几类时滞动力系统的稳定性分析与控制设计

发布时间:2019-01-10 09:58
【摘要】:时滞(Time delay,TD)现象普遍的存在于许多实际工程应用中,例如航天航空、冶金、石化、通信、电力、生物、人口和经济等系统。由于时滞动力系统有着广泛的应用价值而受到国内外很多学者的关注。同时,时滞经常是导致动力系统不稳定、震荡、甚至系统性能降低的一个重要根源。于是时滞动力系统的稳定性分析和控制设计是目前研究的热点问题。如何掌握和运用时滞动力系统的性能是一个重要的研究课题。基于Lyapunov-Krasovskii泛函(Lyapunov-Krasovskii functional,LKF)理论、Shur补引理、时滞分割方法、不等式处理技巧、线性矩阵不等式(LMIs)等工具,研究了中立型时滞神经网络(Neural Networks,NNs)、分布时滞NNs、混合时滞NNs以及时滞Lurie系统(Lurie Systems,LSs)的稳定性分析和控制设计。本文研究的主要成果如下:1.中立型时滞NNs的稳定性分析。通过构建新的包含三重积分和四重积分的LKF,导出了改进的时滞依赖稳定准则。我们充分的考虑了二次凸组合方法,二次凸函数的性质和激活函数的信息,进一步降低结果的保守性。最后提供四个数值例子和仿真实验来表明了所得理论结果的可行性和优越性。2.分布时滞NNs的稳定性分析。本章的主要思想是借助一个新的积分不等式,它已被证实它的保守性比詹森不等式的保守性还小,由于它充分考虑了Leibniz-Newton公式中各项之间的关系。通过采用更普遍的时滞分割方法,构造一个合适的LKF。基于这个新的积分不等式和时滞分割方法,得到拓展的时滞依赖稳定准则。最后给出四个数值算例和仿真实验来说明了所提出方法的有效性和优越性。3.混合时滞NNs的稳定性分析。借助一个多重积分不等式,它可以提供比Jensen’s不等式更好的上界,建立了新的稳定准则。通过构建一个包含多重积的LKF,获得改进稳定条件,这些条件以LMIs形式表现出来。再者,把分布时滞区间分割成多个不等式子区间,推导出保守性较小的稳定结果。最后给出三个数值例子和仿真实验来展现了所得理论结果的可行性和优越性。4.时滞NNs的H∞控制设计。本章的主要目标是设计一个有效的H∞控制器,使得闭环系统在扰动衰减性能指标γ0下渐近稳定。通过引入恰当的LKF和提出更一般的时滞分割方法,新颖的时滞依赖稳定准则被建立。再者,通过充分利用改进的Wirtinger’s的积分不等式,获得了一个改善的充分条件,而确保了H∞控制问题的存在性。最后给出两个数值例子和仿真实验来说明了所提出方法的有效性和可行性。5.不确定中立型混合时滞LSs的稳定性分析。这个系统不仅包含实变不确定项和扇形有界非线性项,而且还有离散和分布时滞。通过构建合适的LKF和有效的数学技术,导出保守性较小的鲁棒稳定条件。最后提供三个数值例子和仿真实验来表明了所得理论结果的可行性和优越性。6.混沌Lurie系统(Chaotic Lurie Systems,CLSs)同步的时滞反馈控制设计。通过引入两个可调节的是实参数,一个新的积分不等式被提出,它可以把改进的Wirtinger’s积分不等式和詹森积分不等式作为两种特殊情况。通过引入一个扩张的LKF,它充分的考虑了时变时滞的范围,保守性较小的时滞依赖同步准则被建立。再者,基于新的非线性函数条件,理想的控制增益矩阵被成功设计。最后给出两个关于Chua’s电路系统的数值例子和仿真实验来展现了所设计方法的可行性和优越性。7.时滞CLSs同步的采样控制设计。本章提出了一种新的积分不等式来研究时滞CLSs的主从同步问题。首先,假定采样区间是任意有界变量。通过充分考虑采样区间的信息和非线性函数条件,以及时滞分割方法,一个新地扩张的LKF被构建。其次,为了获得保守性较小的同步准则,引入一个可变的是参数,建立了一个新的积分不等式。再者,基于双重积分的Wirtinger-based积分不等式,一个较长的采样周期被获得。最后通过三个数值例子和数值仿真来验证了所提出方法的优越性和可行性。8.CLSs同步的随机采样控制设计。本章通过一种新的方法来研究CLSs主从同步的随机采样控制设计问题。首先我们假定采样区间发生的概率是个固定的常数,且满足Bernoulli分布。为了充分考虑采样区间的信息,基于改善的Wirtinger积分不等式,我们引入了一个改进的LKF。其次,通过利用新的自由矩阵积分不等式,导出一个保守性较小的指数均方同步稳定准则,用来分析相应的误差同步系统。再者,基于上述方法,一个理想的反馈增益矩阵被成功设计。最后通过三个数值例子和数值仿真来说明了所提出方法的优越性和可行性。
[Abstract]:Time delay (TD) phenomena are common in many practical engineering applications, such as aerospace, metallurgy, petrifaction, communication, power, biology, population and economy. Due to the wide application value of time-delay power system, many scholars at home and abroad are concerned. At the same time, time-delay is an important source of the instability, oscillation and even system performance of the power system. Therefore, the stability analysis and control design of the time-delay power system is a hot issue in the current research. How to master and apply the performance of time-delay power system is an important research subject. The neutral-type time-delay neural network (NNs), the distributed time-delay NNs, the hybrid time-delay NNs and the time-delay Lurie systems (Lurie Systems) are studied based on the Lyapunov-Krasovskii functional (LKF) theory, the Shur complement approach, the time-delay segmentation method, the inequality processing technique, the linear matrix inequality (LMIs), and the like. The stability analysis and control design of LSs. The main results of this study are as follows: 1. Stability analysis of neutral time-delay NNs. The improved time-delay-dependent stability criterion is derived by the construction of new LKF with triple integral and four-point integration. We fully consider the secondary convex combination method, the property of the secondary convex function and the information of the activation function, and further reduce the conservativeness of the result. Finally, four numerical examples and simulation experiments are provided to show the feasibility and superiority of the obtained theoretical results. Stability analysis of distributed time-delay NNs. The main idea in this chapter is to use a new integral inequality, which has been proved to be more conservative than that of the Johnson's inequality, because it fully considers the relationship between the various Leibniz-Newton formulas. A suitable LKF is constructed by adopting a more general time-delay segmentation method. Based on this new integral inequality and time-delay segmentation, the extended time-delay-dependent stability criterion is obtained. Finally, four numerical examples and simulation experiments are given to illustrate the effectiveness and superiority of the proposed method. Stability analysis of mixed time-delay NNs. By means of a multi-integral inequality, it can provide a better upper boundary than the Jensen's inequality, and set up a new stability criterion. Improved stability conditions are obtained by constructing an LKF that contains multiple products, which are presented in the form of LMIs. In addition, the distribution time-delay interval is divided into a plurality of inequalities subintervals, and a stable result with less conservative property is derived. Finally, three numerical examples and simulation experiments are given to show the feasibility and advantages of the obtained theoretical results. The H-type control design of the time-delay NNs. The main objective of this chapter is to design a valid H-controller, so that the closed-loop system is asymptotically stable under the condition of disturbance attenuation performance. A novel time-delay-dependent stability criterion is established by the introduction of the appropriate LKF and a more general time-delay segmentation method. Furthermore, by making full use of the improved Wirtinger's integral inequality, an improved sufficient condition is obtained to ensure the existence of the H-level control problem. Finally, two numerical examples and simulation experiments are given to illustrate the effectiveness and feasibility of the proposed method. The stability analysis of the neutral-type mixed-time-delay LSs is not determined. The system not only includes real variable uncertainty and sector-bound non-linear terms, but also has a discrete and distributed time-delay. By constructing the appropriate LKF and efficient mathematical techniques, the stable condition of the low-conservative Rurod is derived. Finally, three numerical examples and simulation experiments are provided to show the feasibility and advantages of the obtained theoretical results. Time-delay feedback control design for synchronous Lurie Systems (CLSs). By introducing two adjustable real parameters, a new integral inequality is proposed, which can use the modified Wirtinger's integral inequality and the Jensen integral inequality as two special cases. By introducing an extended LKF, it fully considers the range of time-varying time-delay, and the time-delay-dependent synchronization criterion with less conservative property is established. Furthermore, based on the new nonlinear function, the ideal control gain matrix is successfully designed. Finally, two numerical examples and simulation experiments on the Chua's circuit system are given to show the feasibility and advantages of the designed method. The sampling control design for the time-delay CLSs synchronization. In this chapter, a new integral inequality is proposed to study the master-slave synchronization of the time-delay CLSs. First, it is assumed that the sampling interval is any bounded variable. A newly expanded LKF is constructed by taking full consideration of the information of the sampling interval and the non-linear function condition and the time-delay splitting method. Secondly, in order to obtain a small conservative synchronization criterion, a variable parameter is introduced, and a new integral inequality is established. Furthermore, a longer sampling period is obtained based on the double-integral Wirtinger-based integral inequality. Finally, the superiority and feasibility of the proposed method are verified by three numerical examples and numerical simulation. This chapter studies the design of the random sampling control of the master-slave synchronization of the CLS by a new method. First we assume that the probability of occurrence of the sampling interval is a fixed constant and the Bernoulli distribution is satisfied. In order to take full consideration of the information of the sampling interval, we introduce an improved LKF based on the improved Wirtinger integral inequality. Secondly, by using the new free-matrix integral inequality, a conservative and low-index homogeneous stability criterion is derived, which is used to analyze the corresponding error synchronization system. Furthermore, based on the above-described method, an ideal feedback gain matrix is successfully designed. Finally, three numerical examples and numerical simulation are used to illustrate the advantages and feasibility of the proposed method.
【学位授予单位】:电子科技大学
【学位级别】:博士
【学位授予年份】:2016
【分类号】:TP13

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