Research On Synchronization Control Of Chaotic Time-delay Systems Based On State Observer

The research of synchronization control approaches for chaotic time-delay systems has been a hot topic in the field of control theory.Most of the control methods focus on analyzing from the perspective that the system state variables are completely measurable.However,due to the complexity of chaotic time-delay systems,it is difficult to directly measure all the system states and the system parameters are also unknown.State observer is mainly used when the system states cannot be fully measured,a lot of results have been obtained in its application in linear time-invariant systems,but there are fewer researches related to the synchronization problem of chaotic time-delay systems.Therefore,based on the existing results,this paper focus on the study of state observer-based synchronization control for chaotic time-delay systems.Take the typical Lur'e system and coronary artery system as examples,combining the Bessel-Legendre inequality,Wirtinger inequality,new double integral inequality,and improved reciprocally convex inequality to improve the upper bound of the system time-delay and reduce the conservativeness,the main work is as follows:Firstly,owning to the existence of unmeasurable system states of the chaotic timedelay systems,we research the Luenberger-type observer-based chaos synchronization.Based on Bessel-Legendre inequality,new double integral inequality,the Lyapunov Krasovskii functions have been constructed.By introducing the improved reciprocally convex inequality,the upper bound of the system time-delay has been improved and a synchronization control condition with less conservatism is obtained via mathematical derivation.The observer gain matrices and controller gain matrix have been calculated by a decoupling approach.Finally,take Lur'e system as an example to verify the effectiveness of this control method.Moreover,with the unmeasurable system states as well as unknown parameters,we study the adaptive observer-based synchronization control for chaotic time-delay systems.Utilize the Wirtinger inequality,new double integral inequality and the improved reciprocally convex inequality to reduce the conservatism.H_? control is employed to enhance system robustness.Finally,take coronary artery system as an example to verify the effectiveness of this control method.Both of the Luenberger-type observer and the adaptive observer designed above are base on the simulation of the original system states.The dimension of the observing system is the same as the dimension of the original system,it's known as the fulldimensional observer.But in practical applications,the system output vectors can be directly measured.Therefore,part of the system states can be from the system outputs directly,for the unmeasurable part,the system reconstruction can be achieved via reduced-order observer.For the uncertain nonlinear chaotic system with unknown parameters,a reduced-order observer is designed.The nonlinear terms satisfy the quadratically inner-bounded condition.A synchronization control law is derived based on the Lyapunov theory.