Research On Sliding Mode Synchronization Control Of Fractional-Order Chaotic System And Its Application

Fractional calculus has a history of more than 300 years.With the development of the theoretical study and the extensive application in the engineering field,the notable progress about fractional calculus have been made in the recent years.Chaos,as a unique motion of nonlinear dynamical systems,has received extensive attention and research in the various fields s such as physics,chemistry,biological sciences,geology,and economics.The fractional-order chaotic systems(FOCSs),as an extension of the integer-order chaotic systems(IOCSs)at arbitrary order,not only has the characteristics of the traditional IOCSs but also has historical memory.It has been widely accepted that the dynamic characteristics of the FOCSs are more complex than the IOCSs due to the fact that system characteristics are closely related to system order.Therefore,the FOCSs has been widely used in the fields of secure communication and image processing.With the rapid development of computer science and technology in recent years,more and more scholars pay attention to the theoretical research of the FOCSs and many achievements about the synchronization control of the FOCSs have been obtained.However,the FOCSs,as one of the research focuses,need to be further studied in both theory and application.Therefore,the synchronization control of the FOCSs and its application in secure communication is further investigated based on the previous studies in this thesis.The main studying contents are briefly summarized as follows:Firstly,two different synchronization schemes were proposed for achieving the synchronization of the FOCSs by using the sliding mode variable structure control method.An adaptive sliding mode synchronization problem for a class of the FOCSs with disturbances and unknown uncertainties was investigated in the first place.Furthermore,the adaptive fuzzy sliding mode synchronization problem of a class of the FOCSs with uncertainty was studied.Finally,the simulation examples were presented to verify the effectiveness of the proposed methods.Secondly,based on the backstepping method,the structural characteristics of a class of the FOCSs with uncertainties and external disturbances are analyzed.During the recursion process,the Lyapunov subfunctions and virtual inputs are designed,and a slip is added to the backstepping terminal modal control has completed the design of an backstepping sliding mode synchronization controller capable of asymptotically synchronizing a class of FOCSs with uncertainty and external disturbances.The simulation examples were presented to verify the effectiveness of the proposed methods.Finally,the application of the fractional-order chaotic synchronization in secure communication was investigated by combining with the chaotic masking algorithm,where a new secure communication scheme with better security was presented.The effectiveness of the designed method is verified by the simulation examples.