关于有限时间混沌同步的若干问题研究

In the recent years，finite-time chaos synchronization has become a hot subject in the domain of the chaos synchronization. The proposer and the research team have found that the research on the finite-time chaos synchronization in the certain conditions is faced with some shortages such as the complex configuration of the designed controller, the discontinuousness of the designed controller, and so on. Research on the finite-time chaos synchronization under the uncertain conditions is rare and just restricted within the situations in presence of parameter mismatches or external disturbances in the existing literatures. Up to now, there has been no relative work on the finite-time chaos synchronization under the uncertain condition with time delay. Accordingly, this project will investigate the work as follows: (1) a simple and continuous controller is designed to achieve finite-time synchronization of the master and slave chaotic systems under the certain conditions, and then finite-time stability theory is employed to prove some synchronization criteria which are then optimized under some rules;(2) the finite-time stability theory is used to investigate the finite-time chaos synchronization under the uncertain conditions with parameter mismatches, external disturbances and time delay, and then some criteria are proved and optimized. By combination with engineering practice, this project will improve and promote the theory on the finite-time chaos synchronization which will provide theory supports for the engineering application such as synchronization tracing control of robot, underwater vibration noise control, and so on.

近年来，有限时间混沌同步已成为混沌同步领域的一个热点问题。申请人和项目组成员在研究中发现，目前关于确定性环境下的有限时间混沌同步研究存在控制器结构复杂，不连续等缺陷。关于不确定性环境下的有限时间混沌同步问题，目前的研究结果较少且仅限于只有参数失配或只有外部扰动的情形，对于时间延迟这种不确定性环境下的有限时间混沌同步问题，还未见相关文献。对此，本项目拟开展如下研究：（1）设计一种结构简单且连续的广义替代变量控制器来实现确定性环境下的主从混沌系统的有限时间同步，采用有限时间稳定性理论等方法证明同步判据，并按一定的准则进行优化；（2）应用有限时间稳定性理论，研究参数失配、外部扰动和时间延迟不确定性环境下的有限时间混沌同步问题，证明同步判据并进行优化。本项目旨在结合工程实际，完善和拓展有限时间混沌同步理论，为机器人的同步跟踪控制、水下振动噪声控制等应用领域提供理论支持。

本项目按照研究计划，分别研究了确定性环境下和不确定环境下的有限时间混沌同步及其在军事中的应用问题。通过设计几型简单、连续的控制器，构造了混沌系统的有限时间同步框架，证明了一些有限时间同步判据并验证了其有效性。然后，将所得到的研究结果应用到无人艇集结控制、子母型水下无人航行器回收控制等军事应用问题。此外，我们还对研究的问题进行了拓展，分别研究了主-从Euler-Lagrange系统的同步问题、非自治时延电力系统的全局同步问题、量化和噪声约束条件下多Lagrange 航行体编队的分布式跟踪控制等问题，取得了一些结果。