本文選題：隨機(jī)搜索　切入點(diǎn)：隨機(jī)源搜索　出處：《東南大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨機(jī)搜索,是指單個(gè)或多個(gè)智能體(車輛或機(jī)器人)按照某種隨機(jī)機(jī)制找到某信號(hào)的源點(diǎn)或目標(biāo)函數(shù)的極值點(diǎn).它在自然界和人類生活中廣泛存在,受到國(guó)內(nèi)外諸多學(xué)者的關(guān)注和研究.因計(jì)算上的需要,離散時(shí)間下的隨機(jī)搜索比連續(xù)時(shí)間隨機(jī)搜索有更重要的研究意義.許多隨機(jī)搜索都需要利用目標(biāo)函數(shù)的信息(如函數(shù)形式或梯度信息),已有的無(wú)目標(biāo)函數(shù)信息的隨機(jī)搜索主要考慮隨機(jī)極值搜索算法(Stochastic Extremum Seeking,SES),也有少數(shù)學(xué)者利用了隨機(jī)逼近思想,但往往事先假設(shè)估計(jì)序列有界.另外,分布式隨機(jī)搜索因?yàn)橐紤]智能體之間的鄰居關(guān)系、數(shù)據(jù)傳輸和時(shí)延等,也沒(méi)有完善的成果.本文給出了離散時(shí)間隨機(jī)搜索算法控制智能體搜索到目標(biāo)函數(shù)的極大值點(diǎn)(或極小值點(diǎn)).基于擴(kuò)展截尾隨機(jī)逼近算法的思想,去掉了有界性的假設(shè)并減弱噪聲條件.本文主要工作如下:1.研究了兩類車輛(速度驅(qū)動(dòng)車輛和力驅(qū)動(dòng)車輛)作為搜索個(gè)體的隨機(jī)源搜索.通過(guò)對(duì)時(shí)間區(qū)間的劃分,離散采樣得到了離散時(shí)間下的運(yùn)動(dòng)模型,并將之與已有的擴(kuò)展截尾隨機(jī)逼近算法結(jié)合,給出了離散時(shí)間隨機(jī)源搜索算法及其收斂的充要條件.最后,給出了兩個(gè)數(shù)值仿真實(shí)例,驗(yàn)證了算法的有效性.2.研究了分布式隨機(jī)源搜索問(wèn)題,即N個(gè)小車通過(guò)交換對(duì)信號(hào)域的量測(cè)值合作式搜索該信號(hào)域的源,更進(jìn)一步考慮分布式隨機(jī)極值搜索問(wèn)題,即N個(gè)小車?yán)煤肼暩蓴_的量測(cè)值合作式搜索全局目標(biāo)函數(shù)(N個(gè)局部?jī)r(jià)值函數(shù)的和)的極大值點(diǎn).首先將N個(gè)小車(速度驅(qū)動(dòng)車輛或力驅(qū)動(dòng)車輛)看成節(jié)點(diǎn)后構(gòu)成了 一個(gè)網(wǎng)絡(luò),把每個(gè)車輛的動(dòng)態(tài)模型通過(guò)相同的時(shí)間區(qū)間劃分做離散化處理.隨后給出了距離的定義,由此確定智能體之間的鄰居關(guān)系并構(gòu)造了權(quán)重矩陣.然后給出了分布式隨機(jī)源搜索算法并證明了其收斂性.加強(qiáng)假設(shè)條件、修改分布式源搜索算法后,極值點(diǎn)的分布式搜索問(wèn)題得以解決.最后通過(guò)數(shù)值仿真驗(yàn)證了算法的有效性.
[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.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O224

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