【作者】 李娟；

【导师】 郑继明；

【作者基本信息】 重庆邮电大学 ， 系统科学， 2022， 硕士

【摘要】 混沌系统作为非线性科学的重要研究方向之一,在许多学术领域都产生了深远的影响。混沌金融系统是混沌在经济金融领域中的应用,随着各个国家地区经济贸易发展的不平衡,金融市场中各不稳定因素之间的相互作用,金融系统很容易受到波及从而表现出不稳定的特性,使得世界各地的经济受到影响,可能会产生大范围严重的金融危机。为了经济的稳定发展,对金融系统进行探索与同步控制,可以为金融政策的制定提供理论基础。本文对参数不确定的混沌金融系统的同步问题进行了研究,基于稳定性定理与现代控制技术,分别实现了参数不确定金融系统的完全同步、标度矩阵同步以及有限时间同步。1.基于稳定性定理与现代控制技术,将反馈控制方法和自适应控制方法相结合,设计适当的混合控制器和参数自适应函数,使得具有不确定参数的混沌金融系统达到完全同步。2.针对混沌系统中不同维度的混沌系统之间存在着的同步行为,利用标度矩阵,设计合适的控制方案,将参数不确定的金融系统与不同维度的混沌系统进行同步。同时考虑到实际应用中不可避免的外界干扰,针对存在外部扰动和不确定参数的混沌系统,设计适当的控制策略,使得带有外部扰动的参数不确定混沌金融系统与其他不同维度的混沌系统在同一维度下达到同步。3.介绍了不同维混沌系统有限时间同步的定义,在外部扰动和参数不确定的情况下,设计了相应的有限时间自适应控制器和参数自适应律,使得带有外界扰动和不确定参数的混沌金融系统与其他不同维度的混沌系统在有限时间内达到同步,并给出系统到达同步时间的表达式。对于上述提出的控制策略,本文不仅在理论上进行了分析,同时以金融系统为案例进行了数值验证,为进一步深入研究经济金融市场提供了新的思路。更多还原

【Abstract】 Chaotic system,as one of the important research directions of non-linear science,has a profound impact in many academic fields.Chaotic financial system is the application of chaos in the economic and financial fields.With the economic development of each country and the interaction of kinds unstable elements,the financial system is vulnerable to spread and shows unstable characteristics,which affects the economies of all over the world and may result in a widespread and serious financial crisis.In order to ensure the stable development of the economy,the exploration and control of the financial system could provide a theoretical basis for the establishment of financial policy.In this paper,the synchronization of chaotic financial systems with uncertain parameters is researched.Based on the stability theorem and modern control technology,the complete synchronization,scale matrix synchronization and finite time synchronization of financial systems with uncertain parameters are realized respectively.1.Based on the stability theorem and modern control techniques,combining the feedback control method and the adaptive control method,an appropriate hybrid controller and parameter adaptive function are designed to synchronize the financial chaotic system with uncertain parameters.2.In view of the synchronization behavior between chaotic systems of different dimensions in real physical systems,a suitable control scheme is designed by using scale matrix to synchronize financial systems with chaotic systems of different dimensions with uncertain parameters.Considering the unavoidable external disturbances in practical applications,design appropriate control strategies so that the parametric uncertain chaotic financial system with external disturbances can be synchronized with other chaotic systems with different dimensions in the same dimension to cope with the growing development of financial markets.3.The definition of finite-time synchronization for different-dimensional chaotic systems is introduced,under the external disturbance and parameter uncertainty,the corresponding finite-time adaptive controller and parameter adaptive law are designed,in this way,the parametric uncertain chaotic financial system with external disturbances is synchronized with other chaotic systems of different dimensions in finite-time,and the expression of the time when the system reaches synchronization is given.For the above control strategies,this paper not only makes theoretical analysis,but also takes financial system as a case to carry out numerical verification,which provides a new idea for further in-depth research of economic and financial markets.更多还原