Event-Triggered ILC For Discrete-time Nonlinear Systems Under Non-repetitive Conditions

For systems operating over a finite time interval,iterative learning control(ILC)primarily utilizes data from previous iterations to continuously learn and adjust,enabling high-precision tracking tasks.The design process of ILC is typically simple,efficient,and computationally cost-effective.However,it faces several challenges.On the one hand,the systems often show non-repetitive characteristics during operation,which deviates from the assumption of strict repetitiveness in traditional ILC,and restricts the further development and application of ILC.On the other hand,considering the increasing communication demands in control systems,updating the controller in each iteration leads to a significant amount of communication resources occupation by redundant information.This paper investigates the design of event-triggered ILC(ET-ILC)methods for discretetime nonlinear systems under non-repetitive conditions.Specifically,the main content of this paper includes the following aspects:1.Considering a class of discrete-time uncertain nonlinear systems with iteration-varying initial conditions and reference trajectories,an adaptive ET-ILC method is proposed.First,an adaptive parameter update algorithm and an ILC law are designed based on recursive least squares method and the principle of certainty equivalence,respectively.Then,an improved adaptive static event-triggered mechanism is designed,where the triggering condition parameters can be iteratively updated.The proposed ET-ILC scheme ensures that the tracking error converges asymptotically to zero along the iteration axis.2.On the basis of considering iteration-varying initial conditions and reference trajectories,further consideration is given to the issue of non-repetitive non-parametric uncertainties in the SISO systems.A robust ILC algorithm based on a hybrid event-triggered strategy is designed.First,a novel dead-zone function is designed to handle both parametric and non-parametric uncertainties.Then,by embedding the dead-zone function into the parameter update law,the impact of system uncertainties are eliminated.Next,ILC law based on an auxiliary error is designed.The proposed method ensures that the tracking error asymptotically converges to zero along the iteration axis.The proposed algorithm is further extended to parametric strict-feedback systems and MIMO systems,and the asymptotic convergence of tracking error is also guaranteed.3.Furthermore,considering iteration-varying unknown system parameters,control input gain,initial states,reference trajectory,and external disturbance,when iterative variation patterns of the non-repetitive factors are partially known or completely unknown,two different ET-ILC methods are proposed.(1)Considering that the variation patterns of system parameters,input gain,and external disturbance are known,and characterized in the form of high-order internal models(HOIMs),an ET-ILC scheme based on multiple iteration-varying HOIMs is designed.First,the non-repetitive factors are represented as the product of iterationvarying terms and iteration-invariant terms by using constructed high-order internal model matrices.Then,adaptive iterative learning law is designed based on HOIM.Moreover,a mixed event-triggered mechanism is designed.The proposed method enables the tracking error to converge asymptotically to zero along the iteration axis.(2)Considering that the iterative variation patterns of all non-repetitive factors are totally unknown,a more general and versatile robust adaptive ET-ILC framework based on fixed threshold strategy is designed.First,a lumped iteration-varying uncertainty parameter is constructed.Then,a dead-zone-like auxiliary error function is designed and embedded into the parameter update laws to mitigate the impact of uncertainties.Based on the designed control method,the tracking error can converge to a bounded tunable residual set.4.Finally,considering the application of ET-ILC algorithms into nonlinear multi-agent systems,where the system exhibits iteration-varying communication topologies,two distributed adaptive ET-ILC algorithms are designed.(1)Considering the system dynamics with non-repetitive initial conditions and reference trajectory,a model-based distributed adaptive ET-ILC method is designed.Firstly,distributed parameter update law and iterative control law are designed,respectively.In addition,a distributed event-triggered mechanism is designed by constructing an adaptive triggering function.The proposed control algorithm can ensure that the tracking error of each agent relative to the desired traj ectory is asymptotically convergent to zero along the iteration axis.(2)Considering the system dynamics with iteration-varying or iteration-invariant reference trajectories,a data-driven distributed adaptive ET-ILC method,only using I/O data,is proposed.Firstly,based on a linear model,a fully data-driven adaptive parameter update law and adaptive iterative learning law are constructed.Then,the identified optimal parameter estimation value is used in the design of the eventtriggered mechanism.By constructing a Lyapunov function,a distributed adaptive event-triggered mechanism is designed.The proposed control method effectively achieves the consensus tracking task in the multi-agent systems,guaranteeing that the tracking errors can asymptotically converge to zero along the iteration axis.The algorithms proposed in this paper not only guarantee the good tracking performance of the systems but also significantly reduce the number of controller updating,thus reducing the communication burden and saving system resources.The effectiveness of the algorithms is demonstrated through rigorous theoretical analysis and simulation examples.