【作者】 周爱军；

【导师】 任光；

【作者基本信息】 大连海事大学 ， 轮机工程， 2012， 博士

【摘要】 近年来,混沌控制与同步方法的研究有了很大的发展,不仅在理论上不断完善,而且在非线性电路、保密通讯、激光、等离子体和人体生命科学等领域取得了初步的成果并展现出十分诱人的应用前景。混沌实验系统建模的不确定性是混沌的同步所必须考虑的,其中控制方向未知又是不确定性处理中难度较大的一种情况。本文以不确定混沌系统的Nussbaum增益同步为研究主线,主要进行了以下内容研究：1.增益受限与控制受限情况下的Nussbaum增益控制问题；2.不确定驱动-响应混沌系统的自适应同步问题；3.增益受限混沌系统的Nussbaum增益与非线性滑模复合同步问题；4.参数未知情况下的混沌系统受限Nussbaum增益同步问题。围绕上述问题展开的具体研究内容包括：1.对Nussbaum增益基本理论进行了深入研究,提出受限Nussbaum增益控制方法。(1)针对传统Nussbaum增益算法存在的初始段控制量过大与增益过大问题,提出增益受限与输入受限的Nussbaum增益算法的概念。(2)针对一阶控制方向未知系统,研究了增益受限与输入受限情况下的Nussbaum增益控制规律,分别对Nussbaum增益控制算法面临的高增益与控制量饱和威胁,提出了相应的控制策略。2.对存在参数与未知函数不确定情况下的驱动-响应混沌系统进行自适应同步研究,提出了三种自适应同步策略。(1)基于有界不确定的假设,采用自适应算法对不确定的界进行估计,结合PID控制的优点,研究了不确定混沌系统的自适应PID同步算法；(2)进一步简化上述有关界条件的假设,采用鲁棒控制算法完成对不确定非线性函数的补偿,采用自适应算法完成未知参数的估计,提出了一类不确定混沌系统的鲁棒自适应同步算法；(3)基于线性系统极点反馈的思想,利用混沌系统有界性提出极点自调节同步策略,该设计不需要驱动响应系统的精确结构与不确定形式,能够广泛应用于各类混沌系统的同步中。在此基础知识,对三种控制策略的同步精度问题进行了对比与改进研究。3.对增益受限要求下的不确定混沌系统进行非线性滑模与Nussbaum增益复合同步研究。(1)为了进一步提高同步精度以满足Nussbaum控制算法的匹配需要,提出了两类非线性滑模的构造设计方法,针对两类非线性滑模,分别设计了常系数同步律与自适应同步律,并进行了比较研究。(2)针对系统对大误差增益过高而对小误差的反映迟钝的问题,提出了变增益非线性滑模自适应同步算法,能够进一步提高同步精度并避免控制算法增益过高。(3)在此基础之上,研究了非线性滑模同步与增益受限Nussbaum控制算法的匹配结合,解决了方向未知与增益受限情况下的不确定系统同步问题。4.控制方向未知与参数未知情况下的增益受限与控制受限Nussbaum增益同步研究。(1)针对不存在控制方向未知的简单情况,研究了参数未知混沌系统的参数自适应同步问题,取得了较好的同步效果。(2)针对控制方向未知的复杂情况,尤其是在增益受限的约束条件下,设计了参数未知混沌系统的增益受限Nussbaum增益同步算法,从理论上保证了对Nussbaum增益约束。同时仿真结果也表明了该Nussbaum增益能够满足预定的增益限制要求。(3)针对存在控制方向未知与参数未知情况,考虑增益受限与控制量受饱和限制双重约束的复杂情况,提出了参数自适应同步与输入受限Nussbaum增益控制算法的匹配与复合控制问题。仿真结果表明了本文算法能够保证对传统Nussbaum增益算法的增益与控制约束。综上所述,本文考虑了控制方向未知、系统可用增益有限以及控制输入饱和等复杂情况下的不确定混沌同步问题,增大了同步系统的抗干扰能力,为混沌保密通信的实际应用拓宽了道路。更多还原

【Abstract】 In recent years, one can see some great developments in the area of chaos control and synchronization methods, not only some improvements in theoretical concern, but also many successful applications in the area of nonlinear circuits, security communications, laser, plasma, and bioscience, etc, which exhibits enormous and exciting application prospects. It is also necessary to consider the uncertainties caused by modeling a chaotic system in laboratory, where unknown control direction is one of the most difficult uncertainties that are hard to solve with common adaptive methods.Synchronization of chaotic systems with Nussbaum gain method is the main line of our research and it contains the following part. The first part is about the Nussbaum gain control problem for the situation that the controller with limit gain or limit control input. The second part is about the adaptive synchronization problem of uncertain driven-response system. The third part is about the nonlinear sliding mode synchronization of chaotic systems with limit Nussbaum gain method.The fourth part is about the limit Nussbaum gain synchronization of chaotic system with uncertain parameters.The main research is surrounded with the above context and it can be expended as follows:First, some basic Nussbaum gain theories are studied and a limit Nussbaum gain control method is proposed.(1)With common Nussbaum gain method, the initial control and the gain of the controller sometimes is too big and over the reasonable scope. The concepts of limit gain Nussbaum algorithm and limit input Nussbaum algorithm are proposed respectively to solve the problem.(2) For a simple one order system with unknown control direction, the Nussbaum gain method is studied for the special situations with limit gain or limit input, and two strategies are proposed to cope with the high gain and saturation threatens respectively.Second, a kind of adaptive synchronization for uncertain driven and response system with unknown parameters is studied and three adaptive strategies are proposed.(1) Based on the assumption that all uncertainties are bounded, adaptive method is used to estimate the bounds of uncertainties. Integrated with the advantage of PID control, a kind of adaptive PID algorithm is studied and applied in synchronization of uncertain chaotic systems.(2) With a further simplification of the above assumption, a kind of robust algorithm is used to compensate the uncertain nonlinear functions. With all unknown parameters estimated by adaptive method, a robust adaptive synchronization is proposed for uncertain chaotic systems.(3) Based on the concept of poles feedback in linear systems, a kind of synchronization method with adaptive poles is studied with the use of boundless characteristics of chaotic systems. It is unnecessary to known the accurate structure and forms of uncertainties with this design method. Also, some compare improvement for the above three methods are done.Third, the hybrid synchronization with nonlinear sliding mode method and Nussbaum gain method is researched for uncertain chaotic systems with limit gain.(1) Two kinds of construction methods for nonlinear sliding mode are proposed to improve the accuracy of synchronization such that it can satisfied the match condition of Nussbaum gain algorithm. Also, adaptive synchronization laws with constant coefficients or adaptive coefficients are designed respectively.(2) For some chaotic synchronization systems, if choose a small a gain, the response speed is very slow for the situation with a small error; but if choose a big gain, the gain is viewed too high for the situation with big errors. A kind of variety gain synchronization with nonlinear sliding mode is proposed to solve the problem. So with this method, the accuracy of synchronization can be improved and also the high gain feedback problem can be avoided.(3) Based on above research work, the match of limit Nussbaum gain method and nonlinear sliding mode synchronization is researched. And both the unknown control direction and limit gain problem are solved for the synchronization of uncertain chaotic systems.At last, the synchronization of chaotic systems with both unknown control direction and unknown parameters is researched with the restriction that the gain of the system is limit or the input of the system is limit. (1) For the simple situation that there is no unknown control direction, a kind of synchronization with adaptive algorithm for unknown parameters is studied and good performance is achieved.(2) For the complex situation with unknown control directions, especially with the requirement that the gain of control system is limit, a kind of limit gain Nussbaum synchronization method is proposed for chaotic systems with unknown parameters and unknown control directions. So the Nussbaum gain is guaranteed to be limit in theory. Also, simulation results show that the Nussbaum gain can satisfy to the desired limitation.(3) Consider the requirement that both the gain and the actuator of the system are limited, a kind of hybrid synchronization with limit input Nussbaum gain and adaptive algorithm, is proposed for chaotic systems with both unknown control directions and unknown parameters. Simulation results testify that the proposed strategy can guarantee the limitation for Nussbaum gain and input.Above all, synchronizations of uncertain chaotic systems with some complex situations are studied, such as unknown control direction situation; the available gain of the synchronization system is limit or actuator saturation problem. All of the proposed methods make the synchronization of chaotic systems have a strong stability under some bad conditions such as there exist big disturbances. It also provides a solid base for the application of chaotic systems in secure communication.更多还原