一种新的非线性离散时间系统迭代学习控制的前馈－反馈机制

This paper presents a new feedback-feedforward configuration for the iterative learning control (ILC) design withfeedback, which consists of a feedback and a feedforward component. The feedback integral controller stabilizes the system,and takes the dominant role during the operation, and the feed-forward ILC compensates for the repeatable nonlinear/unknowntime-varying dynamics and disturbances, thereby enhancing the performance achieved by feedback control alone. As the mostfavorable point of this control strategy, the feedforward ILC and the feedback control can work either independently or jointlywithout making efforts to recongurate or retune the feedforward/feedback gains. With rigorous analysis, the proposedlearning control scheme guarantees the asymptotic convergences along the iteration axis.     

含多状态时滞的连续时间迭代学习控制系统稳定性分析

探讨了含多状态时滞连续时间迭代学习控制系统的稳定性分析问题, 尤其是当系统参数带有多面体不确定性时的鲁棒稳定性分析问题. 通过引入一个扩展算子, 利用迭代学习控制中的二维分析方法给出了时滞系统整个学习动态过程的连续离散Roesser系统描述. 基于所得的Roesser系统, 首先利用二维系统理论给出了保证迭代学习控制系统渐近稳定的充要条件, 然后结合鲁棒H∞控制理论提出了以线性矩阵不等式形式描述的充分条件来保证迭代学习控制系统的单调收敛性. 结果表明, 通过求解线性矩阵不等式确定的学习增益可以使控制输入误差随着迭代次数的增加单调收敛于零. 仿真结果表明, 通过增加满足一组线性矩阵不等式条件的P型学习增益能够使得一个鲁棒渐近稳定的迭代学习控制方案变为鲁棒单调收敛的, 同时还可以大大提高收敛速率.     

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.     

时变机器人系统的重复学习控制: 一种混合学习方案

Repetitive learning control is presented for finite-time-trajectory tracking of uncertain time-varying robotic systems. A hybrid learning scheme is given to cope with the constant and time-varying unknowns in system dynamics, where the time functions are learned in an iterative learning way, without the aid of Taylor expression, while the conventional differential learning method is suggested for estimating the constant ones. It is distinct that the presented repetitive learning control avoids the requirement for initial repositioning at the beginning of each cycle, and the time-varying unknowns are not necessary to be periodic. It is shown that with the adoption of hybrid learning, the boundedness of state variables of the closed-loop system is guaranteed and the tracking error is ensured to converge to zero as iteration increases. The effectiveness of the proposed scheme is demonstrated through numerical simulation.     

具有时变时滞的Lurie系统绝对稳定性的时滞相关条件

Some delay-dependent absolute stability criteria for Lurie control systems with time-varying delay are derived, in which some free-weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI. Moreover, the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems. Finally, some examples are provided to demonstrate the effectiveness of the proposed methods.     

线性离散奇异系统的不定二次最优控制问题: Krein空间方法

The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter. Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

基于迭代学习的离散线性时变系统故障诊断

针对一类离散线性时变系统的故障诊断问题,提出一种新的故障检测与估计算法.该算法通过引入虚拟故障构建离散故障跟踪估计器,在选取的优化时域内,利用估计器输出和系统实际输出产生的残差信号,采用迭代学习算法来调节虚拟故障,使虚拟故障逼近系统中实际发生的故障,从而达到对系统故障诊断的目的.该方法不仅能检测出系统不同类型的故障,还可以实现对故障信号的精确估计.仿真结果验证了所提出方法的有效性.     

一类非线性时变系统的迭代学习控制

针对一类具有任意初态的不确定非线性时变系统,应用校正期望轨迹方法把任意初态问题转换为零初始误差的变期望轨迹的迭代学习控制问题,提出了求解校正期望轨迹的过渡轨迹的计算方法.然后,针对变期望轨迹问题提出了一种新的迭代学习控制算法,在算法中引入了期望轨迹的高阶导数来克服期望轨迹的变化,并通过设计稳定的跟踪误差滑动面来处理系统中非线性时变不确定性.论文给出了相关定理,并应用类Lyapunov方法给出了详细证明.仿真结果表明所提出的算法是有效的,该算法不需要系统的模型结构信息,比自适应迭代学习控制算法具有更宽的适用范围.     

参数不确定离散广义大系统的保性能控制

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper. The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities (LMIs), and a desired state feedback controller is obtained via convex optimization. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

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.     

严格反馈非线性时变系统的迭代学习控制

针对一类含未知时变参数的严格反馈非线性系统, 提出一种实现有限作业区间轨迹跟踪控制的迭代学习算法. 基于Lyapunov-like方法设计控制器, 回避了常规迭代学习控制中受控系统非线性特性需满足全局Lipschitz连续条件的要求. 以反推设计(Backstepping)方法设计控制器, 为使得虚拟控制项可导, 引入一级数收敛序列; 将时变参数展开为有限项多项式形式, 在控制器设计中采取双曲正切函数处理余项对于系统跟踪性能的影响. 理论分析表明, 闭环系统所有信号有界, 并能够实现系统输出完全收敛于理想轨迹.     

Closed-loop P-type Iterative Learning Control of Uncertain Linear Distributed Parameter Systems

An iterative learning control problem for a class of uncertain linear parabolic distributed parameter systems is discussed, which covers many processes such as heat and mass transfer, convection diffusion and transport. Under condition of allowing system state initially to have error in the iterative process a closed-loop P-type iterative learning algorithm is presented, and the sufficient condition of tracking error convergence in L2 norm is given. Next, the convergence of the tracking error in L2 and W1,2 space is proved by using Gronwall-Bellman inequality and Sobolev inequality. In the end, a numerical example is given to illustrate the effectiveness of the proposed method.      

一类离散模糊系统的迭代学习控制算法

针对离散T-S模糊系统的终端控制问题,提出了一种基于离散Legendre正交多项式的迭代学习算法。该算法把待求控制量表示为离散Legendre正交多项式的线性组合,将求控制量问题转化为求离散Legendre正交多项式系数问题。在此基础上,用迭代学习的方式来修正控制量的离散Legendre系数,并运用不确定离散系统的H∞设计方法求解学习增益矩阵。最后以机器人为例进行仿真,仿真结果表明了所提算法能实现工业机器人的精确定位。     

Recent Advances in Iterative Learning Control

In this paper we review the recent advances in three sub-areas of iterative learning control (ILC): 1) linear ILC for linear processes, 2) linear ILC for nonlinear processes which are global Lipschitz continuous (GLC), and 3) nonlinear ILC for general nonlinear processes. For linear processes, we focus on several basic configurations of linear ILC. For nonlinear processes with linearILC, we concentrate on the design and transient analysis which were overlooked and missing for a long period. For general classes of nonlinear processes, we demonstrate nonlinear ILC methods based on Lyapunov theory, which is evolving into a new control paradigm.     

Adaptive Iterative Learning Control for a Class of Nonlinear Time-varying Systems with Unknown Delays and Input Dead-zone

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of dead-zone nonlinearity is presented. The assumption of identical initial condition for iterative learning control (ILC) is removed by introducing boundary layer function. The uncertainties with time-varying delays are compensated for by using appropriate Lyapunov-Krasovskii functional and Young0s inequality. Radial basis function neural networks are used to model the time-varying uncertainties. The hyperbolic tangent function is employed to avoid the problem of singularity. According to the property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closedloop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

Optimal Terminal Iterative Learning Control for the Automatic Train Stop System

The train stop control is a typical set‐point control task, where only the final state (i.e., the terminal train stop position) is of concern and specified. For such a control problem, an optimal terminal iterative learning control (TILC) approach is presented in this paper, where the stopping position and initial braking speed are chosen as the terminal system output and the control input, respectively. The controller design only depends on the measured input/output (I/O) data without requiring any modeling information of the train operation system, and the learning gain is updated by the system I/O data iteratively to accommodate the system uncertainties. The monotonic convergence of the terminal tracking error is guaranteed by rigorous mathematical analysis. Extensive simulation results are provided to show the applicability and effectiveness of the proposed approach.     

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.     

An Iterative Learning Control of Nonlinear Systems Using Neural Network Design

In this paper, a feedforward neural network with sigmoid hidden units is used to design a neural network based iterative learning controller for nonlinear systems with state dependent input gains. No prior offline training phase is necessary, and only a single neural network is employed. All the weights of the neurons are tuned during the iteration process in order to achieve the desired learning performance. The adaptive laws for the weights of neurons and the analysis of learning performance are determined via Lyapunov‐like analysis. A projection learning algorithm is used to prevent drifting of weights. It is shown that the tracking error vector will asymptotically converges to zero as the iteration goes to infinity, and the all adjustable parameters as well as internal signals remain bounded.     

Analysis Of Linear Iterative Learning Control Schemes Using Repetitive Process Theory

The purposes of this paper are (i) to critically review existing results on the use of the systems theory for repetitive processes in the analysis of a wide class of linear iterative control laws, and (ii) to present some new results on controller design using this general approach. This paper first presents results on the stability and convergence properties of a general class of iterative learning control schemes using, in the main, theory first developed for the subclass of so‐called differential and discrete linear repetitive processes. A general learning law that uses information from the current and a finite number of previous trials is considered and the results are interpreted in terms of basic systems theoretic concepts such as the relative degree and minimum phase characteristics. It is also shown that a number of other approaches reported in the literature are, in fact, special cases of the results obtained in the repetitive process setting. In the second part of the paper, new results on controller design are given based on 2D transfer function matrices together with new results on the robustness of norm optimal iterative learning control schemes.