基于二阶分布式算法的无线传感网络效用最大化问题研究

高效分布式算法设计是保证无线传感网络性能的关键问题。提出了一种基于信道容量约束的无线传感网络效用最大化问题模型。针对传统一阶算法存在收敛速度慢、步长选择敏感等缺点,文章设计了具有二阶收敛速度的快速分布式牛顿算法。研究和仿真实验表明,该算法在与传统一阶算法交互几乎相同信息的情况下具有二次收敛速度,算法迭代次数和运行时间改进了近两个数量级。     

一种新型高效的计算机寻优算法

提出一种全新的寻找无约束最优解的计算机算法。该算法能使得目标函数梯度的模逐渐收缩到零,以达到目标函数极小化,因此命名“梯度收缩法”。它同时利用了牛顿法和共轭梯度法的优点,应用目标函数的二阶导数,收敛很快,且具有牛顿法的“二次终止”特性。但Hessian矩阵奇异时,牛顿法将无法进行下去,该文算法可以克服这个缺点且能快速确定是否收敛到一个鞍点。     

基于负熵最大化改进的语音音乐信号分离

负熵是一种重要的非高斯性度量方法,最大化负熵使随机变量的非高斯性达到最大,从而使输出的各分量之间相互独立。负熵最大化算法以负熵作为目标函数,牛顿迭代法作为优化算法,针对牛顿迭代法中对初始值选择敏感的问题,用牛顿下山法代替牛顿迭代法,通过改变下山因子,使目标函数呈下降趋势,降低算法对初始值的依赖性。实验结果表明,改进后的算法在不同初始值下均能较好地分离语音音乐混合信号,改善了初值敏感问题。     

Finite‐time distributed control with time transformation

In this article, we propose distributed control algorithms for first‐ and second‐order multiagent systems for addressing finite‐time control problem with a priori given, user‐defined finite‐time convergence guarantees. The proposed control frameworks are predicated on a recently developed time transformation approach. Specifically, our contribution is twofold: First, a generalized time transformation function is proposed that converts the user‐defined finite‐time interval to a stretched infinite‐time interval, where one can design a distributed control algorithm on this stretched interval and then transform it back to the original finite‐time interval for achieving a given multiagent system objective. Second, for a specific time transformation function, we analytically establish the robustness properties of the resulting finite‐time distributed control algorithms against vanishing and nonvanishing system uncertainties. By contrast to existing finite‐time approaches, it is shown that the proposed algorithms can preserve a priori given, user‐defined finite‐time convergence regardless of the initial conditions of the multiagent system, the graph topology, and without requiring a knowledge of the upper bounds of the considered class of system uncertainties. Illustrative numerical examples are included to further demonstrate the efficacy of the presented results.     

分布式累加梯度算法在目标定位问题中的应用

通过对基于能量目标定位问题的分析,建立声源能量衰退模型,并把定位问题转化为非线性最小二乘问题,引入分布式累加梯度算法来求解目标函数的最优值。由于目标函数是严格凸函数,使得算法无论初始点如何选取总能较快地收敛到目标位置,算法执行仅需要相邻传感器信息,是一种分布式算法。数值实验表明：分布式累加梯度算法不仅收敛速度快,而且定位更精准。     

A hybrid algorithm for finding a global minimum

One of the most important problems in non-linear programming is to find out the global minimum of a given objective function. In this paper, a new hybrid algorithm which combines the random optimization method of Matyas (1965) and one of the well-known ordinary descent algorithms having an effective convergence property (for example, the Fletcher-Reeves conjugate gradient method, the Davidon-Fletcher-Powell quasi Newton method, etc.) is proposed in order to find out a global minimum in as small a number of steps as possible. Several computational experiments on multimodal objective functions are carried out in order to test the efficiency of the proposed hybrid algorithm. The results obtained imply that the proposed hybrid algorithm is useful for finding out a global minimum in a small number of steps. A theorem that predicts convergence to a global minimum is also given.     

Distributed primal-dual optimisation method with uncoordinated time-varying step-sizes

This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm.     

A perturbation approach for a type of inverse linear programming problems

We consider an inverse linear programming (LP) problem in which the parameters in both the objective function and the constraint set of a given LP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a linear complementarity constrained minimization problem. With the help of the smoothed Fischer–Burmeister function, we propose a perturbation approach to solve the inverse problem and demonstrate its global convergence. An inexact Newton method is constructed to solve the perturbed problem and numerical results are reported to show the effectiveness of the approach.     

非线性迭代学习控制问题的延拓修正牛顿法

对于非线性迭代学习控制问题,提出基于延拓法和修正Newton法的具有全局收敛性的迭代学习控制新方法.由于一般的Newton型迭代学习控制律都是局部收敛的,在实际应用中有很大局限性.为拓宽收敛范围,该方法将延拓法引入迭代学习控制问题,提出基于同伦延拓的新的Newton型迭代学习控制律,使得初始控制可以较为任意的选择.新的迭代学习控制算法将求解过程分成N个子问题,每个子问题由换列修正Newton法利用简单的递推公式解出.本文给出算法收敛的充分条件,证明了算法的全局收敛性.该算法对于非线性系统迭代学习控制具有全局收敛和计算简单的优点.     

无线传感网络中拥塞控制与路由的跨层设计:分布式牛顿法

无线传感网络应用广泛, 其性能与路由选择和拥塞控制密切相关. 致力于拥塞控制与多径路由的跨层优化, 以实现在链路容量受限和节点能量受限情况下的无线传感网络效用最大化. 针对对偶次梯度算法具有收敛速度慢与信息交互量大等缺陷, 设计了具有二阶收敛性能的分布式牛顿算法来实现网络效用最大化. 通过矩阵分裂技术, 实现了只需单跳信息交互的牛顿对偶方向的分布式求解方法. 仿真结果表明, 分布式牛顿算法的收敛性能显著优于对偶次梯度算法.     

Q‐learning for continuous‐time graphical games on large networks with completely unknown linear system dynamics

In this paper, we consider the problem of leader synchronization in systems with interacting agents in large networks while simultaneously satisfying energy‐related user‐defined distributed optimization criteria. But modeling in large networks is very difficult, and for that reason, we derive a model‐free formulation that is based on a separate distributed Q‐learning function for every agent. Every Q‐function is a parametrization of each agent's control, of the neighborhood controls, and of the neighborhood tracking error. It is also evident that none of the agents has any information on where the leader is connected to and from where she spreads the desired information. The proposed algorithm uses an integral reinforcement learning approach with a separate distributed actor/critic network for each agent: a critic approximator to approximate each value function and an actor approximator to approximate each optimal control law. The derived tuning laws for each actor and critic approximators are designed appropriately by using gradient descent laws. We provide rigorous stability and convergence proofs to show that the closed‐loop system has an asymptotically stable equilibrium point and that the control policies form a graphical Nash equilibrium. We demonstrate the effectiveness of the proposed method on a network consisting of 10 agents. Copyright © 2016 John Wiley & Sons, Ltd.     

Asynchronously compensated synchronization algorithm for multiple harmonic oscillators with communication delay

Synchronization problem is investigated for multiple harmonic oscillators with identical communication delay in this paper. We propose a new distributed control algorithm in asynchronously compensated form and a corresponding reduced‐order observer‐based distributed control algorithm. By using frequency‐domain analysis, delay‐dependent and delay‐independent convergence conditions are obtained for our proposed algorithms under leader‐following and leaderless coordination control structures, respectively, and the results can be directly extended to the observer‐based algorithm based on the separation principle. Numerical examples illustrate the validity of the theoretical findings. Copyright © 2016 John Wiley & Sons, Ltd.     

Distributed resource allocation of second‐order multiagent systems with exogenous disturbances

In this paper, we study the resource allocation problem of second‐order multiagent systems with exogenous disturbances, and the communication networks are weight‐balanced digraphs. Different from the well‐studied resource allocation problems, our problem involves the disturbed second‐order dynamics of agents. In order to achieve the optimal allocation, we propose a distributed algorithm based on gradient descent and internal model approach. Furthermore, we analyze the convergence of the algorithm by constructing a suitable Lyapunov function. Moreover, we prove that the agents in the network can achieve the exact optimal allocation even in the presence of external disturbances. Finally, we provide two examples to illustrate our result.     

Performance Analysis of The Auxiliary‐Model‐Based Multi‐Innovation Stochastic Newton Recursive Algorithm for Dual‐Rate Systems

The stochastic Newton recursive algorithm is studied for dual‐rate system identification. Owing to a lack of intersample measurements, the single‐rate model cannot be identified directly. The auxiliary model technique is adopted to provide the intersample estimations to guarantee the recursion process continues. Intersample estimations have a great influence on the convergence of parameter estimations, and one‐step innovation may lead to a large fluctuation or even divergence during the recursion. In the meantime, the sample covariance matrix may appear singular. The recursive process would cease for these reasons. In order to guarantee the recursion process and to also improve estimation accuracy, multi‐innovation is utilized for correcting the parameter estimations. Combining the auxiliary model and multi‐innovation theory, the auxiliary‐model‐based multi‐innovation stochastic Newton recursive algorithm is proposed for time‐invariant dual‐rate systems. The consistency of this algorithm is analyzed in detail. The final simulations confirm the effectiveness of the proposed algorithm.     

一种改进的FastICA算法及其应用

独立分量分析是基于信号高阶统计量的信号分析方法,它可以找到隐含在数据中的独立分量,已经广泛应用到语音信号处理、图像处理及信息通信等方面。目前应用较多的快速独立分量分析（FastICA）利用了牛顿迭代法原理,具有较快的收敛速度,但对初始值的选择比较敏感。为克服其缺点,改进其优化学习算法,在牛顿迭代方向增加一维搜索,使改进后的算法的收敛性不依赖于初始值的选择。将改进的FastICA算法应用到运动目标检测中,取得稳定性较强的结果。     

Variable Structure Control with Chattering Reduction of a Generalized T‐S Model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non‐linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi‐Sugeno (T‐S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T‐S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T‐S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T‐S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T‐S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC‐VSC shows that both alleviation of chattering and robust performance are achieved.     

Newton's method for solving parametric linear quadratic control problems

Newton's method is applied to parametric linear quadratic control problems, including the optimal output feedback problem and the optimal decentralized control problem. Newton's equations are obtained as a system of coupled linear matrix equations. They are solved iteratively using the conjugate gradient method. In order to reduce the amount of work associated with the procedure, an inexact newtonian algorithm is also considered. In this algorithm, an approximate solution of the Newton equations is computed in such a way that the asymptotic convergence rate is quadratic.     

改进的正则化模型在图像恢复中的应用

目的 由拟合项与正则项组成的海森矩阵,如果不具有特殊结构,其逆矩阵计算比较困难,为克服此缺点,提出一种海森矩阵可分块对角化的牛顿投影迭代算法。方法 首先,用L₂范数描述拟合项,用自变量是有界变差函数的复合函数刻画正则项,建立能量泛函正则化模型。其次,引入势函数,将正则化模型转化为增广能量泛函。再次,构造预条件矩阵,使得海森矩阵可分块对角化。最后,为防止牛顿投影迭代算法收敛到局部最优解,采用回溯线性搜索算法和改进的Barzilai-Borwein步长更新准则使得算法全局收敛。结果 针对图像去模糊正则化模型容易使边缘平滑和产生阶梯效应“两难”问题,提出一种新的正则化模型和牛顿投影迭代算法。仿真结果表明,“两难”问题通过本文算法得到了很好的解决。结论 与其他正则化图像去模糊模型相比,本文算法明显改善图像的质量,如有效地保护图像的边缘,抑制阶梯效应,相对偏差和误差较小,较高的峰值信噪比和结构相似测度。     

Quantized tracking control for a multi‐agent system with high‐order leader dynamics

This paper presents a study of a tracking control problem for a multi‐agent system with an active leader and quantized communication constraints. We first design a discrete‐time distributed estimator‐based tracking control for each follower‐agent and analyze the tracking convergence with the help of the Riccati equation and common Lyapunov function when the communication channel is perfect and the interconnection topology is time‐varying. Then a stochastic quantization strategy is applied to model the information communication in the agent coordination and the corresponding solution to the tracking control problem is also given. Finally, a numerical example is given to illustrate the tracking control algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

人口系统迁移过程的参数辨识及其仿真

本文以系统辨识为工具，提出了迁移过程定量研究的一种方法，即运用随机牛顿法于时变系统中以辨识模型迁移表参量，同时结合卡尔曼滤波技术辨识迁移过程中另一参数－总和迁移率，将这两者融为一体，形成了辨识迁移模型参量的递推算法。本文又借助微分方程的稳定性理论讨论了净迁移情形下的辨识算法的收敛性，给出算法收敛的一个充分条件。