基于时变神经网络的非线性时变系统建模

提出时变神经网络模型,用以逼近未知非线性时变映射,实现非线性时变系统建模.将时变神经网络的权值学习作为时变系统的时变参数估计问题,并基于迭代学习机制,给出在同一时刻沿迭代轴训练网络权值的迭代学习最小二乘算法.理论上证明了该算法的全局收敛性.给出的数值算例表明所提算法在非线性时变系统建模方面的有效性.     

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.     

基于数据驱动的非线性网络系统自适应迭代学习控制

针对非线性网络控制系统中测量数据的量化及随机丢包问题,给出一种基于数据驱动的自适应迭代学习控制算法.该算法能够保证系统在数据量化、随机丢包以及不确定迭代学习长度等因素的影响下,经过有限次迭代后输出轨迹跟踪误差收敛到零;借助伪偏导线性化方法,将非线性系统转换为线形时变系统形式;在线性系统框架下利用前一批次的系统输出信息更新自适应学习增益.与传统迭代学习控制算法不同的是,该算法无需预知迭代长度的先验信息和控制系统模型信息.最后通过Matlab仿真实验验证所提出算法的有效性.     

齿隙非线性输入系统的迭代学习控制

针对一类具有输入齿隙特性的非线性系统, 提出一种实现有限作业区间轨迹跟踪的迭代学习控制方法. 在系统不确定项可参数化的情形下, 基于类Lyapunov方法设计迭代学习控制器, 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. 对未知时变参数进行泰勒级数展开, 参数估计采用微分学习律, 并在控制器设计中, 采用双曲函数处理级数展开后的余项以及齿隙特性里的有界误差项, 以保证控制器可导, 且可抑制颤振. 引入一级数收敛序列确保系统输出完全跟踪期望轨迹, 且闭环系统所有信号有界.     

基于约束总体最小二乘的泰勒级数定位算法

目前基于到达时间差(Time Difference of Arrival,TDOA)的无线定位算法既不能在基于距离平方差(Squared Range-Difference,SRD)的误差平方和最小模型中获得总体最小二乘准则下的全局最优解,也不能在基于距离差(Range-Difference,RD)的误差平方和最小模型中获得普通最小二乘准则下的全局最优解。将泰勒级数法与约束总体最小二乘法(Constraint Total Least Square,CTLS)相结合,提出一种基于约束总体最小二乘的泰勒级数定位算法(CTLS-Taylor)。利用CTLS方法获得目标节点的粗估计位置,并将该位置作为泰勒级数展开法的初始点,通过迭代,获得目标节点的精估计位置。仿真结果表明,CTLS-Taylor算法不仅能够获得与QCLS-Taylor算法相同的定位精度,而且迭代次数有了明显减少;同时与CTLS定位算法相比,当测量噪声较高时,CTLS-Taylor算法的定位精度更高。     

一种带参考批次的线性时变系统迭代学习控制算法

针对线性时变系统的轨迹跟踪控制问题,提出一种带参考批次的迭代学习控制算法,并给出了算法的收敛性分析.该迭代学习控制算法不需要事先了解线性时变对象的太多知识,而是将当前批次输入轨迹的较小变化所引起的输出轨迹作为参考批次,并以当前批次与参考批次的输入变化与对应的输出变化之比作为学习律,从而实现目标轨迹的跟踪.以一个典型的线性时变系统为例进行仿真分析,验证了所提出算法的有效性.     

一类线性时变系统组合自适应迭代学习辨识

针对一类在有限时间区间上可重复运行的既含时变参数又含时不变参数的高阶线性时变系统,提出了一种模型参考组合自适应迭代学习参数辨识算法.应用Lyapunov方法,给出了时不变参数的时域自适应学习律和时变参数的迭代域自适应学习律,分析了参数估计和模型状态跟踪误差的有界性与收敛性.该算法适于时变和时不变参数并存的线性系统的参数辨识,可加快参数估计的收敛速度.仿真例子验证了所提出的辨识算法的有效性.     

一种带参考批次的线性时变系统迭代学习控制算法

!针对线性时变系统的轨迹跟踪控制问题,提出一种带参考批次的迭代学习控制算法,并给出了算法的收敛性分析.该迭代学习控制算法不需要事先了解线性时变对象的太多知识,而是将当前批次输入轨迹的较小变化所引起的输出轨迹作为参考批次,并以当前批次与参考批次的输入变化与对应的输出变化之比作为学习律,从而实现目标轨迹的跟踪.以一个典型的线性时变系统为例进行仿真分析,验证了所提出算法的有效性.

     

基于多神经元模型的非线性系统预测控制

利用单神经元来逼近非线性系统在平衡点邻域内的泰勒展开式的直至二次项,首次提出了一种用多个单神经元模型来拟合非线性系统的建模方法,引入多模型参考轨迹,得到一种新的多模型预测控制。仿真结果表明,基于二阶泰勒级数得到的多神经元模型的预测控制器的性能要优于采用泰勒级数一阶线性项得到的多模型预测控制器,但计算量并未显著增加。     

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。     

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.     

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.     

Analysis of linear time-varying systems and bilinear systems via Taylor series

Linear time-varying systems and bilinear systems are each analysed via Taylor series. Using the operational matrix for integration and the product operational matrix, the dynamical equation of a linear time-varying system (or a bilinear system) is reduced to a set of simultaneous linear algebraic equations. The coefficient vectors of the Taylor series expansions can be determined recursively by the algorithm derived. The algorithm proposed here is similar to those already developed for orthogonal functions; however, owing to the simplicity of the operational matrix of integration and the product operational matrix, Taylor series present considerable computational advantages compared with the other polynomial series, provided that both the input and the output signals are analytic functions of t.     

一种新的时变大系统递阶控制求解方法

研究了一种新的大系统求解方法,利用Taylor级数的性质,将大系统时变递阶控制问题 转化为代数方程的求解问题.该方法简单,易于编成计算机程序.算例表明了它的有效性.     

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.     

环卫车辆轨迹跟踪系统的无模型自适应迭代学习控制

针对环卫车辆周期重复性工作特点,考虑模型时变以及未知扰动问题,提出一种基于无模型自适应迭代学习的环卫车辆轨迹跟踪控制方法.首先,针对环卫车辆建立了两轮移动机器人的运动学模型,然后,给出带时变参数和非线性不确定项的迭代域下全格式动态线性化数据模型,引入时间差分估计算法,设计基于最优性能指标的轨迹跟踪无模型自适应迭代学习控...     

时变非线性系统迭代学习控制遗忘因子算法

针对迭代学习P型控制算法对初始偏差和输出误差扰动的敏感性问题,研究了一种带有遗忘因子的时变非线性系统的迭代学习控制方法.在有扰动的情况下,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,通过有界学习增益和批次时变因子设计学习控制器,并基于算子理论给出了控制算法存在的充分必要条件及其收敛性分析,改善了系统的鲁棒性和动态特性.最后以注塑机的注射速度控制仿真验证了本文算法的有效性.     

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control (AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance. To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control (ILC), a new boundary layer function is proposed by employing Mittag-Leffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function (CEF) containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

New approach to analysis and optimal control of time-varying systems via Taylor series

A new approach with three novel operations is proposed to deal with analysis of linear and bilinear time-varying systems and optimal control of linear time-varying systems via the Taylor series. The use of the three operations: polynomial mapping, general multiplication and integral transformer can greatly simplify the algorithm derivations and computations. Recursive algorithms are obtained and several illustrative examples are given.