正则系统在Lebesgue-p范数意义下的快速迭代学习控制

针对一类线性正则系统,传统迭代学习控制算法收敛速度较低的问题,设计了一种快速迭代学习控制算法。该算法在传统P型迭代学习控制算法基础上,增加了由相邻两次迭代时跟踪误差构成的上一次差分信号和当前差分信号,并在Lebesgue-p范数度量意义下,利用卷积推广的Young不等式严格证明了,当迭代次数趋于无穷大时,系统的跟踪误差收敛于零,并给出了算法的收敛条件。该算法与传统P型迭代学习控制算法相比,不仅提高了收敛速度,而且还避免了采用λ范数度量跟踪误差的缺陷,最后通过仿真结果进一步验证了所提算法的有效性。     

基于迭代学习的多智能体系统分布式跟踪控制

文章考虑了具适多智能体系统的分布式跟踪控制问题。通过设计带有初始学习机制的$P$型和$PD^{\alpha}$ 型迭代学习控制策略求解跟踪问题。具适导数具有良好的性质且可以刻画不同步长的实际数据采样情况。初始学习机制放松了初始值条件且提高了算法实现趋同跟踪的性能。在可重复操作环境和有向通信拓扑的假设下,提出了一种分布式迭代学习方案,通过重复同一轨迹的控制尝试和用跟踪误差修正不满意的控制信号来实现有限时间趋同。严格证明了随着迭代次数增加,提出的$P$型和$PD^{\alpha}$ 型迭代学习控制策略使得所有智能体能渐近跟踪上参考轨迹。两个代表性数值仿真验证了算法的有效性。     

PD型模糊学习控制及其在可重复轨迹跟踪问题中的应用

针对可重复轨迹跟踪问题,提出了一种PD型模糊学习算法.该算法集成两种控 制:作为基础的PD型模糊逻辑算法和改善系统性能的学习算法.模糊学习控制在模糊控制 基础上引入迭代学习算法,使得模糊PD控制器可以精确地跟踪可重复轨迹以及消除周期性 扰动.本文在能量函数和泛函分析的基础上,通过严格的推导表明PD型模糊学习算法可达 到:1)系统跟踪误差一致收敛到零;2)学习控制序列几乎处处收敛到理想的控制信号.     

多变量非线性系统的变阶采样迭代学习控制

针对存在初态误差的情形, 提出多变量非线性系统的变阶采样迭代学习控制方法. 相对固定阶迭代学习算法, 变阶算法可有效降低跟踪误差. 对变阶采样迭代学习算法进行了收敛性分析, 推导出收敛充分条件. 给出了变阶学习的两种实现策略-DD (Direct division)和DIP (Division in phases)策略. 数值仿真表明, 基于DIP策略的变阶采样迭代学习算法在获得较高的控制精度的同时, 具有较快的收敛速度.     

非参数不确定时滞系统的重复控制

针对非参数不确定时滞系统,给出能够实现跟踪误差本身沿整个周期完全跟踪的重复控制器设计．针对系统不确定特性的界函数已知和未知两种情形,分别分析闭环系统的稳定性与收敛性．控制器中学习部分采用完全饱和形式,使得参数估计囿于一预先给定的范围内．该控制律可保证闭环系统内所有信号有界以及跟踪误差本身趋于零．数值仿真表明算法的有效性．     

基于泰勒级数的迭代学习算法

针对存在不确定扰动的线性时变系统的轨迹跟踪控制问题,提出了基于泰勒级数的迭代学习算法．该算法利用泰勒级数将系统参数化,导出一种基于泰勒级数的线性时变系统的近似模型．在此模型的基础上,利用迭代学习方式修正输入量的泰勒展开系数,并用LMI方法求解学习增益矩阵．所提出算法在系统不满足正则性或无源性时,仍可用输出误差信号来构造学习律．仿真结果表明了该算法的有效性．     

即时学习算法在非线性系统迭代学习控制中的应用

运用即时学习算法来解决一类非线性系统的迭代学习控制初值问题。对于任何类型的迭代学习控制算法，即时学习算法都能有效地估计初始控制量，减小了初始输出误差，加快了算法的收敛速度，使得经过有限次迭代后系统输出能严格跟踪理想信号。对机器人系统的仿真结果表明了该方法的有效性。     

非线性时滞系统的周期自适应学习跟踪控制

针对一类参数未知的周期非线性时滞系统的输出跟踪控制问题,设计了一种周期自适应迭代学习跟踪控制算法,该方法利用信号置换的思想重组系统,并在假设未知时变参数和参考输出的周期具有已知最小公倍数的情况下,将时滞以及其他不确定的时变项合并为一个周期性的辅助时变参数新变量,进而用周期自适应算法来估计该辅助量.通过构造一个Lyapunov-Krasovskii型复合能量函数,分析了系统的收敛性,证明了经过多次重复迭代学习,所有闭环信号有界且输出跟踪误差收敛,最后通过构造数值实例进行了仿真验证.理论分析和仿真结果表明,该算法简单有效,对于非线性时滞系统的跟踪问题具有很好的控制效果.     

基于向量图分析的一种迭代学习控制算法 及其鲁棒性

为了增强迭代学习控制的鲁棒性,加快学习过程的收敛速度,而又不过多地依赖于系统内部信息,本文基于向量图分析思路,利用输入空间的向量构造三角形修正结构,得到了一种新的迭代学习控制算法．该算法根据跟踪误差的大小,调节输入控制量在三角形的一条边上滑动,在跟踪误差较大时,算法能找到控制期望的大致位置并加速收敛,在跟踪误差较小时,能将控制量稳定在其期望的很小邻域内,理论上证明了该邻域直径大小为跟踪误差的二阶无穷小．数值仿真结果说明了它的有效性和优越性．     

一种基于CMAC的自学习控制器

现有的基于CMAC的自学习控制器能够有效地减小跟踪误差,但是在跟踪连续变 化信号如正弦波时,由于累积误差的影响会产生过学习现象,进而导致系统的不稳定.为此, 提出一种新的基于CMAC的自学习控制器,它以系统的动态误差作为CMAC的激励信号, 从而避免了累积误差的影响.仿真结果表明,该控制器不仅是有效的,而且具有很强的鲁棒 性.此外,它可以使用较高的学习速率,实时性强.     

一种参数优化的非线性离散系统鲁棒迭代学习控制方法

针对带有扰动的一类离散非线性系统的鲁棒迭代学习控制问题, 设计一种基于参数优化的迭代学习控制算法. 该算法能够保证在有初始状态误差和状态、输出扰动的情况下使闭环系统具有鲁棒BIBO 稳定性, 系统输出能够单调收敛于给定输出轨迹的邻域内; 在没有初始状态误差和扰动的情况下能够以零稳态误差跟踪给定输出轨迹. 最后通过仿真分析验证了所提出算法的有效性.

     

非线性系统迭代跟踪控制的批次遗忘学习算法

针对P型迭代学习算法对初始偏差和输出误差扰动敏感,以及PD型迭代学习算法容易放大系统噪声,降低系统鲁棒性的问题,研究了具有任意有界扰动及期望输出的重复运行非线性时变系统的PD型迭代学习跟踪控制算法.利用迭代学习过程记忆的期望轨迹、期望控制以及跟踪误差,给出基于变批次遗忘因子的学习控制器设计,并借助λ范数理论和Bellman-Gronwall不等式,讨论保证闭环跟踪系统批次误差有界的学习增益存在的充分必要条件,及分析控制算法的一致收敛性.本算法改善了系统的鲁棒性和动态特性,单关节机械臂的跟踪控制仿真验证了方法的有效性.     

Iterative learning control of molten steel level in a continuous casting process

In this paper, an iterative learning control (ILC) method is introduced to control molten steel level in a continuous casting process, in the presence of disturbance, noise and initial errors. The general ILC method was originally developed for processes that perform tasks repetitively but it can also be applied to periodic time-domain signals. To propose a more realistic algorithm, an ILC algorithm that consists of a P-type learning rule with a forgetting factor and a switching mechanism is introduced. Then it is proved that the input signal error, the state error and the output error are ultimately bounded in the presence of model uncertainties, periodic bulging disturbances, measurement noises and initial state errors. Computer simulation and experimental results establish the validity of the proposed control method.     

加速抑制随机初态误差影响的迭代学习控制

针对一类具有不确定性的多输入多输出非线性系统,提出一种迭代学习控制算法.该算法具有的特点是:针对任意初态情形,结合开环 D型迭代学习控制器的优点,在时间轴上设计了一个随迭代次数增加而缩短的时间段.在该时间段上,控制算法对状态偏差进行修正,以使系统输出在此段时间后跟踪期望输出,且系统跟踪误差收敛到一个界内.这个界仅由系统自身不确定性和不确定的外界干扰决定,与初态误差无关.当外界扰动为0,以及迭代次数趋于无穷时,经过上述时间段后,系统输出精确跟踪期望输出.理论证明和仿真结果都说明了该算法的有效性.     

离散非线性系统的迭代学习轨迹跟踪鲁棒算法优化及应用

针对一类存在随机输入状态扰动、输出扰动及系统初值与给定期望值不严格一致的离散非线性重复系统,提出了一种P型开闭环鲁棒迭代学习轨迹跟踪控制算法．基于λ范数理论证明了算法的严格鲁棒稳定性,并通过多目标函数性能指标优化P型开闭环迭代学习控制律的增益矩阵参数,保证了优化算法下系统输出期望轨迹跟踪误差的单调收敛性,达到提高学习算法收敛速度和跟踪精度的目的．最后应用于二维运动移动机器人的实例仿真,验证了本文算法的可行性和有效性．     

Kinematic path‐tracking of mobile robot using iterative learning control

This paper develops a kinematic path‐tracking algorithm for a nonholonomic mobile robot using an iterative learning control (ILC) technique. The proposed algorithm produces a robot velocity command, which is to be executed by the proper dynamic controller of the robot. The difference between the velocity command and the actual velocity acts as state disturbances in the kinematic model of the mobile robot. Given the kinematic model with state disturbances, we present an ILC‐based path‐tracking algorithm. An iterative learning rule with both predictive and current learning terms is used to overcome uncertainties and the disturbances in the system. It shows that the system states, outputs, and control inputs are guaranteed to converge to the desired trajectories with or without state disturbances, output disturbances, or initial state errors. Simulations and experiments using an actual mobile robot verify the feasibility and validity of the proposed learning algorithm. © 2005 Wiley Periodicals, Inc.     

Neuro-fuzzy control of antilock braking system using sliding mode incremental learning algorithm

A neuro-fuzzy adaptive control approach for nonlinear dynamical systems, coupled with unknown dynamics, modeling errors, and various sorts of disturbances, is proposed and used to design a wheel slip regulating controller. The implemented control structure consists of a conventional controller and a neuro-fuzzy network-based feedback controller. The former is provided both to guarantee global asymptotic stability in compact space and as an inverse reference model of the response of the controlled system. Its output is used as an error signal by an incremental learning algorithm to update the parameters of the neuro-fuzzy controller. In this way the latter is able to gradually replace the conventional controller from the control of the system. The proposed new learning algorithm makes direct use of the variable structure systems theory and establishes a sliding motion in terms of the neuro-fuzzy controller parameters, leading the learning error toward zero. In the simulations and in the experimental studies, it has been tested on the control of antilock breaking system model and the analytical claims have been justified under the existence of uncertainty and large nonzero initial errors.     

Output regulation of uncertain nonlinear systems with nonlinear exosystems

An adaptive control algorithm is proposed for output regulation of uncertain nonlinear systems in output feedback form under disturbances generated from nonlinear exosystems. A new nonlinear internal model is proposed to generate the desired input term for suppression of the disturbances. The proposed internal model design is based on boundedness of the disturbance, high gain design and saturation. It is capable to tackle disturbances in any specified initial conditions. Some uncertainties in the systems are allowed, provided that they do not affect the desired feedforward control term, and they are tackled by using nonlinear dominant functions and an adaptive control coefficient. The proposed control algorithm ensures the global convergence of the state variables to the invariant manifold, which implies that the measurement or the tracking error approaches to zero asymptotically.     

A discrete-time stochastic learning control algorithm

In this paper, the learning gain, for a selected learning algorithm, is derived based on minimizing the trace of the input error covariance matrix for linear time-varying systems. It is shown that, if the product of the input/output coupling matrices is a full-column rank, then the input error covariance matrix converges uniformly to zero in the presence of uncorrelated random disturbances. However, the state error covariance matrix converges uniformly to zero in presence of measurement noise. Moreover, it is shown that, if a certain condition is met, then the knowledge of the state coupling matrix is not needed to apply the proposed stochastic algorithm. The proposed algorithm is shown to suppress a class of nonlinear and repetitive state disturbance. The application of this algorithm to a class of nonlinear systems is also considered. A numerical example is included to illustrate the performance of the algorithm     

Disturbance compensation incorporated in predictive control system using a repetitive learning approach

In this paper, a disturbance compensation scheme is incorporated into a predictive control scheme using a repetitive learning approach. It has the following contributions. First, based on the assumption of the presence of both state and output disturbances, a predictive control algorithm is derived. Secondly, to estimate the disturbances, two feedforward disturbance learning schemes are proposed. Thirdly, the rigid mathematic proof is given to guarantee the convergence of the tracking error under the proposed disturbance learning laws used in conjunction with the predictive controller formulated. Finally, simulation results are provided to illustrate the good performance achievable by the proposed control law.