Robust Control Of A Class Of Chaotic Systems With Complex Variables

Chaos systems are a type of complex dynamic system characterized by highly sensitive dependence on initial conditions.The theoretical study of chaos systems originated from the development of nonlinear science in the late twentieth century,and with the continuous advancement of computer technology,the research on chaos systems has been further advanced and applied.In chaos systems,the state vector can take va Lües in either the real or complex field.Chaos systems whose state vectors are located in the complex field are called complex variable chaos systems,because their state vectors have imaginary parts,making them more complex and rich compared to real variable chaos systems.The research on complex variable chaos systems inc Lüdes their dynamic characteristics,stability control,and tracking,among other issues.The research objects inc Lüde individual complex variable chaos systems,multi-variable complex chaos systems,and coupled complex variable chaos systems,among others.The study of complex variable chaos systems has a wide range of disciplinary backgrounds and application areas.For example,in the fields of communication and image processing,research on the synchronization problem of complex variable chaos systems can be used to ensure the security of communication and image transmission.In the fields of power systems and chemical reaction control,research on the stabilization and control of complex variable chaos systems can be used to improve the stability and efficiency of power systems and chemical reaction processes.Therefore,in-depth research and application of complex variable chaos systems have important theoretical and practical significance.In chaos systems,due to the complexity of their dynamic behavior,the design of controllers becomes more difficult,especially when facing disturbances.Therefore,robust control of chaos systems has become an important research area.Robust control methods can ensure that the system can maintain specific behavior patterns under disturbances by improving the system’s stability and controllability,such as suppressing chaos phenomena and achieving synchronization control.The development of modern control theory and technology provides new ideas and methods for robust control of chaos systems,such as feedback linearization,adaptive control,fuzzy control,neural network control,and so on.As chaos systems are widely used in practice,research on their robust control will become increasingly important.This article addresses the stabilization and tracking problem of a complex variable chaotic system under external disturbances by designing suitable filters to accurately estimate the disturbances and developing a controller to eliminate them.The main contributions of this article are as follows:(1)The designed filter can achieve asymptotic estimation of external disturbances,effectively suppressing the influence of external disturbances and improving the robustness and control performance of the system.It should be noted that this article not only designs suitable filters for periodic bounded external disturbances,but also designs corresponding asymptotic estimation filters for some unbounded disturbances(such as polynomial growth and exponential growth types).Designing corresponding asymptotic estimation filters for unbounded disturbances is an original contribution of this article.(2)Based on the designed filter,this article proposes a new robust control strategy based on disturbance estimation.This control strategy can achieve stabilization and precise tracking of complex variable chaotic systems under external disturbances.Numerical simulation results show that the proposed control strategy has good performance in suppressing external disturbances and can achieve high-precision tracking of the system.These research results have certain guiding significance for practical engineering applications.Designing a new control strategy based on disturbance estimation for complex variable chaotic systems under external disturbances is another innovation of this thesis.(3)This article investigates the stabilization problem of complex variable chaotic systems.The stabilization problem of complex variable chaotic systems under external disturbances is solved in two steps.In the first step,the stabilization problem of the nominal complex variable chaotic system is solved by designing a controller.In the second step,corresponding filters are designed according to the type of external disturbances,and an observer for asymptotic estimation of external disturbances based on the filter is designed.Based on the two steps,a disturbance estimation-based stabilization controller is designed based on dynamic gain feedback control method and quasi-linear feedback method.Numerical examples combined with simulation results verify the correctness and effectiveness of the above theoretical results.(4)This thesis investigates three tracking problems of complex variable chaotic systems: complete synchronization,anti-synchronization,and projection synchronization,achieving identical tracking,opposite tracking,proportional tracking of partial variables,and opposite tracking of partial variables.A two-step control design method is proposed to solve the tracking problem of complex variable chaotic systems subject to external disturbances.In the first step,the tracking problem of nominal complex variable chaotic systems is solved.In the second step,a corresponding filter is designed according to the type of external disturbance,and an observer for asymptotic estimation of external disturbance is designed based on the filter.Based on the dynamic gain feedback control method and the quasi-linear feedback method,a tracking controller based on disturbance estimation is proposed by combining the two steps.Numerical examples and simulation results verify the correctness and practicality of the proposed method.The third innovation of this thesis is to provide a necessary and sufficient condition for the existence of anti-synchronization and projection synchronization problems.