基于最小二乘算法及神经网络的非线性离散系统的自适应控制

针对有关文献所设计的控制律，在一较弱的条件下，去掉了符号运算部分，证明该控制律可避免“零除”问题，提高了运算速度。对于这种基于神经网络和LS算法的自适应控制问题，证明了系统状态落入一紧集中，闭环系统的所有信号都是有界的，且系统输出和参考输出之间的跟踪误差收敛于以零为原点的某一有界球中。     

基于RBF神经网络与RLS算法的均衡器

将径向基函数神经网络与横向均衡器相结合,采用递推最小二乘算法更新权值。将最小二乘误差作为代价函数以及与误差相关的变步长,使输出误差较传统的神经网络均衡器进一步减小,收敛速度得到提高。仿真结果表明,该均衡器对线性信道和非线性信道都表现出较好的性能,在较严重的非线性情况下其优越性更明显。     

参数估计的Systolic算法

本文根据最小二乘原理在三角形Ｓｙｓｔｏｌｉｃ阵列上实现了单输入单输出系统的递推参数估计算法，首先利用矩阵的三角分解给出了待估参数及协方差阵的递推公式，然后利用正交平面旋转并结合三角形Ｓｙｓｔｏｌｉｃ阵列的特点给出了相应的Ｓｙｓｔｏｌｉｃ递推参数估计算法，最后还考虑了算法实现时的性能指标，其后是一些数值仿真结果，由于文中利用了正交平面旋转，因而所得算法是数值稳定的。     

自适应滤波RLS算法研究与DSP实现

自适应滤波器一直是随机信号处理当中的一个重要的研究课题,可以不需要预先知道给定信号及噪声的自相关函数,它可以利用前一时刻已获得的滤波器参数自动地调节现时刻的滤波器参数,从而实现最佳滤波.研究了自适应滤波器的基本结构和自适应滤波递推最小二乘(RLS)算法在DSP上的实现,采用定点TMS320VC5416 DSP为平台,通过C语言设计了一个RLS算法的16阶自适应滤波器,在CCS环境下进行仿真结果查看,并通过与MATLAB进行仿真比较.实验结果表明,该滤波器有效、性能良好,实现了较好的滤波功能,在数字信号处理领域有很好的应用价值.     

一类非线性随机系统的自适应控制

本文在文献「１，２」的基础上，对一类仿射非线性随机系统的最小二乘（ＬＳ）自适应控制问题进行了分析，给出了稳定性及收敛速度结果，在这里，我们仅要求非线性函数具有线性增长速度，而无需任何其它结构假设。     

基于LabVIEW的自适应滤波器设计与研究

针对自适应滤波器编程复杂,难以按照虚拟仪器系统的形式来测试工程应用中的实际性能等问题。文中利用LabVIEW8.6提供的自适应滤波器工具包,设计了基于最小均方误差算法、递推最小二乘算法的自适应滤波器,并对影响两种算法的参数对滤波器的敏感性进行了分析;进而,利用音频信号验证了滤波器性能。仿真结果表明,所设计的自适应滤波器功能全面,人机交互界面良好,便于工程技术人员快速开发,具有较好的工程实用价值。     

基于递推最小二乘自适应滤波算法的图像去噪

递推最小二乘RLS(Recursive of Least Square)算法是自适应滤波算法中的精确分析算法。它具有收敛速率快,精确度高等特点,但是发现目前RLS算法多用于对一维信号的去噪处理。使用递推最小二乘(RLS)算法对二维图像进行去噪,从处理一维信号变成处理二维图像信号,需要对RLS算法进行改进。先迭代得到滤波器参数,形成3×3滤波掩模,再改进算法对图像进行滤波;同时与常数比率维纳滤波和自相关函数的维纳滤波算法的去噪效果进行对比。结论证明在对图像进行较严重的模糊和加噪处理后,其他两种算法对图像的还原能力差,而递推最小二乘自适应滤波(RLS)算法具有优良的图像去噪性能。     

基于Legendre多项式微分变换的随机连续系统无偏一致参数估计

基于Legendre多项式微分变换,导出随机连续线性系统的统计无关逼近模型,然后由最小二乘原理给出参数估计算法。理论分析和仿真结果表明该估计是无偏一致的。     

基于迭代优化算法的AUV水下运动目标航行参数估计

为了解决自主水下机器人（autonomous underwater vehicle,AUV）对水下运动目标进行实时动态追踪的技术难题,本文将渐消记忆递推最小二乘算法与平方根算法相结合,提出一种迭代优化算法。该算法充分利用渐消记忆递推最小二乘算法的快速收敛性能,利用平方根算法解决迭代过程中的数值不稳定问题。迭代优化算法能够快速解算出运动目标的初始距离、航向角及运动方向,数值收敛时间约为3\min,目标运动速度信息也能够在5\min左右收敛。该算法的收敛时间短、计算速度快,甚至AUV无需进行任何形式的机动即可令其保持悬停,这些优点使本算法适用于AUV水下运动目标追踪的工程实际问题。     

一种新的非线性回归模型参数估计算法

提出一种新的基于混合基因算法（HGA）的非线性回归模型参数估计算法,新算法通过对问题的解空间交替进行全局和局部搜索,达到快速收敛至全局最优解,较好地解决了传统算法通用性差、易陷入局部极小的问题,实验验证了算法的通用性和有效性。     

A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems

In this paper, we propose a novel identification algorithm for a class of dual-rate sampled-data systems whose input–output data are measured by two different sampling rates. A polynomial transformation technique is employed to derive a mathematical model for such dual-rate systems. The proposed modified stochastic gradient algorithm has faster convergence rate than stochastic gradient algorithms for parameter identification using the dual-rate input–output data. Convergence properties of the algorithm are analyzed. Finally, illustrative and comparison examples are provided to verify the effectiveness and performance improvement of the proposed method.     

Adaptive dual control of discrete-time distributed-parameter stochastic systems

The problem of adaptive dual control of discrete-time distributed-parameter stochastic systems is examined. It is shown that there exists an important difference between feedback and closed-loop policies of control for this type of system as for the lumped parameter case. This difference is based on the adaptivity feature of the control. Namely, when the control policy affects both the state and its uncertainty (dual effect) it possesses the so-called feature of active adaptivity and can only be a characteristic of a closed-loop policy, whereas a feedback policy can only be passively adaptive. These results can be used to develop a control algorithm for non-linear problems for which the realization of optimal control laws involves control strategies with both learning and control features.     

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.     

Optimal estimation of linear discrete-time systems with stochastic parameters

This paper considers optimal linear state estimation in the general case of linear discrete-time systems with stochastic parameters which are statistically independent with respect to time. The estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise. It is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence, uniqueness and stability of the time invariant estimator.     

Optimal nonlinear estimation for a class of discrete-time stochastic systems

Recursive estimation for nonlinear discrete-time stochastic systems with additive white Gaussian observation noise is investigated. It is proved that for certain classes of systems, described either by finite Volterra series expansions or by state-linear realizations under certain algebraic conditions, the optimal conditional mean estimator is recursive and of fixed finite dimension. An example is presented to illustrate the structure of the estimators.     

Suboptimal state estimation algorithm for non-linear discrete-time distributed-parameter systems

A non-linear discrete-time distributed-parameter system may be described by stochastic partial differential equations. Some state variables are measured at selected points of the system space. For this system a suboptimal state estimation algorithm is proposed. The error covariance matrix is calculated by an approximate approach. This simplification considerably reduces computer calculations in comparison with an optimal algorithm. Finally, the digital simulation of a non-linear DPS demonstrates the effectiveness of the suboptimal estimator.     

Adaptive policies for discrete-time stochastic control systems with unknown disturbance distribution

We introduce adaptive policies for discrete-time, infinite horizon, stochastic control systems x₁₊₁ = F(x₁, a₁, ξ₁, T =0, 1, …, with discounted reward criterion, where the disturbance process ξ₁ is a sequence of i.i.d. random elements with unknown distribution. These policies are shown to be asymptotically optimal and for each of them we obtain (almost surely) uniform approximations of the optimal reward function.     

Robust state estimation for uncertain discrete-time stochastic systems with missing measurements

In this paper, results of robust estimation of Zhou (2010a) are extended to state estimation with missing measurements. A new procedure is derived which inherits the main properties of that of Zhou (2010a). In this extension, a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult. Though introducing a monotonic function and using the so-called squeeze rule, this new robust estimator is proved to converge to a stable system. Numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of Wang, Yang, Daniel, and Liu (2005).     

Numerical differentiation and parameter estimation in higher-orderlinear stochastic systems

For a linear time-invariant system of order d⩾2 with a white noise disturbance, the input and the output are assumed to be sampled at regular time intervals. Using only these observations, some approximate values of the first d-1 derivatives are obtained by a numerical differentiation scheme, and the unknown system parameters are estimated by a discretization of the continuous-time least-squares formulas. These parameter estimates have an error which does not approach zero as the sampling interval approaches zero. This asymptotic error is shown to be associated with the inconsistency of the quadratic variation estimate of the white noise local variance based on the sampled observations. The use of an explicit correction term in the least-squares estimates or the use of some special numerical differentiation formulas eliminates the error in the estimates