Composite Learning Fuzzy Control For A Class Of Fractional-order Systems

Fractional differential equations are more accurate than integer differential e-quations in modeling real systems.With the improvement of accuracy requirement in control process,they are widely used in modeling real systems.Generally,in systems with uncertainties,unbounded parameters will surely lead to limitless or divergent controller and plant state trajectories.However,the persistent excitation condition ensuring parameter convergence is too strict to meet.In this paper,Takagi-Sugcno fuzzy method is used to deal with unknown non-linear functions and to model actual systems,and a novel composite learning fuzzy control strategy is proposed in accordance with a parallel distributed compensation tech and a fractional Lyapunov stability norm.A fractional-order composite learn-ing law and a two-level adaptive controller are designed,which not only ensures the boundedness of all variables in the closed-loop system and the Mittag-Leffler stability of tracking errors,but also achieves the convergence of parameters,thus synchroniz-ing two incommensurate fractional-order time-varying delayed chaotic systems with unknown external disturbances and parameter mismatching uncertainties.Finally,the feasibility of the proposed control strategy is verified by a simulation example.This algorithm has the following unique advantages:1).A supervisory control law is designed to compensate the total disturbance.2).The unknown parameters of the fuzzy system are updated by combining prediction error with tracking error.3).The parameter convergence is guaranteed when the internal excitation condition is satisfied(which is weaker than the continuous excitation condition which is usually needed to be satisfied).The remainder of this work is summarized as follows.Chapter 1 Firstly,some basic preliminaries on the definitions of Caputo frac-tional differential and integral as well as several important properties are reviewed.Then,the related contents of Takagi-Sugeno fuzzy logic system are introduced.Chapter 2 In this chapter,the main results of adaptive fuzzy synchroniza-tion for fractional-order chaotic systems with unknown external disturbances are given.In view of parallel distributed compensation tech and fractional Lyapunov standard,an adaptive fuzzy controller and fractional-order parameter adaptive laws are designed to ensure the stability of the system and the boundedness of all signals.However,the convergence of the parameters of the fuzzy system is not taken into account.Chapter 3 In this chapter,the main results of fuzzy synchronization control for incommensurate fractional-order chaotic systems with time-delay of account of composite learning technology are presented.Based on parallel distributed compen-sation tech,an adaptive fuzzy controller and supervisory controller together with fractional-order parameter composite learning law are designed.In view of fractional Lyapunov criterion,the stability and parameter convergence analysis of fractional-order chaotic systems with time-delay are provided.Finally,a simulation example is given to demonstrate the validity and feasibility of the proposed algorithm.