Sliding Mode Synchronization Control Of Chaotic Systems

As a branch subject in the field of nonlinear science, Chaos reveals lots of unexplainable phenomena in the world,which attracts scientists to study it. The chaotic system can be described like this: it can enlarge or shrink on movement in at least one or more ring surface with extremely complicated esoteric dynamic characteristics. so the dynamic performance is also highly complex. As a result,research on chaos theory as well as the synchronization method has a bright development prospect. However, hyperchaos system stability theory is not as common as chaos system, the synchronization of hyperchaos system theory development is limited. As hyperchaos system is more complicated, it is of great significance to conduct the thorough research on the synchronization of hyperchaos system. This topic mainly carried out the following research:By introducing the nonlinear state controller into the state equation, this paper developed two new hyperchaos system on the basis of the two new three-dimensional system.The symmetry, dissipation and balance point of the two new 4d hyperchaos system are analyzed respectively. Matlab numerical simulation draw the Lyapunov index and phase diagram, which verified the existence of 4d hyperchaos system.In this paper, the sliding mode variable structure control theory is applied to implement the synchronization of the two new 4d hyperchaos system. The hyperchaos system synchronization control of Lorenz-like system was achived by using equivalent sliding mode controller based on index reaching law and the control results can be concluded that the sliding mode controller can make the system achieve synchronization within a certain amount of time. For the new hyperchaos system, the former sliding mode synchronization controller used ordinary exponential reaching law and a long control time. Therefor, a new adaptive sliding mode synchronization controller with a short control time was designed and the sufficient conditions of system stability were given based on Lyapunov stability theory.