一类混沌系统基于哈密顿系统框架的控制与同步

本项目拟采用哈密顿系统框架研究混沌系统,建立该类系统的哈密顿函数研究方法，给出该类系统在控制、同步及其应用方面的若干新结果。首先，基于申请者已有的混沌系统和广义哈密顿实现的理论与方法，寻求混沌系统的广义能量函数，建立其哈密顿结构。其次，利用得到的哈密顿结构，研究该系统的控制与同步。最后，运用得到的新结果，建立混沌电机驱动系统的哈密顿模型，并设计鲁棒控制方案。应用基于能量的控制方法研究混沌系统，具有重要的学术价值和广阔的应用前景。一方面，混沌系统是非线性科学中的一类重要系统，研究该类系统基于能量的控制属混沌学、控制论与应用数学的交叉学科，是非线性科学研究前沿之一，应用基于能量的控制方法研究混沌系统不仅是混沌学本身发展的要求，而且是控制科学本身发展的要求；另一方面，该类系统又有众多的实际背景（如保密通信），对其研究也是解决众多实际问题的需要。

With hamilton system structure the project aims to study chaos system to establish its hamilton function approach, and to give out some new achievements in control, synchronization and its application. First, the research will try to find the generalized energy function of chaos system so as to establish its hamilton structure on the basis of the applicants’ previous researches . Sencond, the research will study its control and synchronization with the hamilton structure. Last, the project will establish hamilton model of chaos motor system and design robust control strategy in terms of the new result. It is not only of acdemic importance but also has a wide prospect of application to study the chaos system with the control method based on energy. For one, the chaos system is the important one of nonlinear science. The research in the system of the control based on energy engages in a cross-subject of chaos, control science and applied mathematics, meanwhile, it is one of forefronts in nonlinear science. It is the requirement of the chaos development as well as the control science to study the chaos system with the control method based on energy. On the other hand, the syetem has a variety of real background , for instance, secret communications. Accordingly, the research is needed to solve the actual problems.