Research On Convergence And Robustness Of Fractional Order Nonlinear Systems Based On Iterative Learning Control

Under the background of the rapid development of fractional calculus theory and the continuous improvement of the performance requirements of control systems,the control problem of fractional order systems has gradually attracted people's attention,the control problem of fractional order systems has gradually attracted people's attention.Among them,the study of the convergence and robustness of fractional order systems is two important research directions.Iterative learning control is an important intelligent control algorithm in the control field.It requires only a small amount of prior knowledge and system information to learn,so that the system has good performance.Therefore,this paper proposes a new iterative learning control algorithm for fractional-order systems,and studies the convergence and robustness problems.Firstly,for a class of fractional-order nonlinear time-delay systems,from the point of view of system convergence speed,a kind of a-order derivative correction term with error is added based on the previous P-type iterative learning control algorithm.The PD? type iterative learning control algorithm gives the sufficient conditions for the tracking error convergence of the system under the action of the algorithm,and carries out theoretical analysis and mathematical proof.Through numerical comparison,the proposed algorithm has good tracking accuracy and is better than the previous control algorithm.Then,we continue to study the fractional-order system of the previous chapter.It is found that the pure PDa-type learning law is the convergence rate of the system error before the error correction term and the learning gain before the a-derivative correction term of the error are determined.Will be sure.Therefore,from the perspective of improving the system convergence speed,an adjustable parameter item can be added to the learning rate.Therefore,a new PDa type iterative learning control algorithm with variable gain feedback structure is proposed,and the convergence of the system under the action of the algorithm is analyzed and verified.The simulation is compared with the previous PDa type iterative learning control algorithm.The algorithm has good tracking accuracy and the control effect has been further improved.Finally,the convergence and robustness of fractional-order nonlinear systems under iterative learning control are considered.Based on a new robust iterative learning control scheme,the robustness problem of a class of fractional nonlinear systems with norm-bounded uncertainties is solved.The main feature of the proposed controller is that it can handle norm bounded uncertainties,including input uncertainty and state uncertainty.The iterative learning control part of the controller adopts a second-order form,which improves the convergence speed of the system.Through the new fractional-order composite energy function method given in this paper,the proposed robust iterative learning control scheme can guarantee the system state progressive tracking and the two norm convergence of state error.Finally,an example of numerical simulation is carried out to verify that the system has good robustness under the action of the algorithm.