Stabilization And Optimal Control Of Fractional-order Systems With Input Delays

The concept of fractional calculus was put forward three centuries ago.It has developed rapidly as a research direction.It extends the order of integral calculus to the real number field.In system science,because of its memory and infinite dimension characteristics,it has unique advantages in describing viscoelastic system,economy,biological system and other complex systems and movements.In control theory,it provides a new possibility for the controller design,but also increases the difficulty of the fractional order dynamic system analysis.It is a very valuable and challenging field.This thesis firstly introduces the research background and development status of fractional calculus and fractional systems,and then it investigates the fractional systems with input delay.We analyze the properties of such systems on the basis of previous achievements and focus on the stabilization control of this kind of systems.The main work of this thesis is as follows:(1)The observer-based feedback stabilization problem for fractional order systems(FOS)with input delay is studied by using state transformation.The observer-based controller is designed by using Smith predictor and matrix variable decoupling technology.The necessary and sufficient conditions based on Linear Matrix Inequalit(LMI)for the stability of fractional order systems are given.At the same time,the approximation algorithm for the integer order case is extended to solving the fractional order case,and a controller is proposed to reduce the error to any small value by adjusting the parameters.The effectiveness of the control effect is verified by simulation examples.(2)The optimal control of fractional order systems with input delay are studied.The necessary and sufficient conditions in stabilizing the FOS are given.The method of solving the fractional linear quadratic optimal control problem is given.By using the outstloup recursive filter,the integer order approximation of fractional order system is obtained.Finally,the Riccati equations are obtained.