Some Control Problems Of Fractional Order Uncertain System

As a generalization of integral calculus in any order,fractional calculus provides a new theoretical basis and analytical tool for the development of many subjects with its unique advantages.In recent years,more and more complex systems have established mathematical models of fractional order systems by virtue of the advantages of fractional order calculus in modeling.The traditional integer order system control theory is relatively perfect,but the result of integer order control system theory cannot be directly applied or extended to fractional order system.This dissertation mainly focuses on fractional order parameter uncertain linearity system,discusses several control problems of fractional order uncertain linear system,including passification control,guaranteed cost control and non-fragile control,and obtains the following results:The robust passivity and feedback passification of a class of fractional order parametric uncertain linear systems are studied.The parameter uncertainties of time-varying norm bounded exist in both the system matrix and the control output matrix.The basic concepts and definitions of passivity and dissipativity of fractional order systems are presented and the relationship between passivity and stability of fractional order systems is established.A sufficient condition for robust passivity in the form of linear matrix inequalities is given.According to the obtained passivity condition,the passification state feedback controller is designed when the state is measurable.When the state is unmeasurable,a passification controller based on state observer is designed by using matrix singular value decomposition(SVD).The correctness and validity of the results are verified by theoretical proof and numerical simulation.The guaranteed cost control of output feedback for a class of fractional uncertain parametric linear systems with time delay is studied.The uncertain parameters of the system studied are time-varying and meet the matching conditions.A new definition of guaranteed cost control for fractional order system is established.By means of fractional order Razumikhin theorem and matrix correlation theories,the static output feedback control law and the dynamic output feedback control law are designed respectively to realize the guaranteed cost control of the system.The results are in the form of linear matrix inequalities,and the feasible solutions are easily verified by Matlab calculation.The feasibility and effectiveness of the proposed control method are verified by theoretical derivation and numerical simulation.The design of a non-fragile controller for a class of fractional linear delay systems with structural uncertainty is studied.The linear matrix inequality(LMI)method,singular value decomposition(SVD)and fractional Razumikhin theorem are used to stabilize the system.When the state of the system is unmeasurable,a robust state feedback controller based on non-fragile state observer is designed to stabilize the system.The proposed controller design method is not only related to the time delay of the system,but also to the order of the system.Theoretical proof and numerical simulation verify the correctness and effectiveness of the designed method.