Finite-time Control Problem For A Class Of Hyper-chaotic Systems

Chaos is widely used in mechanical engineering,artificial intelligence,optoelectronics and so on.Chaotic attractors with multiple positive Lyapunov exponents are usually called hyperchaotic phenomena.Because hyperchaotic systems have more complex dynamic characteristics than chaos,they are more widely used.Many researchers have studied chaos and its control from different research backgrounds.In recent years,various chaos synchronization problems have been reported,such as complete synchronization,projective synchronization,finite time synchronization,etc.Compared with other control problems,the controller selected for finite time control problems can achieve faster convergence and stronger robustness.In practice,the model of the system is often uncertain and inevitably affected by the external disturbance,so how to study the finite time control problem of this kind of system will be very meaningful.Stabilization problem is the most basic control problem.Synchronization problem is the stabilization problem of error system(the difference between the master system and the slave system),while projective synchronization problem is a special synchronization problem.This paper studies stabilization,synchronization and projective synchronization of control problems,the main work is as follows:(1)For eight common types of external disturbance,such as constant disturbance,trigonometric disturbance,exponential disturbance and unbounded disturbance,a filter is designed to realize the asymptotic estimation of external disturbance.The design of an asymptotically estimated filter for unbounded external perturbations is one of the originations of this thesis.(2)The finite time stabilization of hyperchaotic systems is studied.This chapter is divided into three parts.The first part studies the stabilization of hyperchaotic system subjected to external disturbance.Firstly,a stabilization controller is designed for nominal hyperchaotic systems.Then,a controller based on disturbance observer is designed to realize the asymptotic suppression of external disturbance.Finally,the two controllers are combined to stabilize the hyperchaotic system subjected to external disturbance.In the second part,the finite time stabilization of hyperchaotic systems is studied.First,a finite time controller is designed to realize the finite time stabilization of the nominal hyperchaotic system.The second step is to design a controller based on UDE.The finite time stabilization of hyperchaotic systems with model uncertainty and external disturbance is realized by combining the finite time controller with the UDE controller.The third part verifies the correctness and validity of the above theory through numerical examples and simulation results.(3)The finite time stabilization of hyperchaotic systems is studied.This chapter is divided into three parts.The first part studies the stabilization of hyperchaotic system subjected to external disturbance.Firstly,a stabilization controller is designed for nominal hyperchaotic systems.Then,a controller based on disturbance observer is designed to realize the asymptotic suppression of external disturbance.Finally,the two controllers are combined to stabilize the hyperchaotic system subjected to external disturbance.In the second part,the finite time stabilization of hyperchaotic systems is studied.First,a finite time controller is designed to realize the finite time stabilization of the nominal hyperchaotic system.The second step is to design a controller based on UDE.The finite time stabilization of hyperchaotic systems with model uncertainty and external disturbance is realized by combining the finite time controller with the UDE controller.The third part verifies the correctness and validity of the above theory through numerical examples and simulation results.(4)The finite time projective synchronization of hyperchaotic systems is studied.This chapter is divided into three parts.In the first part,projective synchronization of hyperchaotic system subjected to external disturbance is studied.First of all,judge whether the nominal system meets the condition of existence of projection synchronization.If so,design an appropriate controller to realize projection synchronization of the nominal system.Then,the projective synchronization of hyperchaotic systems with unbounded perturbations is realized by using the control method based on disturbance observer.In the second part,finite time projective synchronization of hyperchaotic systems is studied.Firstly,a finite time controller is designed to realize finite time projection synchronization.Then,a controller based on UDE is designed to eliminate uncertainty and external disturbance.Finally,the finite time projective synchronization of hyperchaotic systems with uncertainties and external disturbances is realized by combining the two controllers.In the third part,the correctness of the proposed method is verified by numerical examples combined with MATLAB simulation.The combination of the finite time control method with the control method based on UDE is another innovation of this thesis.