随机分布控制系统的自适应迭代学习控制

介绍输出概率密度函数（PDF）常规的迭代学习控制（ILC）的收敛条件,并利用此条件设计相应的迭代学习律。主要讨论如何解决输出PDF迭代学习控制（ILC）中的过迭代,收敛速度等问题。以离散输出概率密度函数（PDF）控制模型为基础,介绍了直接迭代学习控制算法收敛的必要条件,提出自适应的迭代学习参数调节方法和避免过迭代的迭代结束条件,这些措施能够保证输出PDF的迭代控制收敛且具有较快的收敛速度。仿真结果表明,输出PDF的自适应迭代学习控制具有较快的收敛速度,而学习终止条件能很好地避免过迭代。     

具有扰动的非线性系统高阶迭代学习控制

迭代学习控制(ILC)利用系统的重复性不断改进控制性能.本文讨论一类具有扰动的非线性、时变系统高阶迭代学习控制算法及其迭代学习收敛的充分条件,并与D型迭代学习算法相比,讨论典型PD高阶ILC算法的收敛速度.仿真结果证实高阶ILC算法具有更快的收敛速度,并且当系统满足收敛条件、不确定项及输出扰动项有界时迭代学习收敛.     

基于互补滑模控制和迭代学习控制的永磁直线同步电动机速度控制

为满足永磁直线同步电动机(PMLSM)伺服系统高速度高精度的要求,抑制不确定性对系统性能的影响,提出一种互补滑模控制(CSMC)和迭代学习控制(ILC)相结合的控制方法.该方法结合了CSMC强鲁棒性的优点和ILC跟踪精度高的特点,以CSMC中积分滑模面为基础设计新型迭代学习律,既可利用ILC对系统未建模动态进行估计,抑制端部效应、齿槽效应和摩擦力等周期不确定性的影响,又可利用CSMC减小参数变化和外部扰动等非周期不确定性对系统的影响,从而提高控制器的收敛速度和收敛精度,保证系统具有较强的速度跟踪性能.实验结果表明,该方法有效地提高了系统的动态响应能力,改善了速度跟踪精度.     

分数阶线性系统二阶P型迭代学习控制收敛性分析北大核心CSCD

针对一类α(0≤α<1)分数阶线性系统,讨论其P型迭代学习控制(ILC)问题。首先,通过引入λ-范数并借助广义Gronwall不等式,分别获得了开环系统一阶和二阶P型ILC收敛的充分条件。然后,借助Qp因子概念,对上述两种ILC的收敛速度进行了比较,并用数值仿真验证了该方法的有效性。     

基于BP神经网络的迭代学习初始控制策略研究

针对传统迭代学习控制(ILC)在面临新的环境或控制任务时学习时间长、收敛速度慢的问题,提出基于BP神经网络的迭代学习初始控制策略。通过BP神经网络拟和经验数据,对以往控制经验加以充分利用,避免了对初始控制输入量的盲目选择。仿真验证了方法的可行性和有效性。     

基于未知高频增益的非线性系统自适应迭代学习控制

针对一类单输入单输出不确定非线性重复跟踪系统,提出一种基于完全未知高频反馈增益的自适应迭代学习控制.与普通迭代学习控制需要学习增益稳定性前提条件不同,自适应迭代学习控制通过不断修改Nussbaum形式的高频学习增益达到收敛.经证明当迭代次数i→∞时,重复跟踪误差可一致收敛到任意小界δ.仿真结果表明了该控制方法的有效性.     

一类线性离散切换系统的迭代学习控制

考虑具有任意切换序列线性离散切换系统的迭代学习控制问题. 假设切换系统在有限时间区间内重复运行, P型ILC算法可实现该类系统在整个时间区间内的完全跟踪控制. 采用超向量方法给出了算法在迭代域内收敛的条件, 并在理论上分析了的收敛性. 仿真示例验证了理论的结果.     

非一致目标跟踪的混合自适应迭代学习控制

针对一类含有时变和时不变参数的高阶非线性系统,结合Backstepping方法,提出了一种新的自适应迭代学习控制方法,该方法由微分-差分型自适应率和学习控制率组成,保证对非一致目标的跟踪误差平方在一个有限区间上的积分渐近收敛于零,克服了传统的迭代学习控制(ILC)对目标轨线限制,可以跟踪非一致目标轨线.通过构造复合能量函数,给出了闭环系统收敛的一个充分条件,仿真结果说明了该方法的有效性和可行性.     

基于H∞方法的鲁棒迭代学习控制器在精密工件台中的应用

针对精密工件台系统,研究迭代学习控制器(ILC)的设计问题,提出一种基于H∞法的ILC设计方法,分析该方法的可解性,推导出误差收敛的充要条件,并通过此方法将迭代学习控制器的综合问题转化为H∞最(次)优控制器的综合问题.同时介绍一种可明确处理过程不确定性的鲁棒ILC方法,这种ILC算法可使系统的学习性能最大化.精密工件台的实验结果表明所提出的设计方法是有效的.     

基于未知控制增益的非线性系统自适应迭代反馈控制

针对一类单输入单输出不确定非线性重复跟踪系统, 提出一种基于完全未知控制增益的自适应迭代反馈控制. 与普通迭代学习控制需要学习增益稳定性前提条件不同, 所提自适应迭代反馈控制律通过不断修改Nuss baum形式的反馈增益达到收敛. 证明当迭代次数i→δ时, 重复跟踪误差可一致收敛到任意小界δ. 仿真显示了所提控制方法的有效性.     

Learning control for discrete-time nonlinear systems with sensor saturation and measurement noises

The iterative learning control (ILC) is investigated for a class of nonlinear systems with measurement noises where the output is subject to sensor saturation. An ILC algorithm is introduced based on the measured output information rather than the actual output signal. A decreasing sequence is also incorporated into the learning algorithm to ensure a stable convergence under stochastic noises. It is strictly proved with the help of the stochastic approximation technique that the input sequence converges to the desired input almost surely along the iteration axis. Illustrative simulations are exploited to verify the effectiveness of the proposed algorithm.     

Stochastic Iterative Learning Control With Faded Signals

Stochastic iterative learning control (ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists. Illustrative examples are provided to verify the effectiveness of the proposed schemes.      

Enhancing Iterative Learning Control With Fractional Power Update Law

The P-type update law has been the mainstream technique used in iterative learning control (ILC) systems, which resembles linear feedback control with asymptotical convergence. In recent years, finite-time control strategies such as terminal sliding mode control have been shown to be effective in ramping up convergence speed by introducing fractional power with feedback. In this paper, we show that such mechanism can equally ramp up the learning speed in ILC systems. We first propose a fractional power update rule for ILC of single-input-single-output linear systems. A nonlinear error dynamics is constructed along the iteration axis to illustrate the evolutionary converging process. Using the nonlinear mapping approach, fast convergence towards the limit cycles of tracking errors inherently existing in ILC systems is proven. The limit cycles are shown to be tunable to determine the steady states. Numerical simulations are provided to verify the theoretical results.      

Sampled‐data iterative learning control for continuous‐time nonlinear systems with iteration‐varying lengths

In this work, sampled‐data iterative learning control (ILC) method is extended to a class of continuous‐time nonlinear systems with iteration‐varying trial lengths. In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled‐data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant. To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases.     

间歇过程最优迭代学习控制的发展:从基于模型到数据驱动

本文综述了间歇过程的基于模型的和数据驱动的最优迭代学习控制方法.基于模型的最优迭代学习控制方法需要已知被控对象精确的线性模型,其研究较为成熟和完善,有着系统的设计方法和分析工具.数据驱动的最优迭代学习控制系统设计和分析的关键是非线性重复系统的迭代动态线性化.本文简要综述了基于模型的最优迭代学习控制的研究进展,详细回顾了数据驱动的迭代动态线性化方法,包括其详细的推导过程和突出的特点.回顾和讨论了广义的数据驱动最优迭代学习控制方法,包括完整轨迹跟踪的数据驱动最优迭代学习控制方法,提出和讨论了多中间点跟踪的数据驱动最优点到点迭代学习控制方法,和终端输出跟踪的数据驱动最优终端迭代学习控制方法.进一步,迭代学习控制研究中的关键问题,如随机迭代变化初始条件、迭代变化参考轨迹、输入输出约束、高阶学习控制律、计算复杂性等.本文突出强调了基于模型的和数据驱动的最优迭代学习控制方法各自的特点与区别联系,以方便读者理解.最后,本文提出数据驱动的迭代学习控制方法已成为越来越复杂间歇过程控制发展的未来方向,一些开放的具有挑战性的问题还有待于进一步研究.     

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control (AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance. To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control (ILC), a new boundary layer function is proposed by employing Mittag-Leffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function (CEF) containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

A note on causal and CITE iterative learning control algorithms

The convergence properties of causal and current iteration tracking error (CITE) discrete time iterative learning control (ILC) algorithms are studied using time and frequency domain convergence criteria. Of particular interest are conditions for monotone convergence, and these are evaluated using a discrete-time version of Bode's integral theorem.     

Iterative learning control design with high‐order internal model for discrete‐time nonlinear systems

In this paper, a high‐order internal model (HOIM)‐based iterative learning control (ILC) scheme is proposed for discrete‐time nonlinear systems to tackle the tracking problem under iteration‐varying desired trajectories. By incorporating the HOIM that is utilized to describe the variation of desired trajectories in the iteration domain into the ILC design, it is shown that the system output can converge to the desired trajectory along the iteration axis within arbitrarily small error. Furthermore, the learning property in the presence of state disturbances and output noise is discussed under HOIM‐based ILC with an integrator in the iteration axis. Two simulation examples are given to demonstrate the effectiveness of the proposed control method. Copyright © 2016 John Wiley & Sons, Ltd.