随机逼近算法与随机搜索相关问题研究

发布时间：2018-03-21 00:36

本文选题：随机搜索　切入点：随机源搜索　出处：《东南大学》2017年硕士论文　论文类型：学位论文

【摘要】：随机搜索,是指单个或多个智能体(车辆或机器人)按照某种随机机制找到某信号的源点或目标函数的极值点.它在自然界和人类生活中广泛存在,受到国内外诸多学者的关注和研究.因计算上的需要,离散时间下的随机搜索比连续时间随机搜索有更重要的研究意义.许多随机搜索都需要利用目标函数的信息(如函数形式或梯度信息),已有的无目标函数信息的随机搜索主要考虑随机极值搜索算法(Stochastic Extremum Seeking,SES),也有少数学者利用了随机逼近思想,但往往事先假设估计序列有界.另外,分布式随机搜索因为要考虑智能体之间的邻居关系、数据传输和时延等,也没有完善的成果.本文给出了离散时间随机搜索算法控制智能体搜索到目标函数的极大值点(或极小值点).基于扩展截尾随机逼近算法的思想,去掉了有界性的假设并减弱噪声条件.本文主要工作如下:1.研究了两类车辆(速度驱动车辆和力驱动车辆)作为搜索个体的随机源搜索.通过对时间区间的划分,离散采样得到了离散时间下的运动模型,并将之与已有的扩展截尾随机逼近算法结合,给出了离散时间随机源搜索算法及其收敛的充要条件.最后,给出了两个数值仿真实例,验证了算法的有效性.2.研究了分布式随机源搜索问题,即N个小车通过交换对信号域的量测值合作式搜索该信号域的源,更进一步考虑分布式随机极值搜索问题,即N个小车利用含噪声干扰的量测值合作式搜索全局目标函数(N个局部价值函数的和)的极大值点.首先将N个小车(速度驱动车辆或力驱动车辆)看成节点后构成了一个网络,把每个车辆的动态模型通过相同的时间区间划分做离散化处理.随后给出了距离的定义,由此确定智能体之间的邻居关系并构造了权重矩阵.然后给出了分布式随机源搜索算法并证明了其收敛性.加强假设条件、修改分布式源搜索算法后,极值点的分布式搜索问题得以解决.最后通过数值仿真验证了算法的有效性.
[Abstract]:Random search means that a single or multiple agents (vehicles or robots) find the extremum of a signal's source or objective function according to a random mechanism. It exists widely in nature and human life. It has attracted the attention and research of many scholars at home and abroad. Random search in discrete time is more important than continuous time random search. Many random searches need to use the information of objective function (such as function form or gradient information). Random search mainly considers stochastic Extremum searching algorithm, and a few scholars make use of the idea of stochastic approximation. But it is often assumed that the estimated sequence is bounded. In addition, the distributed random search takes into account the neighbor relationship between agents, data transmission and delay, etc. The discrete-time random search algorithm is used to control the maximum point (or minimum point) of the objective function, which is based on the idea of extended truncated random approximation algorithm. In this paper, the assumption of boundedness is removed and the noise condition is attenuated. The main work of this paper is as follows: 1. Two types of vehicles (velocity-driven vehicle and force-driven vehicle) are studied as random source search for individual search. The motion model under discrete time is obtained by discrete sampling, and combined with the existing extended truncated random approximation algorithm, the sufficient and necessary conditions for the discrete time random source search algorithm and its convergence are given. Finally, two numerical simulation examples are given. The validity of the algorithm is verified. 2. The distributed random source search problem is studied, that is, N cars search the source of the signal domain by exchanging the measurement values of the signal domain, and further consider the distributed random extreme value search problem. That is to say, N cars use the cooperative method of measuring value with noise to search the maximum points of the global objective function and the sum of N local value functions. First, N cars (velocity-driven vehicles or force-driven vehicles) are regarded as nodes. To form a network, The dynamic model of each vehicle is discretized by the same time interval partition. Then the definition of distance is given. Then the distributed random source search algorithm is given and its convergence is proved. The assumption condition is strengthened and the distributed source search algorithm is modified. The distributed search problem of extremum point can be solved. Finally, the validity of the algorithm is verified by numerical simulation.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

【相似文献】