Research On Sliding Mode Control Method Of Chaotic System Under The Framework Of Delta Operato

In recent years,with the rapid development of nonlinear science,as an important part of nonlinear science,chaos has also developed rapidly.Different from the general nonlinear system,the motion process of chaotic system is very sensitive to the initial value,and its behavior is unrepeatable and unpredictable in the long-term development trend.On the other hand,with the continuous development of science and technology,people’s requirements for digitization are gradually improving,and there is an urgent need for a suitable discrete control method under high-speed sampling.Therefore,a delta operator method which can effectively unify continuous time systems and discrete-time systems is proposed.Then,based on the delta operator theory,a unified model under the framework of the delta operator is established for the continuous-time and discrete-time chaotic systems.In addition,there are some problems in the modeling process of nonlinear coupled chaotic system,such as modeling uncertainty,transmission fault between subsystems,network failure,Do S attack and so on.In order to solve these existing system problems,this thesis studies the synchronization and stabilization of chaotic system by using the methods of sliding mode control.The specific research work is as follows:(1)Based on the delta operator theory,the sliding mode control of continuous T-S fuzzy model chaotic system is studied.Firstly,the delta operator discretization method is used to discretize the continuous T-S model.Secondly,the linear sliding surface is designed,and the coefficient parameters of the sliding surface are solved by linear matrix inequality method.Thirdly,an effective control law is designed to ensure that the system state can reach the sliding mode surface in a finite time and achieve bounded stability.Finally,through the experimental simulation,the feasibility of this method is verified.(2)The nonlinear coupled chaotic system model under the framework of delta operator is established.At the same time,combined with the isolated network system,the synchronization error system under the framework of delta operator can be obtained.Firstly,aiming at the synchronization error system under DOS attack and network fault,the linear sliding mode surface is designed,and the solution method of sliding mode surface parameters is obtained by using linear matrix inequality technology.Secondly,a new sliding mode arrival control law is proposed to ensure that the synchronization error system reaches the sliding mode surface in limited time and realize chaotic synchronization.Finally,through the experimental simulation,the feasibility of this method is verified.(3)Based on the nonlinear coupled chaotic system model under the framework of delta operator obtained in work(2).Firstly,a suitable linear sliding mode surface is designed to ensure the stability of the system on the sliding mode surface.Secondly,an adaptive sliding mode controller is designed to make the system reach the desired sliding mode surface in finite time and asymptotically converge to the equilibrium state to realize chaos stabilization.Finally,through the experimental simulation,the feasibility of this method is verified.