复杂Lurie混沌系统的非脆弱同步与可靠性控制设计

随着网络信息安全需求的日益增加，Lurie混沌系统的同步控制问题受到了广泛关注。但目前的研究成果主要集中在单因素或单模式场景，没有考虑现实环境的复杂性和多样性。本项目围绕具有时滞、参数不确定性、增益摄动以及随机故障等多种非理想因素影响下的复杂Lurie混沌系统，研究其非脆弱同步与可靠性控制设计。具体内容如下：（1）根据概率论、随机分析和鲁棒控制等理论，充分考虑和分析各种因素的特性，应用电磁学定律，建立复杂Lurie混沌系统的微分方程模型；（2）构造新的 Lyapunov 泛函结合不等式分析技巧等方法，在增益加性摄动、增益乘性摄动以及增益随机摄动下，分别给出有效的非脆弱同步算法；（3）在上述工作基础上，考虑多重故障并发，利用能量函数、误差估计以及采样反馈控制等方法，设计优化的可靠性控制算法。通过本项目的研究，以期完善Lurie混沌系统的研究方法和理论体系，为实际问题的解决提供一定的理论依据。

With the increasing demands of network information safety, the synchronization control problem for Lurie chaotic system has attracted considerable attention. However, the existing results focus mainly on the single factor or the single model scene without considering the complexity and diversity of the real environment. This project aims to investigate the non-fragile synchronization and reliable control design under the influence of non-ideal factors, such as time delay, parameter uncertainty, gain perturbation, stochastic fault and so on. Detailed contents are as follows: (1) Based on the probability theory, stochastic analysis theory, robust control theory and so on, we will fully consider and analyze the characteristics of various factors and establish the differential equation model for complicated Lurie chaotic system by applying the law of electromagnetism. (2) By constructing new Lyapunov functionals and combining the inequalities analysis techniques, some effective non-fragile synchronization algorithms will be obtained under gain additive perturbation, gain multiplicative perturbation and gain random perturbation, respectively; (3) On the basis of previous work, by considering the multi-fault concurrency, the optimization of reliable control algorithm will be designed by using energy function, error estimation, sampling feedback control, etc. After the study of this project, we are expecting to promote the research method and theoretical system of Lurie chaos system, as well as to provide some theoretical basis for solving practical problems.