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.     

高阶无模型自适应迭代学习控制

针对一类非线性非仿射离散时间系统,提出了高阶无模型自适应迭代学习控制方案.控制器的设计和分析仅依赖于系统的输入/输出(I/O)数据,不需要已知任何其他知识.该方法采用了高阶学习律,可利用更多以前重复过程中的控制信息提高系统收敛性,且学习增益可通过"拟伪偏导数"更新律迭代调节.仿真结果验证了所提出算法的有效性.     

非最小相位系统的基函数型自适应迭代学习控制

针对重复运行的未知非最小相位系统的轨迹跟踪问题, 结合时域稳定逆特点, 提出了一种新的基函数型自适应迭代学习控制(Basis function based adaptive iterative learning control, BFAILC)算法. 该算法在迭代控制过程中应用自适应迭代学习辨识算法估计基函数模型, 采用伪逆型学习律逼近系统的稳定逆, 保证了迭代学习控制的收敛性和鲁棒性. 以傅里叶基函数为例, 通过在非最小相位系统上的控制仿真, 验证了算法的有效性.     

高阶参数优化迭代学习控制算法

针对线性时不变离散系统的跟踪问题提出一种高阶参数优化迭代学习控制算法.该算法通过建立考虑了多次迭代误差影响的参数优化目标函数,求解得出优化后的时变学习增益参数.从理论上证明了:对于线性离散时不变系统,该算法在被控对象不满足正定性的松弛条件下仍可保证跟踪误差单调收敛于零.同时,采用之前多次迭代信息的高阶算法具有更好的收敛性和鲁棒性.最后利用一个仿真实例验证了算法的有效性.     

迭代学习控制研究现状与趋势

系统论述了迭代学习控制的发展历史、研究进展.指出了基于可重复性的经典迭代学习控制特点与不足,阐述了迭代学习控制理论的现状:线性与非线性迭代学习、因果与非因果型迭代学习、滤波器型与鲁棒H∞迭代学习、高阶与最优迭代学习、2D复合迭代学习、迭代域超级矢量w变换学习系统分析理论等.简要介绍了与Lyapunov方法结合的新迭代学习控制,最后讨论了迭代学习控制存在问题和发展趋势.同时给出了几个迭代学习控制在工程应用中的成功范例.     

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.     

一类非线性采样系统高阶迭代学习控制

迭代学习控制能够实现期望轨迹的完全跟踪而被广泛关注,但是采样迭代学习控制成果目前还比较少。针对一类有相对阶和输出延迟的非线性采样系统,研究了高阶迭代学习控制算法。利用Newton-Leibniz公式、贝尔曼引理和Lipschiz条件证明了当系统的采样周期足够小,迭代学习初态严格重复,且学习增益满足要求的条件,那么系统输出在采样点上收敛于期望输出。对一阶和二阶学习算法的仿真表明高阶算法在收敛速度上比一阶有明显改善。     

非线性系统高阶迭代学习算法

结合迭代学习控制算法中的开环和闭环方案，本文针对更一般的非线性系统，讨论高阶算法的广泛适用性。理论和仿真结果表明了高阶算法在输出跟踪和干扰抑制方面的有效性。     

执行器饱和多智能体系统的自适应学习一致性算法

针对一类受到执行器饱和高阶多智能体系统在有限时间区间[0,T]上的精确一致性问题,利用自适应迭代学习控制的方法,设计了具有全饱和差分型自适应更新律的时变增益.通过构造适当的复合能量函数,严格证明了一致性误差向量随着迭代次数趋于无穷而一致趋于零,得到了不依赖于网络通信拓扑矩阵特征值的自适应学习一致性算法.最后,给出一个仿真例子,仿真结果说明了所提算法的有效性.     

高阶PID采样迭代学习控制

针对一类非线性带扰动系统提出了高阶PID采样速代学习控制算法,讨论了高阶算法的收敛性问题以及该算法的优势与缺陷.与传统的证明方法不同,利用泰勒级数展开法证明了被控对象在输入干扰和输出测量噪声均有界的情况下,高阶PID采样速代学习控制算法的收敛性,并且得出了收敛条件.由于收敛条件中没有积分项,因此更加利于分析计算.与传统的一阶采样迭代学习控制算法相比,高阶采样迭代学习控制算法由于利用了更多先前的控制信息而能使被控对象的实际输出更加接近理想输出.给出了相应的数值仿真,证明了理论分析的有效性.与此同时,结合啤酒生产过程中糖化阶段中酒花添加等实际问题对该算法的应用前景作了一定的分析.     

基于几何分析的分布参数系统的迭代学习控制

研究了一类不确定非线性分布参数系统的迭代学习控制问题.基于几何分析方法,给出了分布参数系统一种新的具有自适应因子的非线性迭代学习控制算法.导出了新算法的收敛条件,并利用广义λ范数从理论上证明了新算法的收敛性.     

基于向量图分析的分布参数系统迭代学习控制

针对一类不确定线性分布参数系统的迭代学习控制问题进行了讨论。基于向量图分析方法,提出了分布参数系统的一种新的迭代学习控制算法,该算法与现有算法不同,具有非线性形式。此外,利用 范数对所提新算法进行了完整的收敛性分析。     

非正则分布参数系统的迭代学习控制

针对一类非正则分布参数系统的迭代学习控制问题进行讨论, 该类分布参数系统由抛物型偏微分方程构成. 基于非正则系统的特点, 使用D型学习律构建得到迭代学习控制律, 并基于压缩映射原理, 证明得到输出跟踪误差在??² 范数意义下沿迭代轴方向的收敛性结论. 仿真算例表明了所提出结论的有效性.

     

Distributed adaptive fuzzy iterative learning control of coordination problems for higher order multi-agent systems

In this paper, the adaptive fuzzy iterative learning control scheme is proposed for coordination problems of Mth order (M ≥ 2) distributed multi-agent systems. Every follower agent has a higher order integrator with unknown nonlinear dynamics and input disturbance. The dynamics of the leader are a higher order nonlinear systems and only available to a portion of the follower agents. With distributed initial state learning, the unified distributed protocols combined time-domain and iteration-domain adaptive laws guarantee that the follower agents track the leader uniformly on [0, T]. Then, the proposed algorithm extends to achieve the formation control. A numerical example and a multiple robotic system are provided to demonstrate the performance of the proposed approach.     

一阶强双曲分布参数系统的迭代学习控制

研究了一阶强双曲分布参数系统的迭代学习控制问题.首先利用Fourier变换和半群方法导出了系统状态的适应解.进而基于强双曲条件和Plancheral定理,在允许迭代过程中初值存在一定偏差条件下,给出并证明了系统在P型迭代学习控制算法下的收敛条件.最后应用实例说明了所提方法的有效性.     

Iterative learning control for hyperbolic distributed parameter systems based on sensor–actuator networks

This paper proposes two kinds of iterative learning control (ILC) schemes for a class of the distributed parameter systems based on sensor–actuator networks which can be described by hyperbolic partial differential equations. A D-type ILC algorithm is first considered and the convergent condition of the output error is obtained via the contraction mapping methodology. Then, the PD-type ILC algorithm is considered in this hyperbolic distributed parameter systems based on sensor–actuator networks. Finally, a cable equation with air and structural damping is given to illustrate the effectiveness of the proposed methods.     

Iterative Learning Control for Distributed Parameter Systems Based on Non-Collocated Sensors and Actuators

In this paper, an open-loop PD-type iterative learning control (ILC) scheme is first proposed for two kinds of distributed parameter systems (DPSs) which are described by parabolic partial differential equations using non-collocated sensors and actuators. Then, a closed-loop PD-type ILC algorithm is extended to a class of distributed parameter systems with a non-collocated single sensor and m actuators when the initial states of the system exist some errors. Under some given assumptions, the convergence conditions of output errors for the systems can be obtained. Finally, one numerical example for a distributed parameter system with a single sensor and two actuators is presented to illustrate the effectiveness of the proposed ILC schemes.      

Iterative learning control for a class of mixed hyperbolic-parabolic distributed parameter systems

This paper deals with the problem of iterative learning control algorithm for a class of mixed distributed parameter systems. Here, the considered distributed parameter systems are composed of mixed hyperbolic-parabolic partial differential equations. The domain of the system is divided into two parts in which the system is hyperbolic and parabolic, respectively, with transmission conditions at the interface. According to the characteristics of the systems, iterative learning control laws are proposed for such mixed hyperbolic-parabolic distributed parameter systems based on P-type learning scheme. Using the contraction mapping method, it is shown that the scheme can guarantee the output tracking errors on L ² space converge along the iteration axis. A simulation example illustrates the effectiveness of the proposed method.     

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.      

High‐order internal model‐based iterative learning control design for nonlinear distributed parameter systems

This article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L²,λ) ‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.