Forgetting Learning Algorithm with Batches for Iterative Tracking Control of Nonlinear Systems

As the P-type iterative learning control algorithm is sensitive to the initial error and the output error disturbance, and the PD-type iterative learning control algorithm can easily amplify the noise and reduce the robustness of the system,a PD-type iterative learning tracking control algorithm for repetitive nonlinear time-varying systems with any desired output and bounded disturbances is investigated.By using the desired trajectory,the desired control and tracking error expectations memorized in the process of iterative learning,the learning controller is designed based on the variable batches of forgetting factors.Based on theλnorm theory and the Bellman-Gronwall inequality,the necessary and sufficient conditions for the existence of the learning gain are discussed,and the uniform convergence of the control algorithm is analyzed to ensure that the batch error of the closed-loop tracking system is bounded.The robustness and the dynamic performance of the system are improved by the algorithm.Simulation on the tracking control of the single-joint robot arm illustrates the effectiveness of the proposed method.