混沌保密系统同步实现和研究

I混沌保密系统同步实现和研究摘要混沌系统的运动是一种确定性的非线性运动，它运动轨迹非常复杂但又不完全随机，在实际的系统中也可以观察到它的存在。由于混沌运动的不稳定性和长时间发展趋势的不可预见性，控制和利用混沌就成了混沌研究的关键环节。混沌信号具有遍历性、非周期、连续宽带频谱、似噪声的特性，特别适合于保密通信领域。由于混沌同步研究的广阔应用前景，它一直是非线性科学领域的热点研究课题之一。本文主要研究了混沌动力学系统中超混沌系统的同步控制方法的。设计了滑模控制器、自适应滑模控制器、鲁棒控制器、状态反馈控制器实现了两个系统的同步。具体内容如下：（1）针对带有外部扰动和不确定性的相同或不同超混沌系统设计了主动滑模控制器，实现了系统的同步与反同步。针对滑模控制器存在的抖振问题，利用tanh函数替代符号函数，达到了消除抖动的目的。以超混沌Lorenz系统和Chen系统为例，实现两系统的同步与反同步，通过数值仿真验证了设计的控制器的有效性。（2）针对一类扰动和不确定性上界未知的超混沌系统，设计了自适应主动滑模控制器，达到了很好的同步与反同步效果。在此基础上对控制器消抖进行了研究，设计了一个新的自适应控制器消除传统滑模的抖动现象。（3）针对一类带不确定性和外界扰动的超混沌系统的同步问题进行了输入状态稳定控制研究。基于输入状态稳定理论和李雅普诺夫稳定理论，设计了线性误差反馈控制器来保证同步误差系统逐渐稳定,反馈增益由Matlab中线性矩阵不等式工具箱解一个线性不等式（LMI）得到。（4）针对一类带不确定性的超混沌系统同步问题进行研究，设计了一个静态输出反馈模糊控制器。基于T-S模型将非线性系统线性化，利用迭代LMI方法得到线性误差反馈增益矩阵误差系统逐渐稳定。关键词：混沌同步；主动滑模控制；自适应主动滑模控制；鲁棒控制；线性矩阵不等式（LMI）；李雅普诺夫稳定；输入状态稳定；T-S模糊模型IIAbstractChaoticmotionisacomplexnonlinearmotion，whosetrajectoryoftheorbitsinthephaseplaneisverycomplexbutnotstochastic.Thechaoticphenomenahavebeenobservedinalotofrealsystemsandtheresearchonchaoshasbeenfocusedonchaoticcontrolandapplicationnow.Thedynamicpropertiesofchaossignalsuchasergodicity,aperodic，uncorrelated，broadbandandnoise-likehavebeenprovedtobeusefulofcommunicationsystemsandindescribinganddiagnosingnonlineardynamicsystems.Thecomplexity，singularityandwidepotentialapplicationofchaoticdynamicsystemsmaketheresearchonthechaoticcontrolandsynchronizationtheorytobemorechallenging.Theresearchinthisfieldbecomesanewresearchfocusinnonlinearsciencefields.Themaincontentsofthispapercontaintheanalysisoncontrolandsynchronizationofchaoticsystems.Thesynchronizationofchaoticsystemshasbeenattainedbyactiveslidingmodecontroller,activeadaptiveslidingmodecontroller,statefeedbackcontroller.Inthispaper，themaincontributionsarefollowing:(1)Undertheexistenceofsystemuncertainties,externaldisturbances,theactiveslidingmodecontrollerisproposedtorealizesynchronizationandanti-synchronizationbetweentwohyperchaoticsystems.Thecontinuoustanhfunctionisusedtoreplacethediscontinuoussignfunctioninthecontrollawandhenceacontrolinputissmoothwithoutchattering.Simulationresultsshowthattheproposedcontrollerscangivegoodcontroleffects.(2)Theactiveadaptiveslidingmodecontrollerisdesignedforsynchronizationofhyperchaoticsystemswithuncertaintiesandexternaldisturbances.Theadaptiveupdatinglawisdesignedtoestatetheboundoftheuncertaintiesandexternaldisturbances.Thecontinuousfunctionisusedtoreplacethediscontinuoussignfunctioninthecontrollawandhenceacontrolsignalissmoothwithoutchatteringaction.(3)Thesynchronizationofhyperchaoticsystemswithuncertaintiesandexternaldisturbancesisinvestigated.BasedonLyapunovtheoryandinput-to-statestabletheory,alinearstatefeedbackcontrollerispresentedtoguaranteetheasymptoticstability.Theerrorfeedbackgainmatrixcanbeobtainedbythelinearmatrixinequality(LMI)usingtheMATLABLMIToolbox.(4)Thestaticoutputfeedbackfuzzy(SOFF)controlapproachisproposedtodealwiththeproblemofsynchronizationoftwoidenticalhyperchaoticsystems.TheT-Sfuzzymodelisemployedtorepresentmanytypicalnonlinearhyperchaoticsystems.Aniterativelinearmatrixinequality(ILMI)algorithmisproposedtocomputethefeedbackgainofthesuboptimalSOFFcontroller.Keywords：chaoticsynchronization;activeslidingmodecontrol;activeadaptiveslidingmodecontrol;robustcontrol;linearmatrixinequality;LyapunovStability;Input-to-StateStability;T-SfuzzymodelIII目录第一章绪论......................................................11.1混沌系统的研究背景...........................................11.2混沌理论概述.................................................11.2.1混沌理论的起源与发展......................................11.2.2混沌的定义................................................21.2.3混沌的几个常用概念........................................31.2.4混沌的基本特征............................................41.2.5几种混沌分析方法..........................................51.2.6常见的几种同步形式........................................61.3国内外发展现状................................................61.3.1混沌同步研究现状..........................................61.3.2混沌同步研究的发展趋势....................................81.4本课题主要研究内容............................................8第二章基于主动滑模控制的混沌同步...............................102.1滑模变结构控制的基本理论.....................................102.1.1滑模变结构控制的定义.....................................102.1.2滑模的定义...............................................112.1.3滑模控制的定义...........................................112.2主动滑模控制器的设计.........................................122.2.1同步误差系统的描述.......................................122.2.2主动滑模控制器的设计.....................................122.2.3稳定性分析...............................................132.3数值仿真....................................................142.3.1两个超混沌Chen系统的同步................................152.3.2超混沌Lorenz系统和Chen系统的反同步.....................182.4本章小结....................................................21第三章基于自适应主动滑模控制的混沌同步.........................223.1自适应控制的基本理论........................................223.1.1自适应控制的介绍.........................................223.1.2模型参考自适应控制器的一般设计方法.......................223.2自适应主动滑模控制器的设计...........................