任意初态下的迭代学习控制策略

针对一类在有限区间上执行重复任务的动态系统,本文提出一种迭代学习初始修正算法,用于解决各次迭代过程中的任意初态问题.通过构造一个虚拟误差函数来分析算法的收敛性,分析结果表明该算法可在指定区间上实现对期望轨迹的一致性跟踪,并通过求解线性矩阵不等式的方法获得具体的矩阵型控制增益.最后,通过数值结果,验证了算法的有效性.     

一类线性离散时间大系统的预见重复控制

文章针对一类线性离散时间大系统提出一种预见重复控制方法.结合预见控制和重复控制的优势,构造带有预见补偿作用和学习能力的控制器,即预见重复控制器,实现对预见周期性目标值信号的跟踪.首先,通过状态增广技术和二维模型方法,构造包含可预见目标值信号的二维扩大误差系统;其次,针对扩大误差系统,分别考虑状态反馈和输出反馈,并基于Lyapunov函数方法及线性矩阵不等式(LMI)技巧给出预见重复控制器设计方法.最后,通过比较预见重复控制、重复控制和预见控制,表明文章结果的有效性.     

有限时间迭代学习控制

针对任意初态情形, 借助于初始修正吸引子的概念,讨论不确定时变系统能够达到实际完全跟踪性能的迭代学习控制方法.闭环系统中含有限时间控制作用, 在预先指定的区间上实现零误差跟踪,且起始段的系统输出轨迹也可预先规划.分别讨论部分限幅学习与完全限幅学习, 证明闭环系统中各变量的一致有界性以及误差序列的一致收敛性. 变量有界性证明得益于提出的限幅学习算法,特别是完全限幅学习算法可确保参数估值的变化范围.     

一类非线性系统的分段迭代学习控制

本文提出并研究一类非线性系统的分段迭代学习控制问题.基于P型学习律和D型学习律构建得到分段迭代学习控制律,利用压缩映射原理,证明这种分段迭代学习律能使得系统的输出跟踪误差沿迭代轴方向收敛.仿真算例验证了算法的有效性.     

Lur'e主从系统的二次反馈型脉冲同步控制

本文研究Lur’e主从系统的脉冲同步控制问题.考虑脉冲控制器带有二次反馈的情况,利用多面体凸组合、线性矩阵不等式(LMI)和Lyapunov稳定性理论,设计两种在二次输出反馈型脉冲控制下主从系统同步的新策略.最后,通过数值模拟验证了所得结果的可行性与有效性.     

一类广义迭代学习控制系统的状态跟踪算法

利用迭代学习控制方法,研究了一类广义系统的状态跟踪问题.针对广义系统的分解形式,提出了一种新的迭代学习控制算法,该算法由部分D型算法和部分P型算法混合而成.给出了新算法的收敛条件,并从理论上对新算法进行了完整的收敛性分析.数值仿真结果说明了所提出的广义系统状态跟踪的迭代学习控制算法的有效性.     

关于“拟线性抛物型方程解的爆破时间的界”的一个注解（英文）

本文研究在空间维数是一维和二维情形下,一类拟线性抛物型方程在狄利克雷边界条件下的初边值问题.我们获得爆破速度和爆破时间的估计.     

基于最小二乘近似的模型平均方法

本文提出基于最小二乘近似的模型平均方法.该方法可用于线性模型、广义线性模型和分位数回归等各种常用模型.特别地,经典的Mallows模型平均方法是该方法的特例.现存的模型平均文献中,渐近分布的证明一般需要局部误设定假设,所得的极限分布的形式也比较复杂.本文将在不使用局部误设定假设的情形下证明该方法的渐近正态性.另外,本文将该方法发展到维数发散的情形.数值结果显示了该方法的优势.     

时滞不确定中立型分布参数系统的稳定性

针对一类时滞不确定中立型分布参数系统,研究该系统基于线性矩阵不等式方法的稳定性判据.基于线性矩阵不等式(LMI)方法,通过构造一系列适当的李雅普诺夫函数,利用散度定理和矩阵不等式技术,给出了系统是渐近稳定的充分条件.充分条件要求满足两个线性矩阵不等式,而线性矩阵不等式容易利用Matlab中的LMI工具箱进行求解.最后,数值算例验证了该方法的有效性.     

基于有限差分法的二阶双曲型分布参数系统的迭代学习控制

研究了一类分布参数系统基于有限差分法的迭代学习控制问题,该类分布参数系统由二阶双曲型偏微分方程所构建.针对系统所满足的初、边值条件,基于有限差分法构建得到迭代学习控制律,利用迭代收敛原理,证明这种学习律能使得系统的状态跟踪误差沿迭代轴方向收敛到原点的一个小邻域内.数值仿真验证了所提算法的有效性.     

线性定常广义系统的D型迭代学习控制收敛性

给出了线性定常广义系统在D型学习律作用下的迭代控制收敛性结果,这一结果是全新的,其对时变系统也成立,而且,本文结果和方法大部分可以移植到线性定常广义离散时间系统.     

A study on ILC for linear discrete systems with single delay

In this article, we utilize a new notation, namely discrete matrix delayed exponential function, to deal with iterative learning control (ILC) problem for linear discrete systems with single delay, which is totally different from the approach in the previous literatures. With the help of a representation of a solution involving discrete matrix delayed exponential function, we can not only present the output clearly on each subinterval determined by the length of time delay, but also we need not to not turn ILC for linear discrete delayed systems to a Roesser model, which is always used to seek the criterion for convergence results. Numerical examples are also presented to verify the theoretical results.     

Iterative learning control for linear discrete delay systems via discrete matrix delayed exponential function approach

ABSTRACT

This paper proposes iterative learning control (ILC) for linear discrete delay systems with randomly varying trial lengths without knowing prior information on the probability distribution of random iteration length. Based on matrix delayed exponential function approach, an explicit solution to the linear discrete delay controlled systems is used to generate a sequence of outputs that approximate the desired reference by adopting two ILC update laws in the presence of randomly iteration-varying lengths. A new and direct mathematical technique is explored to deal with ILC for linear discrete delay systems. Two illustrative examples are provided to verify the theoretical results.     

Iterative sliding mode control

Iterative Learning Control (ILC) methods are described and applied ever-increasingly as powerful tools to control dynamics nowadays.

ILC’s methods in most studies are described as based on repetitive process from the beginning to the end of process or as a kind of repetitive control.

Our newly designed controllers based on a particular case of iterative learning control radically differ from conventional methods in attempting to stabilize a class of non linear systems.

In this paper two kinds of ILC method are introduced in two separate sections. In the first, our newly designed method satisfies the condition of a Lyapunov stability theorem in a class of non linear systems in which their structures have the Lipschitz property. In the second, by freezing the time and moving to a new virtual axis, called the index axis, this newly designed method tries to find the best value for control at this time step and can be used in two modes, on-line and off-line.

In both methods, by satisfying the convergence condition of our designed ILC, closed loop stability is obtained automatically.     

High-Order \mathcal{D}^{\alpha}-Type Iterative Learning Control for Fractional-Order Nonlinear Time-Delay Systems

This paper presents a high-order $\mathcal{D}^{\alpha}$ -type iterative learning control (ILC) scheme for a class of fractional-order nonlinear time-delay systems. First, a discrete system for $\mathcal{D}^{\alpha}$ -type ILC is established by analyzing the control and learning processes, and the ILC design problem is then converted to a stabilization problem for this discrete system. Next, by introducing a suitable norm and using a generalized Gronwall–Bellman Lemma, the sufficiency condition for the robust convergence with respect to the bounded external disturbance of the control input and the tracking errors is obtained. Finally, the validity of the method is verified by a numerical example.     

Iterative learning consensus control with initial state learning for fractional order distributed parameter models multi-agent systems

This paper considers the consensus control problem of multi-agent systems (MAS) with distributed parameter models. Based on the framework of network topologies, a second-order PI-type iterative learning control (ILC) protocol with initial state learning is proposed by using the nearest neighbor knowledge. A discrete system for proposed ILC is established, and the consensus control problem is then converted to a stability problem for such a discrete system. Furthermore, by using generalized Gronwall inequality, a sufficient condition for the convergence of the consensus errors between any two agents is obtained. Finally, the validity of the proposed method is verified by two numerical examples.     

Iterative learning control for a class of nonlinear systems with random packet losses

This paper considers the problem of iterative learning control (ILC) for a class of nonlinear systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a networked control system (NCS), and that during the packet transfer between the remote nonlinear plant and the ILC controller packet dropout occurs. A new formulation is employed to model the packet dropout case, where the random dropout rate is transformed into a stochastic parameter in the system’s representation. Through rigorous analysis, it is shown that under some given conditions, the iterative learning control can guarantee the convergence of the tracking error although some packets are missing. The analysis is also supported by a numerical example.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

一类非线性系统的迭代学习控制

讨论一类非线性系统的迭代学习控制,系统的非线性动态对状态不快于多项式增长,而量测方程含有噪声.控制序列并非直接输给系统,而是先经过死区、预载及饱和等非线性函数.递推地给出了学习控制序列,并证明它的有界性及最优跟踪性.