunov stability theory and LMI technique. a sufficient stabilization condition is derived and robust H∞guaranteed cost filter is designed. Finally, a numerical example is shown to demonstrate the usefulness of the proposed techniques.
引文
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