Tolerant Control Of Fractional-order Singular Systems

Modern systems are developing towards more complicated scale.Large loss of wealth and lives is caused if systems failures Occur in this kind of control systems.It is important to improve the reliability of systems.Fault-tolerant control pioneers a new way to enhance the reliability of complicated systems.Fault-tolerant control for fractional-order singular systems is a reasonable extension to control for normal systems,which has abundant applied backgrounds.So it is of important to study the fault-tolerant control for singular systems.In this paper,a detailed analysis of the current situation of study fault-tolerant control for fractional-order singular systems and a discussion about the problems of fault-tolerant for fractional-order singular systems are stressed.This paper includes a class of fault-tolerant control for uncertain fractional-order systems,passive of fault-tolerant control for fractional-order singular linear systems,and a class of fault-tolerant control for uncertain fractional-order singular systems.The main results in this paper can be given as the following:(1)The research background of this paper is introduced.Firstly,the development of the fractional-order calculus theories and the research status of control systems are introduced.Then,the development of singular system theories and the model of fractional-order singular systems are introduced.Furthermore,the concept and classification of fault-tolerant control and the research status of fault-tolerant control of singular systems are introduced.Finally,the main work of this paper is listed.(2)The mathematical basic concept and preliminary knowledge are given.Firstly,the definitions for the fractional-order calculus are introduced.Then,the definition and nature of the Gamma function and the Mittag-Leffler function are given.Finally,the concept and application of the linear matrix inequality(LMI)are introduced.(3)On the a class of fault-tolerant control for uncertain fractional-order systems,its issue is studied by considering the design of dynamic output feedback controller.The sufficient conditions for the dynamic output feedback controller are given by linear matrix inequalities(LMIs).Finally,a numercial example is used to verify the effectiveness of the method.(4)On the passive fault tolerant control for fractional-order singular systems,its issue is studied by considering the design of controller for fractional-order singular systems.Firstly,based on linear matrix inequalities(LMIs),a necessary and sufficient condition of controller possessing integrity for fractional-order linear singular systems is given.Furthermore,against the case of actuator and sensor failures,the above LMIs are appropriately amended.Then the circular regional controller possessing integrity for fractional-order singular systems is obtained.(5)On the fault tolerant control of a class of uncertain fractional-order singular systems,the design method of the controller is studied when the actuator fails.When the actuator fails,the LMI design state feedback is used to allow the closed loop system to be allowed,and then the state feedback is redesigned to allow the system to be allowed when the actuator fails.Finally,a class of fault-tolerant controllers for uncertain fractional order singular systems under state feedback are designed.(6)A summary of this paper is given.Finally,future expectations are given.