Research On Initial State And Convergence Of Iterative Learning Control

Iterative learning control is a repeated operation repeated in a limited time to achieve fast tracking of the desired trajectory,especially for controlled objects with reproducible motion characteristics.Compared with other learning algorithms,the iterative learning algorithm has the advantage of not requiring the system to provide an accurate mathematical model,requiring less prior knowledge and simple theoretical analysis.Therefore,it has important practical value for tracking control of highly non-linear,difficult to model and time-varying systems,such as multi-joint manipulators.In this paper,the initial state of iterative learning algorithm and its three different convergence analysis methods and convergence speed are studied.The details are as follows:Firstly,based on the traditional open-loop D-type tracking control strategy with initial error correction,for time-varying nonlinear systems with external disturbances,a closed-loop D-type fast iterative learning control law with initial error correction is proposed.To speed up the convergence,shorten the time for initial error correction,the iterative learning error is introduced into the design of time-segment function of control law,at the same time,the initial state learning law of the deformation is added to the algorithm,so that the initial state of the system can satisfy the arbitrariness in the radius domain,the closed-loop learning method is used instead of the open-loop learning method in the traditional strategy with initial error correction to improve the control performance of the system.The convergence of the algorithm is analyzed by ? norm theory and compressed mapping method,and the accelerated trajectory tracking control is realized by simulation.Secondly,an exponential variable gain fast iterative learning control law with initial learning and forgetting factors is designed for time-varying nonlinear systems with disturbances.The initial state learning law based on the iteration output error can not only reduce the constraints of the system on the initial state,but also effectively expand the practical range of the algorithm,the exponential variable gain term is added to the algorithm to improve the convergence speed and tracking accuracy of the system.Operator theory and spectral radius method are used to analyze the convergence of open-loop PD iterative learning algorithm,the simulation shows the fast tracking control performance of the algorithm.Finally,a neural network adaptive iterative learning control law with initial state learning is designed for the multi-joint manipulator which can be repeatedly operated in practical applications,in order to avoid the influence of strict repetitive initial state and global Lipschitz condition.The addition of the initial state learning law based on the initial state deviation can effectively avoid the situation that the initial state of the system is strictly the same,at the same time,RBF neural network is used to optimize the parameters of the controller and improve the control accuracy of the system.The convergence of Lyapunov function analysis algorithm is designed,and the high precision tracking control of two-joint manipulator is realized by simulation.