Research On Adaptive Sliding Mode Control For Fractional-order Chaotic Systems

Chaotic systems are highly complex nonlinear systems which are extremely sensitive to initial conditions and changes in system parameters.Due to its inherent randomness,initial value sensitivity and irregular order,chaotic systems have been used by many researchers in the fields of finance,biology,power engineering and medical science.In recent years,scholars have applied the concept of fractional order to chaotic systems.Obvious advantages of factional-order chaotic systems have been found.System dynamics models can be described accurately.What is more,the physical meaning of systems can be expressed clearly.Since fractional-order chaotic systems are practical in terms of cryptographic communication and confidentiality protocols,the research on synchronous control of fractional-order chaotic systems has become popular researching area.To the synchronization problems of fractional-order chaotic systems and fractional-order hyper chaotic systems,all system parameters are unknown can be assumed.Different controllers are designed based on adaptive control theory,sliding mode variable structure control theory and finite-time control theory respectively.In this thesis,the stability analysis of the controlled error system which is based on the Lyapunov stability theory is shown below:1.A feedback controller is designed to achieve synchronization of fractional-order Liu chaotic systems.After that,the parameters of the fractional-order Liu chaotic system are assumed unknown.Basing on the adaptive control method and the stability theory of fractional differential equations,a suitable adaptive rate and a new adaptive controller are designed to identify the unknown parameters and to achieve the synchronization of Fractional Liu chaotic system.Based on the Lyapunov stability theory,the sufficient conditions for the existence of the controller are shown.The effectiveness of the controller is verified by the numerical simulation.2.According to the sliding mode control theory,an equivalent sliding mode controller is designed to realize the synchronization of fractional hyperchaotic systems with unknown parameters.The elimination of nonlinear terms can interfere the quality of the synchronization of fractional hyperchaotic systems is concerned.A new adaptive sliding mode controller with anti-interference should be designed.Without eliminating the nonlinear term of the system,the error system can reach the equilibrium point within a certain time.Moreover,the unknown parameters in the system can be identified.Finally,the stability of the controller is verified bythe Lyapunov stability theory.The feasibility of the controller is verified by the simulations of the statistics.3.Combined with the finite time stability theory,the adaptive sliding mode finite-time controller is designed to steady the system error in the finite time.By adjusting the parameters of the controller,the synchronization time of the control system is tunable.After that,complete synchronization and finite time synchronization of fractional-order hyperchaotic systems with unknown parameters can be achieved respectively.MATLAB is used to do the simulations.The control effects of the finite time synchronization method and the complete synchronization method are compared.The simulation result shows that the finite-time synchronization control method has advantages in synchronization speed.