Study On Parameter Estimation And Control Of Fractional Order Nonlinear Systems

Since the discovery of the fractal dimension in the real physical system for the first time by Mandelbort,more and more research scholars have established the mathematical model to study the real physical sys tem through the fractional calculus theory.It is found that the system characteristics described by the fractional-order system are closer to the physical system characteristics than the integer-order system.On the other hand,in a strictly technical sense,the physical phenomena in nature are all non-linear.In this paper,we mainly study the parameter estimation of fractional-order nonlinear systems,the stability theory of fractional-order nonlinear systems,the design of fractional-order controllers and the realization of fractional-order nonlinear systems control cricuits.Firstly,through constructing an appropriate fitness function,the parameter estimation problem of the fractional-order nonlinear system is transformed into the parameter optimization problem,and then the problem can be solved by swarm intelligence optimization algorithm.Aiming at the existing problems in the current swarm intelligence optimization algorithm,an improved boundary constraint processing method is proposed.Based on this method,the teaching and learning optimization algorithm of improved boundary constraint processing method(ICTBLO)and chicken swarm optimization algorithm of improved boundary constraint processing method(ICCSO)are proposed.The effectiveness and rationality of the proposed method is proved by fractional-order Lorenz system and fractional-order coupling motor system.In addition,the influence of time series on the estimation accuracy of fractional-order nonlinear systems is studied.Secondly,the stability problem of fractional-order nonlinear systems is studied,and a sufficient condition for the stability of fractional-order nonlinear systems is given.Taking fractional-order Lorenz system and fractional-order coupled motor system as an example,the validity of the sufficient conditions given is further proved.Thirdly,we study the problem of fractional-order controller design.Base on the integer-order washout filter,the idea of fractional-order washout filter is given.The fractional-order Hodgkin-Huxley neuron system is taken as an example to illustrate the effectiveness of the fractional order washout filter,which is compared with the integer-order washout filter.Fourthly,the problem of fractional-order nonlinear system circuit is studied.Based on the potier diagram frequency domain approximation method,a linear feedback control of a fractional-order Lorenz system is studied,and a tree circuit unit is designed to realize the linear feedback of fractional-order Lorenz system control.