厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

基于二阶离散变分方法的非线性映射参数估计

提出一种估计非线性映射未知参数的二阶离散变分方法.首先针对非线性离散混沌系统, 利用变分方法导出了伴随方程和目标泛函梯度, 以此为基础利用二阶离散变分方法给出了二阶伴随方程和精确计算Hessian矩阵-向量乘积的显式表达式; 其次设计了估计非线性映射未知参数的新算法, 并以此对Hyperhenón映射和二维抛物映射中的未知参数进行了精确的估计. 数值仿真结果表明了该方法的有效性和优点. 关键词： 非线性映射 参数估计 二阶离散变分方法 伴随方程     

非线性映射参数辨识的离散变分方法

提出一种辨识非线性映射系统中未知参数的离散变分方法, 对以x_k+1 = F(x_k,θ)为状态控制方程的所有映射混沌系统具有通用性. 对典型的Logistic映射和Henón映射中的未知参数进行了估计, 仿真结果表明了该方法的有效性.     

导热几何形状反演的变分原理及边界条件的确立

本文采用变域变分原理,建立了导热几何形状反演问题的变分原理,同时获得了该问题所需满足的边界条件和附加条件.该变分原理能将未知形状的几何变量及控制方程结合在一个变分泛函中,使得数学描述简洁、紧凑,且几何变量及控制方程的求解能耦合地进行.介绍了运用该变分原理并结合有限元方法进行数值计算的方法. 关键词： 几何形状反演 变分原理 有限元 导热     

变分伴随正则化方法从雷达回波反演海洋波导 Ⅰ.理论推导部分

针对传统统计反演算法在雷达回波反演海洋波导(RFC)方面计算量过大的问题,提出一种变分伴随正则化物理反演算法.在变分伴随方法中分别导出切线性模式、伴随方程及伴随边界条件、伴随方程求解表达式、以及泛函梯度的数学表达形式;讨论了伴随方法求泛函梯度对复方程如何协调的问题.考虑到雷达电磁波传播的特征,选择了适当的正则化项来解决反演中的不适定问题.最后给出反演算法实施中的迭代格式.     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.     

不同超混沌系统的自适应修正函数投影

研究了具有未知参数的Lorenz-Stenflo(LS)系统和一种新型超混沌系统以及LS系统和超混沌Chen系统的修正函数投影同步问题.利用Lyapunov稳定性理论和主动控制方法,设计自适应控制器和参数更新规则,实现不同超混沌系统的修正函数投影同步,同时估计出系统的未知参数.数值仿真验证了该自适应控制器的有效性.     

一种基于复数域微分的资料同化新方法

提出了一种基于复数域微分的资料同化新方法. 针对变分资料同化中目标泛函梯度计算复杂和精度不高的问题, 首先利用复变量求导法把梯度分析过程转化为复变泛函的数值计算, 进而高效和高精度地获得梯度值; 然后结合经典的最优化方法, 给出了非线性物理系统资料同化问题的新求解算法; 最后对典型混沌系统和包含“开关”现象的单格点比湿发展方程进行了资料同化数值实验, 结果表明新方法能非常有效地估计出非线性动力预报模式的初始条件. 关键词： 资料同化 复数域微分 非线性物理系统 梯度分析     

不同超混沌系统的自适应修正函数投影

研究了具有未知参数的Lorenz-Stenflo(LS)系统和一种新型超混沌系统以及LS系统和超混沌Chen系统的修正函数投影同步问题.利用Lyapunov稳定性理论和主动控制方法,设计自适应控制器和参数更新规则,实现不同超混沌系统的修正函数投影同步,同时估计出系统的未知参数.数值仿真验证了该自适应控制器的有效性.     

基于稀疏贝叶斯学习的复杂网络拓扑估计

提出了一种噪声环境下复杂网络拓扑估计方法, 仅利用含噪时间序列估计未知结构混沌系统的动力学方程和参数, 以及由混沌系统组成的复杂网络的拓扑结构、节点动力学方程、所有参数、 节点间耦合方向和耦合强度.通过采用动力学方程的统一形式, 将动力系统方程结构和参数估计看成线性回归问题的系数估计, 该估计问题利用贝叶斯压缩传感的信号重建算法求解, 含噪信号的模型重建使用相关向量机方法,即通过稀疏贝叶斯学习求解稀疏欠定线性方程得到上面提到的可估计对象.以单个Lorenz系统及由200个 Lorenz系统组成的无标度网络为例说明方法的有效性. 仿真结果表明,提出的方法对噪声有很强的鲁棒性,收敛速度快,稳态误差极小, 克服了最小二乘估计方法收敛速度慢、 稳态误差大以及压缩传感估计方法对噪声鲁棒性不强的缺点.     

Synchronization between two different noise-perturbed chaotic systems with unknown parameters

In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employing a combination of feedback control and adaptive control, some sufficient conditions of chaos synchronization between these noise-perturbed systems with unknown parameters are established. The model used in the research is the chaotic system, but the method is also applicable to the hyperchaotic systems. Unified system and noise-perturbed RSssler system, hyperchaotic Chen system and nolse-perturbed hyperchaotic RSssler system are taken for illustrative examples to demonstrate this technique.[第一段]     

An investigation into the maximum entropy production principle in chaotic Rayleigh–Bénard convection

The hypothesis is made that the temperature and velocity fields in Rayleigh–Bénard convection can be expressed as a superposition of the active modes with time-dependent amplitudes, even in the chaotic regime. The maximum entropy production principle is interpreted as a variational principle in which the amplitudes of the modes are the variational degrees of freedom. For a given Rayleigh number, the maximum heat flow for any set of amplitudes is sought, subject only to the constraints that the energy equation be obeyed and the fluid be incompressible. The additional hypothesis is made that all temporal correlations between modes are zero, so that only the mean-squared amplitudes are optimising variables. The resulting maximal Nusselt number is close to experimental determinations. The Nusselt number would appear to be simply related to the number of active modes, in particular the number of distinct vertical modes. It is significant that reasonable results are obtained for the optimised Nusselt number in that the dynamics (the Navier–Stokes equation) is not used as a constraint. This suggests grounds for optimism that the maximum entropy production principle, interpreted in this variational manner, can provide a reasonable guide to the dynamic steady states of non-equilibrium systems whose detailed dynamics are unknown.     

On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

Fuzzy adaptive synchronization of uncertain chaotic systems

This Letter presents an adaptive approach for synchronization of Takagi–Sugeno (T–S) fuzzy chaotic systems. Since the parameters of chaotic system are assumed unknown, the adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. The control law to be designed consists of two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples are given to demonstrate the validity of the proposed adaptive synchronization approach.