Sliding Mode Control Of Non-ideal Fractional-order Delayed Memristive Chaotic System

Chaos is an important subject in current scientific research,and the control of fractional-order delayed memristive chaotic systems with uncertainties and external disturbances is a hot subject in chaos research.Memristor is a kind of non-linear circuit element.Its memory characteristics have great application prospects in secure communication and chaotic circuits.The time delay factor is inevitable in the actual engineering system.Therefore,it is important to consider the influence of time delay on the dynamic behavior and control of complex nonlinear systems.At present,great breakthroughs have been 'made in the application of fractional-order time-delay chaotic systems in control engineering,information security and other fields.Uncertainty of non-ideal fractional-order time-delay memristive systems is usually represented by system uncertainties or external disturbances,so the control of non-ideal systems has become a research hotspot.Due to the insensitivity of sliding mode control to interference,it is suitable for the control of uncertain chaotic systems.Therefore,the study of sliding mode control for non-ideal fractional-order delayed memristive chaotic systems has very important engineering practical value and theoretical significance.In this thesis,the fractional sliding mode control of two non-ideal fractional-order time-delay,memristive chaotic systems is studied.Firstly,a fractional sliding surface is proposed.Based on Lyapunov stability theorem,a control law is designed to control chaos of fractional-order time-delay systems.The feasibility of the fractional sliding mode controller is verified by numerical simulation.At the same time,in order to study the system in the presence of uncertainty and external interference,the validity of the scheme is verified by comparing the theoretical proof and experimental results.The main tasks of this thesis are as follows:(1)The model of time-delay memristive system is extended from integer order to fractional order,and a fractional order model of time-delay memristive system is established,which reveals the essential characteristics of memristive system and makes the description of memristive chaotic system more concise.For non-ideal fractional-order chaotic systems,the finite-time robust control is obtained by sliding mode strategy,and the uncertainties and external disturbances are assumed to be bounded.(2)The chaotic behavior of fractional-order time-delay memristive chaotic system is controlled by sliding mode control strategy.Firstly,a sliding mode control scheme is designed to stabilize the system.Then,using Lyapunov stability theorem,the condition of system stability is obtained.The asymptotic stability of non-ideal commensurate and non-commensurate order systems is theoretically analyzed.The conditions that should be followed in the design of controller parameters are deduced to prove the feasibility of the controller.(3)In order to further verify the correctness of the sliding mode control scheme,the chaotic control problem of fractional-order active time-delay memristive system is studied.Then,a fractional sliding mode control method is proposed to stabilize the fractional-order memristive time-delay system with uncertainties and disturbances.In order to ensure the stability of commensurate and non-commensurate order systems with uncertainties and disturbances,we use Lyapunov stability theorem to analyze the control scheme.Numerical simulation proves that the designed fractional sliding mode controller can eliminate chaos and stabilize the system in finite time.