Backstepping Control For Fractional Discrete-time Systems

In recent decades,fractional differential equations have been used to describe optical and blood systems,rheology and Materials and mechanical systems,signal processing and system identification,control and robots and their problems in the application domain.With the differential equation of fractional order,the theoretical analysis of fractional differential equation and the study of numerical calculation are especially urgent.And the fractional order research is very extensive,and the research is calculated.In this thesis,we also study the boundary problem of generalized fractional order,and in practice.Of course,the fractional order system has been greatly concerned over the past decade.This is because using fractional calculus can be described more accurately many systems such as chaos system,polarization process,mechanical system,diffusion wave,circuit system,etc.This article is based on the points sequential discrete systems,adaptive control,backstepping and sliding mode control.The control system is used to discuss the stability of the fractional discrete system and the synchronization of the fractional discrete system.Firstly,this thesis presents a series of anti–step control of the fractional discrete time system of a single input single output.Different from integer order system,fractional order inequality is used in the reverse step process.In the error function,by tracking state variables,the fractional stability theory is based on the Lyapunov function,which designed a controller to make the closed–loop system stable.Finally,in two numerical simulations,by comparing different fractional order and different tracking reference signals,the fractional discrete–time system is stable,and the validity of the proposed controller is also verified.Secondly,a method of reverse step sliding mode control is proposed by using the method of sliding mode control and the anti–step control method to realize the synchronization of the undetermined fractional order discrete strict feedback chaos system.Based on the fractional Lyapunov stability theory and the fractional inequality technique,a fractional sliding mode controller,the fractional sliding mode surface and the sliding mode reaching law are designed to realize the synchronization control of two uncertain fractional chaotic systems.Finally,the feasibility and effectiveness of the proposed control method are verified by numerical simulation.