A general gradient estimation based identification algorithm

A discrete recursive time-domain identification algorithm based on gradient estimation approach is proposed for linear time-invariant lumped-parameter systems. The scheme is quite general. Without invoking the strictly positive real lemma, Landau's proportional plus integral algorithms are shown to be the special cases of the proposed algorithm. Other gradient estimation based algorithms are also shown to be the special cases. The convergence of the scheme is proved using the second method of Lyapunov.     

Parameter adaptive control algorithms—A tutorial

An introduction is given to adaptive (self-tuning) control algorithms with recursive parameter estimation, which have obtained increasing attention in recent years. These algorithms result from combinations of recursive parameter estimation algorithms and easy to design control algorithms. Firstly a short review is given on proper recursive parameter estimation methods, including their application in a closed loop. This is followed by the design equations for various control algorithms and ways for d.c.-value estimation and for offset compensation. Various explicit and implicit combinations can be designed with different properties of the resulting adaptive control algorithms for both deterministic and stochastic disturbances. Their convergence properties are discussed. Simulation examples are presented and examples for the adaptive control of an air conditioner and a pH-process are shown. The introduction of a third feedback level for coordination and supervision is considered. Finally further problems are discussed.     

基于随机牛顿算法的离散系统自适应参数估计

针对一类离散系统,提出一种基于随机牛顿算法的自适应参数估计新框架,相较于已有的参数估计算法,所提出方法仅要求系统满足有限激励条件,而非传统的持续激励条件.所提出算法的核心思想在于通过对原始代价函数的修正,在使用当前时刻误差信息的基础上融入历史误差信息,进而通过对历史信息和历史激励的复用使得持续激励条件转化为有限激励条件;然后,为了解决传统算法收敛速度慢的问题并避免潜在的病态问题,采用随机牛顿算法推导出参数自适应律,并引入含有历史信息的海森矩阵作为时变学习增益,保证参数估计误差指数收敛;最后,基于李雅普诺夫稳定性理论给出不同激励条件下所提出算法的收敛性结论和证明,并通过对比仿真验证所提出算法的有效性和优越性.     

A novel adaptive lattice filtering algorithm for alpha-stable processes

This paper generalizes Burg's formula to be suitable for alpha-stable distribution and proposes a novel adaptive lattice algorithm for adaptive parameter estimation of alpha-stable AR processes. The performance is compared to that of other algorithms with lattice structure for alpha-stable AR processes for different α parameter. Simulations studies indicate that the proposed algorithm shows superior convergence speed over existing well-known lattice algorithms in parameter estimation of alpha-stable processes.     

A parameter estimation perspective of continuous time model reference adaptive control

The problem of adaptive control of continuous time deterministic dynamic systems is re-examined. It is shown that the convergence proofs for these algorithms may be decomposed into “modules” dealing with estimation and control, yielding a “key technical lemma” analogous to that used successfully in the study of discrete time systems. The extra freedom provided by the modular structure is used to formulate existing algorithms in a common framework and to derive several new algorithms. It is also shown how least squares, as opposed to gradient, estimation can be used in continuous time adaptive control.     

Robust recursive identification of multidimensional linear regression models

Stochastic adaptive estimation and control algorithms involving recursive prediction estimates have guaranteed convergence rates when the noise is not ‘too’ coloured, as when a positive-real condition on the noise mode is satisfied. Moreover, the whiter the noise environment the more robust are the algorithms. This paper shows that for linear regression signal models, the suitable introduction of while noise into the estimation algorithm can make it more robust without compromising on convergence rates. Indeed, there are guaranteed attractive convergence rates independent of the process noise colour. No positive-real condition is imposed on the noise model.     

基于非线性主成分分析的自适应变步长盲源分离算法

算法的迭代步长对于算法的收敛性能有着重要影响。针对固定步长的非线性主成分分析(NPCA)算法不能兼顾收敛速度和估计精度的情形,提出基于梯度的自适应变步长NPCA算法和最优变步长NPCA算法两种自适应变步长算法来改善其收敛性能。特别地,最优变步长NPCA算法通过对代价函数进行一阶线性近似表示,从而计算出当前的最优迭代步长。该算法的迭代步长随估计误差的变化而变化,估计误差大,迭代步长相应大,反之亦然;且不需要人工设置任何参数。仿真结果表明,当算法的估计精度相同时,与固定步长NPCA算法相比,两种自适应变步长NPCA算法相对固定步长NPCA算法都具有更好的收敛速度或跟踪性能,且最优变步长NPCA算法的性能优于基于梯度的自适应变步长NPCA算法。     

Speedup convergence and reduce noise for enhanced speech separation and recognition

Novel techniques are proposed to enhance time-domain adaptive decorrelation filtering (ADF) for separation and recognition of cochannel speech in reverberant room conditions. The enhancement techniques include whitening filtering on cochannel speech to improve condition of adaptive estimation, block-iterative formulation of ADF to speed up convergence, and integration of multiple ADF outputs through post filtering to reduce reverberation noise. Experimental data were generated by convolving TIMIT speech with acoustic path impulse responses measured in real room environment, with approximately 2 m microphone-source distance and initial target-to-interference ratio of about 0 dB. The proposed techniques significantly improved ADF convergence rate, target-to-interference ratio, and accuracy of phone recognition.     

扩散式变阶数最大相关熵准则算法

固定阶数的分布式自适应滤波算法只有在待估计向量的阶数已知且恒定的情况下才能达到相应的估计精度,在阶数未知或时变的情况下算法的收敛性能会受到影响,变阶数的分布式自适应滤波算法是解决上述问题的有效途径。但是目前大多数分布式变阶数自适应滤波算法以最小均方误差(Mean square Error, MSE)准则作为滤波器阶数的代价函数,在脉冲噪声环境下算法的收敛过程会受到较大影响。最大相关熵准则具有对脉冲噪声的强鲁棒性,且计算复杂度低。为提高分布式变阶数自适应滤波算法在脉冲噪声环境下的估计精度,利用最大相关熵准则作为滤波器阶数迭代的代价函数,并将得到的结果代入固定阶数的扩散式最大相关熵准则算法,提出了一种扩散式变阶数最大相关熵准则(Diffusion Variable Tap-length Maximum Correntropy Criterion, DVTMCC)算法。通过与邻域的节点进行通信,所提算法以扩散的方式实现了整个网络的信息融合,具有估计精度高、计算量小等优点。仿真实验对比了在脉冲噪声下DVTMCC算法和其他分布式变阶数自适应滤波算法、固定阶数的扩散式最大相关熵准则算法的收敛性能。...     

Adaptive estimation of discrete-time systems with nonlinear parameterization

This paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized. A majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment, which ensures stable estimation when parameters occur linearly. These algorithms, however, do not suffice for estimation in systems with nonlinear parameterization. We introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size. Both concave/convex parameterizations as well as general nonlinear parameterizations are considered. Stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established. For the case of concave/convex parameterizations, parameter convergence is shown to result under certain conditions of persistent excitation.     

Convergence and error bounds of adaptive filtering under model structure and regressor uncertainties

Adaptive filtering algorithms are investigated when system models are subject to model structure errors and regressor signal perturbations.System models for practical applications are often approximati...     

Auto-tuning of parameters in estimation and adaptive control ofrobots with weaker PE conditions

Knowledge of the system parameters is necessary for optimum performance of the system. A new class of parameter estimation and adaptive control algorithms was shown by Ahmad (1995), which was applied to the robotic system. These algorithms require relaxed conditions of persistent excitation for parameter convergence. Here we propose an enhancement of these algorithms via improved initialization resulting from sliding surface in parameter error space. As a result we achieve faster convergence of parameters with proper initialization. Examples giving quantitative results from the robotics systems are provided, comparing the results with the original algorithms and a classical approach of a gradient-type algorithm     

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.     

一种基于二阶梯度估计的自适应算法

在自适应信号处理中得到广泛应用的LMS算法,对信号模型及特性有着极其严格的限制,这些限制在很多实际情况中并不能保证得到满足.相对LMS算法,基于中心差的梯度估计自适应算法,其适应面则要广泛得多.但是,该算法存在着收敛速度慢,所需采样点数多的缺点.为此本文提出一种适应于平稳情况的新的估计算法,除首次估计需做采样外,在收敛过程中无需再做采样.与传统的中心差算法相比,本文算法具有较快的收敛速度和较好的失调性能.     

基于最大后验估计的自适应盲均衡算法

为了减小最大后验概率(MAP)盲均衡算法中稳态误差和收敛速度,提出了一种改进的基于最大后验估计的盲均衡算法.运用不等概思想改进自适应σ的MAP盲均衡算法,得到了基于概率和自适应σ的MAP盲均衡算法.定量分析和仿真结果表明改进算法和MAP的盲均衡算法相比,稳态调整量的理论值更小,稳态剩余根均方误差值小于MAP盲均衡算法,收敛速度快于MAP盲均衡算法.     

基于AdaBelief的Heavy-Ball动量方法

同时使用动量和自适应步长技巧的自适应矩估计(Adaptive Moment Estimation,Adam)型算法广泛应用于深度学习中.针对此方法不能同时在理论和实验上达到最优这一问题,文中结合AdaBelief灵活调整步长提高实验性能的技巧,以及仅采用指数移动平均(Exponential Moving Average,EMA)策略调整步长的Heavy-Ball动量方法加速收敛的优点,提出基于AdaBelief的Heavy-Ball动量方法.借鉴AdaBelief和Heavy-Ball动量方法收敛性分析的技巧,巧妙选取时变步长、动量系数,并利用添加动量项和自适应矩阵的方法,证明文中方法对于非光滑一般凸优化问题具有最优的个体收敛速率.最后,在凸优化问题和深度神经网络上的实验验证理论分析的正确性,并且证实文中方法可在理论上达到最优收敛性的同时提高性能.     

Stochastic adaptive prediction and model reference control

Guo and Chen (1991) have recently shown how to establish the self-optimality and mean square stability of a self-tuning regulator. The idea allows us to proceed with the development of a more comprehensive theory of stochastic adaptive filtering, control and identification. In adaptive filtering, we examine both indirect and noninterlaced direct schemes for prediction, using both least-squares and gradient parameter estimation algorithms. In addition to analyzing similar direct adaptive control algorithms, we propose new generalized certainty equivalence adaptive model reference control laws with simultaneous disturbance rejection. We also establish that the parameters converge to the null space of a certain matrix. From this one may deduce the convergence of several adaptive controllers     

Experimental comparison and application of various parameter-adaptive control algorithms

Various recursive parameter estimation algorithms and controller design procedures can be combined to build up parameter-adaptive control algorithms. Two parameter estimation methods and six control algorithms have been selected, taking into account good convergence properties and small computational expense and regarding the conditions for closed-loop identification. The resulting 12 parameter-adaptive control algorithms are compared and tested with a process computer in on-line operation with analog simulated stable and unstable processes for stochastic disturbances and step changes of the reference signal. The results are very promising. In many cases a good control performance is achieved. As a priori knowledge only the sampling time, the process model order and time delay and in some cases a weighting factor for the process input signal are required. Some parameter-adaptive control algorithms with good properties are applied to digital adaptive control of an air heater. Conclusions are given for the selection of parameter-adaptive control algorithms, depending on the type of process and its disturbances.The adaptive control algorithms may be applied for adaptive control of constant and time variant, linear and weakly non-linear stable and unstable processes with process computers or micro computers or for self-tuning of control algorithms or tuning of conventional analog PID controllers, if external disturbances act on the loop.     

Adaptation in the presence of a general nonlinear parameterization:an error model approach

Parametric uncertainties in adaptive estimation and control have been dealt with, by and large, in the context of linear parameterizations. Algorithms based on the gradient descent method either lead to instability or inaccurate performance when the unknown parameters occur nonlinearly. Complex dynamic models are bound to include nonlinear parameterizations which necessitate the need for new adaptation algorithms that behave in a stable and accurate manner. The authors introduce, in this paper, an error model approach to establish these algorithms and their global stability and convergence properties. A number of applications of this error model in adaptive estimation and control are included, in each of which the new algorithm is shown to result in global boundedness. Simulation results are presented which complement the authors' theoretical derivations     

Spatio–Temporal FastICA Algorithms for the Blind Separation of Convolutive Mixtures

This paper derives two spatio-temporal extensions of the well-known FastICA algorithm of Hyvarinen and Oja that are applicable to the convolutive blind source separation task. Our time-domain algorithms combine multichannel spatio-temporal prewhitening via multistage least-squares linear prediction with novel adaptive procedures that impose paraunitary constraints on the multichannel separation filter. The techniques converge quickly to a separation solution without any step size selection or divergence difficulties, and unlike other methods, ours do not require special coefficient initialization procedures to obtain good separation performance. They also allow for the efficient reconstruction of individual signals as observed in the sensor measurements directly from the system parameters for single-input multiple-output blind source separation tasks. An analysis of one of the adaptive constraint procedures shows its fast convergence to a paraunitary filter bank solution. Numerical evaluations of the proposed algorithms and comparisons with several existing convolutive blind source separation techniques indicate the excellent relative performance of the proposed methods.