Research On Modified Function Projective Synchronization Control Of Chaotic Systems And Applications

Modified function projective synchronization is a new type of synchronization method developedin recent years. The scale factor of modified function projective synchronization is a function, ratherthan a constant,which means that the drive and response system could be synchronized up to a desiredscaling function matrix. This feature can strengthen the security of digital securecommunication. This thesis focuses on the design of chaotic synchronization controller of chaoticsystems with model uncertainties and external disturbances under various conditions, and itsapplication in the secure communication.The main works and innovative points of this paper are asfollows:The concept of reduced-order modified function projective synchronization of chaotic systems isproposed.The given scaling function can be an equilibrium point, a periodic orbit, or even a chaoticattractor in the phase space.Based on Lyapunov stability theory and state feedback control method,thegeneral control methods are given,by which one can realize the modified function projectivesynchronization of chaotic system with same order and the reduced-order modified functionprojective synchronization of chaotic system with different order.A general method of modified function projective synchronization of a class of chaotic systemswith model uncertainties and external perturbation is proposed by designing a suitable responsesystem．Based on unidirectional coupled synchronization,the two schemes of obtaining the responsesystem from chaotic drive system are established. By designing suitable controller and adaptivelaw,the drive and response systems can synchronize to a desired scaling function matrix.The couplingstrength can be automatically adapted to a updated law.A general robust adaptive sliding mode controller is designed to realize the modified functionprojective synchronization of two same-structure chaos system and different-structure chaossystem,which have parameters mismatch、model uncertainities and external disturbances. On thebasis of the previous chapters, the nonlinear control input in the actual system is further considered.The modified function projective synchronization of chaotic system with known or unknown sectornonlinearity input、model uncertainties and external perturbation is discussed. Simulation results ofthe typical chaotic system show the effectiveness of the proposed controller.A new four dimensional continuous time autonomous hyperchaotic system named Fanghyperchaotic system is proposed in this paper,which is built by the two necessary conditions of hyperchaotic system. The hyperchaotic system is analyzed by studying the basic dynamiccharacteristics. The concept of dislocated modified function projective synchronization of chaoticsystems is proposed. Based on Lyapunove stability theory and active control method,a robust adaptivefeedback controller is presented for the dislocated modified function projective synchronization ofFang hyperchaotic system.The modified function projective synchronization method is applied to secure communication.One method is based on the modified function projective synchronization and parameter modulate,theother method is based on the coupled modified function projective synchronization and chaoticmask.The corresponding numerical simulations of Fang hyperchaotic system demonstrate theeffectiveness of the proposed methods.