基于最小二乘算法的最优适应控制器

采用"输入匹配"的方法,建立了"一步超前"最小二乘算法,得以参数估计的收敛速度. 证明了闭环适应系统是全局稳定的,且适应控制收敛于"一步超前"最优控制.     

A variable step-size SIG algorithm for realizing the optimal adaptive FIR filter

In this paper, we propose an optimal adaptive FIR filter, in which the step-size and error nonlinearity are simultaneously optimized to maximize the decrease of the mean square deviation (MSD) of the weight error vector at each iteration. The optimal step-size and error nonlinearity are derived, and a variable step-size stochastic information gradient (VS-SIG) algorithm is developed to approximately implement the optimal adaptation. Simulation results indicate that this new algorithm achieves faster convergence rate and lower misadjustment error in comparison with other adaptive algorithms.     

一种鲁棒的总体最小二乘自适应辨识算法

针对输入输出观测数据均含有噪声的系统辨识问题，提出了一种鲁棒的总体最小二乘自适应辨识算法．该算法在对总体最小二乘问题与向量的瑞利商及其性质研究的基础上，以被辨识系统的增广权向量的瑞利商(RQ)作为损失函数，利用梯度最陡下降原理导出权向量的自适应迭代算法，并利用随机离散学习规律对权向量模的分析修正了算法梯度，提高了算法的噪声鲁棒性，构成了一种噪声鲁棒的总体最小二乘自适应辨识算法．文中研究了该算法的收敛性能．仿真实验结果表明该算法的鲁棒抗噪性能和稳态收敛精度明显高于其它同类方法，而且可使用较大的学习因子，在较高的噪声环境下仍然保持良好的收敛性．     

Stochastic analysis of the Least Mean Kurtosis algorithm for Gaussian inputs

The Least Mean Kurtosis (LMK) algorithm was initially proposed as an adaptive algorithm that is robust to the observation noise distribution. Good performances of this algorithm have been shown for non-Gaussian additive measurement noise. However, the complexity of the algorithm imposes difficulties for the development of a reasonably complete theoretical stochastic model for its behavior. The purpose of this paper is to contribute to the development of such a model. We study the stochastic behavior of Least Mean Kurtosis (LMK) algorithm for Gaussian inputs and for additive noises with even probability density functions. Deterministic recursions are derived for the adaptive weight error covariance matrix in a very novel manner, leading to a recursive model for the excess mean square error (EMSE) behavior that is shown to be accurate for Gaussian, uniform and binary noise distributions. The analysis results are then used to compare the performances of LMK with the least mean squares (LMS) and least mean fourth (LMF) algorithms under different circumstances.     

基于输入匹配的广义预测自校正控制器——有色噪声情况

为随机线性系统建立了全局收敛广义预测自校正控制算法,处理的是有色噪声的情 况,并给出了完整而严格的收敛性证明.在通常假设条件下使用这种算法,能使适应控制律和 最优控制律之差在样本均方意义下收敛到零.     

双线性系统的自校正控制

本文分别对确定和随机双线性系统,首次建立了大范围渐近收敛和稳定的自校正控制算法。该算法具有渐近最优的控制效果,且适用于非最小相位系统情况。仿真实验表明了该算法的有效性。     

Adaptive recursive algorithm with logarithmic transformation for nonlinear system identification in α-stable noise

Although the least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filters outperform the conventional least mean square (LMS) algorithm in the presence of α-stable noise, they still exhibit slow convergence and high steady-state kernel error in nonlinear system identification. To overcome these limitations, an enhanced recursive least mean pth power algorithm with logarithmic transformation (RLogLMP) is proposed in this paper. The proposed algorithm is adjusted to minimize the new cost function with the p-norm logarithmic transformation of the error signal. The logarithmic transformation, which can diminish the significance of outliers under α-stable noise environment, increases the robustness of the proposed algorithm and reduces the steady-state kernel error. Moreover, the proposed method improves the convergence rate by the enhanced recursive scheme. Finally, simulation results demonstrate that the proposed algorithm is superior to the LMP, NLMP, normalized least mean absolute deviation (NLMAD), recursive least squares (RLS) and nonlinear iteratively reweighted least squares (NIRLS) algorithms in terms of convergence rate and steady-state kernel error.     

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.     

全局竞争和声搜索算法

提出一种全局竞争和声搜索(GCHS) 算法, 给出随机局部平均和声和全局平均和声的概念, 建立竞争搜索机制, 实现每次迭代产生两个和声向量并进行竞争选择. 设计自适应全局调整和局部学习策略, 平衡算法的局部搜索和全局搜索, 详细分析参数HMS、HMCR和PAR对算法优化性能的影响. 数值结果表明, GCHS 算法在精度、收敛速度和鲁棒性方面比和声搜索算法及最近文献中提出的7 种优秀改进和声搜索算法要好.

     

基于改进混合算法优化RBF网络的滤波器建模

为构建精确的微带线滤波器神经网络模型,提出一种结合自适应遗传算法和改进粒子群算法的混合算法。在自适应遗传算法中,构造二次型选择策略以提高优秀个体的复制概率,加快收敛到初始全局最优解;利用粒子群算法良好的局部搜索能力,在标准粒子群算法的位置迭代公式中引入高斯扰动项,以克服收敛速度慢和早熟收敛的缺点,提高搜索全局最优解的可能性。通过对测试函数仿真,验证改进算法的可行性。最后将混合算法用于优化神经网络参数,建立平行耦合微带线滤波器模型。结果表明,滤波器参数S21和S11的均方根误差至少减小18.22%与12.68%,微带滤波器建模精度得到提高,验证了该算法对滤波器建模的有效性和可靠性。     

GLOBAL CONVERGENCE OF MINIMUM VARIANCE SELF‐TUNING SCHEME BASED UPON DAMPED LEAST SQUARES

This paper presents an analysis of the stability and convergence of a damped least squares identification algorithm and establishes the global convergence of a minimum variance self‐tuning scheme based upon damped least squares. The results mathematically demonstrate that the damped least squares can generally be applied to achieve system identification and adaptive control.     

State inverse and decorrelated state stochastic approximation

Stochastic approximation algorithms for parameter identification are derived by a sequential optimization and weighted averaging procedure with an instructive geometric interpretation. Known algorithms including standard least squares and suboptimal versions requiring less computational effort are thereby derived. More significantly, novel schemes emerge from the theory which, in the cases studied to date and reported here, converge much more rapidly than their nearest rivals amongst the class of known simple schemes. The novel algorithms are distinguished from the known ones by either a different step size selection, and/or by working with a transformed state variable with components relatively less correlated, and/or by replacing the state vector in a crucial part of the calculations by its componentwise pseudoinverse.The convergence rate of the novel schemes in our simulations is significantly closer to that of the more sophisticated optimal least square recursions than other stochastic approximations schemes in the literature. For the case of extended least squares and recursive maximum likelihood schemes, the novel stochastic recursion performs, in loose terms within a factor of 10 (rms error), of the more sophisticated schemes in the literature. An asymptotic convergence analysis for the algorithms is a minor extension of known theory.     

Kernel-based least squares policy iteration for reinforcement learning.

In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.     

一类全局收敛的多变量自校正控制器*

本文将文[1]提出的多变量自校正控制算法推广到具有一般传输延时的多变量系统并进行了稳定性和收敛性分析。首先表明:即使对于具有任意传输延时的多变量系统,该自校正控制器仍具有全局收敛特性:以概率1输入输出向量采样均方有界,条件均方输出跟踪误差向量范数取得最小值。     

Stochastic adaptive control and prediction based on a modified least squares--The general delay-colored noise case

In [1], global convergence for a stochastic adaptive control based on modified least-squares algorithms has been established. However, the proof of Lemma 3.4 in [1] is questionable. A similar question existed in the proof ofdelta(t - d) rightarrow 0in [2]. Without using this conclusion, the present note attempts to establish global convergence for a discrete-time stochastic adaptive control and prediction based on slightly modified least-squares algorithms for linear time-invariant discrete-time systems having general delay and colored noise.     

基于改进NLMS算法的自适应滤波算法

最小均方算法是应用最广泛的自适应算法之一,但其收敛速度欠佳。在传统NLMS算法的基础上,提出了重复调整归一化最小均方算法(DRNLMS)即在相邻两输入信号样本的间隔时间进行额外调整运算,以提高算法的收敛性,并通过计算机仿真实现该算法。     

多变量离散时间系统的自适应LQ控制

考虑了多变量离散系统的自适应ＬＱ（线性二次）控制问题,利用ＬＳ（最小二乘）算法和ＷＬＳ（加权最小二乘）算法的自收敛性和随机正则化的思想「１」,证明了修改的估计模型是几乎处处自收敛的、一致可控和一致可观的,基于上面的估计,提出了两种自适应ＬＱ控制律,证明了闭环系统是稳定的和最优的。     

Indirect stochastic adaptive control: The general delay-white noise case

Recent papers on adaptive stochastic control have established global convergence for the general delay-colored noise case. However, for delayskgreater than unity they require the implementation ofkinterlaced adaptation algorithms. Using an indirect adaptive control approach, we show that in the white noise case a single adaptation algorithm suffices to establish that, with probability one, the systems input, output and the output tracking error are sample mean-square bounded. Moreover, the conditional variance of the output tracking error is shown to converge to its global minimum value with probability one.     

Almost sure rate of convergence of the parameter estimates instochastic approximation algorithm

This paper presents novel results on the almost sure convergence of the parameter estimates in stochastic approximation algorithm. It is proved that this rate has the same order as the best one established for the least squares algorithm. Although we consider the case of self-tuning controllers, the presented results can easily be extended to some other adaptive processes     

Selective-Tap Adaptive Filtering With Performance Analysis for Identification of Time-Varying Systems

Selective-tap algorithms employing the MMax tap selection criterion were originally proposed for low-complexity adaptive filtering. The concept has recently been extended to multichannel adaptive filtering and applied to stereophonic acoustic echo cancellation. This paper first briefly reviews least mean square versions of MMax selective-tap adaptive filtering and then introduces new recursive least squares and affine projection MMax algorithms. We subsequently formulate an analysis of the MMax algorithms for time-varying system identification by modeling the unknown system using a modified Markov process. Analytical results are derived for the tracking performance of MMax selective tap algorithms for normalized least mean square, recursive least squares, and affine projection algorithms. Simulation results are shown to verify the analysis.