分数阶超混沌系统的动力学行为分析及若干控制问题研究

Considering the stabilization for the periodical orbits and the synchronization of fractional-order hyperchaotic systems as well as the anticontrol of chaos for the unmodeled nonlinear dynamical systems, the following research work will be carried out. 1. The adaptive state delay feedback control method is studied to stabilize the unstable periodical orbits of fractional-order hyperchaotic systems, which considers the dynamical characteristics of the fractional-order hyperchaotic systems sufficiently, but does not counteract the nonlinear terms forcibly. And the corresponding Lyapunov stability criteria are given simultanously.2. The stabilization problem of the unstable periodical orbits of fractional-order hyperchaotic systems with uncertain or unknown parameters is addressed. The corresponding robust controller design scheme is proposed. 3. The robust generalized synchronization approach to synchronize two non-identical fractional-order hyperchaotc systems under the assumption that the parameters of the drive system are unknown. The synchronization patterns include lag synchronization, anti-synchronization and phase synchronization, etc. Moreover, a number of uncertainties are considered, such as time delay in transmission, noise in the channel, even disorder and package loss in a network enviroment. The sufficient creteria for the robust stability of the synchronization error systems are proposed. 4. The anticontrol of chaos for unmodeled dynamical nonlinear systems based on generalized fuzzy hyperbolic models is researched. The relevant theoretical proofs will be presented to prove that the chaos generated from controlled systems satisfies the Li-Yorke or Devaney definition. 5. The secure communication software simulation platform and the hardware experiment platform will be constructed based on the robust synchronization of uncertain fractional-order hyperchaotic systems.

针对分数阶超混沌系统的周期轨道镇定与同步及未建模非线性动态系统的混沌反控制问题，本项目拟开展如下几方面研究：1.探究充分利用其自身动态特性而非强制抵消非线性项作用的分数阶超混沌系统不稳定周期轨道的自适应状态延迟反馈镇定方法，给出相应的Lyapunov稳定性判据；2.探究参数不确定或参数未知条件下分数阶超混沌系统不稳定周期轨道镇定方法，给出参数扰动鲁棒控制器的设计方案；3.探究驱动系统参数未知条件下异构分数阶超混沌系统的鲁棒广义同步方法，所涉及的同步模式包括考虑信道传输延迟和信道噪声干扰的滞后同步、反同步及相同步，给出相应同步误差系统鲁棒稳定的充分判据；4.探究基于广义模糊双曲正切模型的未建模非线性动态系统的混沌反控制方法，并从理论上严格证明系统中产生的混沌满足Li-Yorke定义或Devaney定义；5.搭建基于不确定分数阶超混沌系统鲁棒同步的保密通信软件仿真平台和硬件实验平台。

本项目针对不确定分数阶超混沌系统的鲁棒控制与同步及未建模非线性动态系统的混沌化问题开展相关研究，取得了如下几方面研究成果。1.利用状态变换方法，将一类分数阶混沌系统的不稳定周期轨道的识别与镇定问题转换为整数阶混沌系统的相应问题，进而通过状态延迟反馈方法来确定分数阶超混沌系统的不稳定周期轨道并将系统镇定在该轨道上。2.充分利用分数阶混沌系统的参数极端敏感性等特点，基于拉普拉斯变换方法，研究了参数不确定或参数未知条件下分数阶超混沌系统不稳定周期轨道的鲁棒镇定问题，提出一种参数自适应鲁棒控制策略，实现了目标轨道的镇定。3.综合利用区间系统理论、自适应控制、H无穷鲁棒控制等策略，提出考虑多种不确定性条件下的异构分数阶超混沌系统多模式同步方法，将同步误差系统镇定到零点或一定的误差范围之内。在此过程中，我们综合考虑信道传输延迟、信道噪声甚至网络环境下丢包错序等干扰的分数阶超混沌系统滞后同步、反同步及相同步等科学问题，并引入环境噪声干扰因素引起的参数不确定性，将其归结为一类分数阶非线性系统的稳定性分析与综合问题，基于分数阶微分系统Lyapunov稳定性判据设计同步控制器，实现了不确定分数阶超混沌系统的鲁棒同步。4.基于广义模糊双曲正切模型的万能逼近特性，提出了未建模非线性动态系统的混沌化方法。针对离散非线性系统，设计了正弦形式的非线性状态反馈控制器，并从理论上严格证明了被控系统中产生的混沌满足Li-Yorke定义；针对连续非线性系统，结合庞加莱映射理论，设计时滞状态反馈控制器，并从理论上严格证明了系统中所产生的混沌满足Devaney定义。上述混沌化方法无需计算Lyapunov 指数，大大减小了混沌化的计算量。5.基于不确定分数阶超混沌系统鲁棒同步理论，建立了保密通信软件仿真平台和硬件实验平台，为分数阶超混沌同步保密通信技术研究提供可靠的仿真验证环境。