线性广义系统P型迭代学习控制离散频域收敛性

针对一类线性广义系统,研究其P型迭代学习控制在离散频域中的收敛性态。在离散频域中,对广义系统进行奇异值分解后,利用傅里叶级数系数的性质和离散的Parseval能量等式,推演了一阶P型迭代学习控制律跟踪误差的离散能量频谱的递归关系和特性,获得了学习控制律收敛的充分条件;讨论了二阶P型迭代学习控制律的收敛条件。仿真实验验证了理论的正确性和学习律的有效性。     

初态学习下的迭代学习控制

提出一种新的初态学习律，以放宽常规迭代学习控制方法的初始定位条件．它允许一定的定位误差，在迭代中不需要定位在某一具体位置上，使得学习控制系统具有鲁棒收敛性．针对二阶LTI系统，给出了输入学习律及初态学习律的收敛性充分条件．依据收敛性条件，学习增益的选取需系统矩阵的估计值，但在一定建模误差下，仍能保证算法的收敛性．所提出的初态学习律本身及其收敛性条件均与输入矩阵无关．     

一类广义系统的迭代学习控制

在对广义系统进行标准分解的基础上, 研究了含脉冲快子系统的迭代学习控制问题. 通过 Frobenius 范数给出了快子系统在 P 型学习律作用下收敛的充分性条件, 同时通过梯度法给出求解增益矩阵的方法. 其次, 讨论了单输入单输出不确定广义系统的迭代学习控制问题, 通过优化方法给出该系统在 P 型学习律作用下, 系统实际输出尽可能快地收敛到理想输出的增益矩阵的选择方法.     

提高迭代自学习控制算法收敛速度初探

从学习律、学习律参数、输出误差等三方面讨论了迭代自学习算法的收敛速度,为提高该算法的收剑速度得到了一些有用的结论。     

非线性系统开闭环PID型迭代学习控制算法的鲁棒性

针对非线性时变系统的迭代学习控制问题提出了一种开闭环PID型迭代学习控制律,并证明了系统满足收敛条件时,具有开闭环PID型迭代学习律的一类非线性时变系统在动态过程存在干扰的情况下控制算法的鲁棒性问题.分析表明,系统在状态干扰、输出干扰和初态干扰有界的情况下跟踪误差有界收敛,在所有干扰渐近重复的情况下可以完全地跟踪给定的期望轨迹.     

基于类牛顿学习律的携行外骨骼系统控制

为了提高系统的控制速度及精度,运用携行系统重复运动这一特性,根据类牛顿迭代学习律的理论,构造了时变的下肢外骨骼迭代学习算子,考虑了人机作用力。仿真结果表明了该方法的可行性及有效性。     

可变学习增益的迭代学习控制律

基于迭代学习控制理论提出了一种可变学习增益的迭代学习律,在非线性系统中对期望轨迹进行跟踪,与学习增益不变的迭代学习控制相比较,收敛速度得到很大的提高;通过对其收敛性进行严格的数学证明,得到了迭代学习律收敛的充分条件;在单机无穷大系统中,将该控制律应用于同步发电机的励磁控制,仿真结果表明该控制律的有效性,改善了控制的动态特性,有利于提高电力系统稳定性.     

抑制初态误差影响的自适应迭代学习控制

针对一类参数化高阶不确定非线性连续系统, 设计迭代学习控制算法, 以解决随机初态对系统跟踪性能产生负面影响的问题. 结合滑模控制思想以及部分限幅参数学习律, 控制算法在预设时间段内抑制随机初态偏差对系统跟踪性能的影响. 经过预设时间后, 随着迭代次数的增加, 系统的跟踪误差及其各阶导数一致收敛到零. 且在整个运行时间段内, 系统各个变量一致有界. 此外, 本文回避了非参数化不确定非线性系统在放宽迭代初值假设时常使用的Lipschitz假设条件, 而采用类Lyapunov函数分析法设计迭代学习控制器. 理论证明和仿真结果都说明了该算法的有效性.     

分数阶迭代学习控制的收敛性分析

本文将传统的迭代学习控制时域和频域分析方法扩展到一类针对分数阶非线性系统的分数阶迭代学习控制时域分析方法.提出了一类新的分数阶迭代学习控制框架并简化了收敛条件,且证明了常增益情况下两类分数阶迭代学习控制收敛条件的等价性问题.该讨论进一步引出了如下两个结果:分数阶不确定系统的分数阶自适应迭代学习控制的可学习区域以及理想带阻型分数阶迭代学习控制的框架.上述结果均得到了仿真验证.     

基于Jacobi方法的线性离散时间系统的迭代学习控制

提出线性离散时间系统基于Jacobi方法的迭代学习控制问题.通过构建线性迭代学习控制问题与线性方程组之间的联系,将Jacobi方法引入到迭代学习控制中,并由此构建得到迭代学习控制律.借助于矩阵运算,证明这种学习律能使得系统的输出跟踪误差经有限次迭代后为零.数值例子说明了算法的可适用性.     

具有反馈信息的迭代学习控制律在Lebesgue-p范数意义下的收敛性

针对一类线性时不变系统, 提出了具有反馈信息的PD-型(Proportional-derivative-type)迭代学习控制律, 利用卷积的推广的Young不等式, 分析了控制律在Lebesgue-p范数意义下的单调收敛性. 分析表明, 收敛性不但决定于系统的输入输出矩阵和控制律的微分学习增益, 而且依赖于系统的状态矩阵和控制律的比例学习增益; 进一步, 当适当选取反馈增益时, 反馈信息可加快典型的PD-型迭代学习控制律的单调收敛性. 数值仿真验证了理论分析的正确性和控制律的有效性.     

迭代学习控制在线性时变系统终端控制问题中的应用研究

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.     

Observer‐based Fault Estimators Using Iterative Learning Scheme for Linear Time‐delay Systems with Intermittent Faults

This paper deals with the fault estimation problem for a class of linear time‐delay systems with intermittent fault and measurement noise. Different from existing observer‐based fault estimation schemes, in the proposed design, an iterative learning observer is constructed by using the integrated errors composed of state predictive error and tracking error in the previous iteration. First of all, Lyapunov function including the information of time delay is proposed to guarantee the convergence of system output. Subsequently, a novel fault estimation law based on iterative learning scheme is presented to estimate the size and shape of various fault signals. Upon system output convergence analysis, we proposed an optimal function to select appropriate learning gain matrixes such that tracking error converges to zero, simultaneously to ensure the robustness of the proposed iterative learning observer which is influenced by measurement noise. Note that, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality (LMI) by the Schur complements and Young relation. In addition, the results are both suit for the systems with time‐varying delay and the systems with constant delay. Finally, three numerical examples are given to illustrate the effectiveness of the proposed methods and two comparability examples are provided to prove the superiority of the algorithm.     

Study on the Application of Iterative Learning Control to Terminal Control of Linear Time-varying Systems

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.     

迭代学习控制系统的误差跟踪设计方法

提出能够实现期望误差轨迹完全跟踪的迭代学习控制系统设计方法, 旨在放宽常规迭代学习控制方法的初始定位条件, 在每次迭代时允许初值定位在任意位置. 这种方法对于预先给定的期望误差轨迹, 经迭代学习, 使得实际跟踪误差收敛于预定的误差轨迹, 这样, 预设的误差轨迹即最终形成的误差轨迹. 针对常参数、时变参数以及复合参数三种情形, 分别采用类Lyapunov方法设计迭代学习控制系统. 所设计的未含/含限幅作用的参数学习律, 能够使得跟踪误差轨迹在整个作业区间上与预定轨迹完全吻合, 并保证系统中所有信号的有界性. 给出的仿真结果表明所提方法的有效性.     

未知相对度非线性系统的一阶D型迭代学习控制

The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.     

误差约束严格反馈系统的迭代学习控制

针对一类严格反馈非线性系统, 本文提出误差跟踪学习控制算法, 旨在解决状态约束问题和系统的初值问 题. 文中构造了二次分式型对称障碍Lyapunov函数以及二次分式型非对称障碍Lyapunov函数, 并结合反推技术来分 别设计学习控制器. 两种控制方案里分别采用积分学习律和微分–差分学习律估计未知系数. 系统跟踪误差在控制 器作用下囿于预设的界内, 从而实现迭代过程中对状态的约束; 引入期望误差轨迹, 经迭代学习后, 两种控制方案均 能够实现状态误差在整个作业区间上对期望误差轨迹的完全跟踪, 并且实现系统输出在预指定作业区间上精确跟 踪参考信号. 数值仿真结果表明了控制方案的有效性.     

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.      

基于LMI方法的保性能迭代学习算法设计

研究基于性能的迭代学习算法设计与优化问题.首先定义了迭代域二次型性能函数,然后针对线性离散系统给出了迭代域最优迭代学习算法;基于线性矩阵不等式(LMI)方法,针对不确定线性离散系统给出了保性能迭代学习算法及其优化方法.对于这两类迭代学习算法,只要调整性能函数中的权系数矩阵,便可很好地调整迭代学习收敛速度.另外,保性能迭代学习算法设计及优化过程,可利用MATLAB工具箱很方便地求解.