Numerical solution a class of 2D fractional optimal control problems by using 2D Müntz‐Legendre wavelets

Rahimkhani Parisa; Ordokhani Yadollah

摘要

Summary >In this paper, a method for finding an approximate solution of a class of 2D fractional optimal control problems with fractional‐order dynamical system is discussed. In the proposed method, the fractional derivative is expressed in the Caputo sense. The method consists of expanding unknown functions as the elements of two‐dimensional (2D) Müntz‐Legendre wavelets. The 2D Müntz‐Legendre wavelets are constructed and their properties are presented. The operational matrix of fractional‐order integration for these wavelets is utilized to reduce the solution of 2D fractional optimal control problem to an optimization problem, which can then be solved easily. Some results concerning the error analysis are obtained. Finally, two illustrative test problems are included to demonstrate the validity and applicability of the technique. Moreover, our achievements are compared with the previous results to show the superiority of the proposed method. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”xml：lang =“en”xml：id =“oca2456-abs-abs-0001”> <标题类型=“main”>摘要</ title> 在本文中，讨论了用于找到具有分数阶动态系统的一类2D分数最佳控制问题的近似解的方法。在该方法中，分数衍生物在Caputo意义上表达。该方法包括将未知功能扩展为二维（2D）Müntz-Legendre小波的元素。构建了2DMüntz-Legendre小波，并提出了它们的性质。用于这些小波的分数整合的操作矩阵用于将2D分数最佳控制问题的解决方案降低到优化问题，然后可以容易地解决。获得了一些关于误差分析的结果。最后，包括两个说明性测试问题以证明该技术的有效性和适用性。此外，我们的成就与以前的结果进行了比较，以显示所提出的方法的优越性。</ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-27675/'>《Optimal Control Applications and Methods》</a> <b style="margin: 0 2px;">|</b><span>2018年第6期</span><b style="margin: 0 2px;">|</b><span>共19页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Rahimkhani Parisa&option=202" target="_blank" rel="nofollow">Rahimkhani Parisa;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ordokhani Yadollah&option=202" target="_blank" rel="nofollow">Ordokhani Yadollah;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Department of MathematicsFaculty of Mathematical Sciences Alzahra UniversityTehran Iran;</p> <p>Department of MathematicsFaculty of Mathematical Sciences Alzahra UniversityTehran Iran;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1147.html" title="应用数学">应用数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Caputo derivative&option=203" rel="nofollow">Caputo derivative;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=fractional optimal control problem&option=203" rel="nofollow">fractional optimal control problem;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=numerical solution&option=203" rel="nofollow">numerical solution;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Riemann‐Liouville fractional integral operator&option=203" rel="nofollow">Riemann‐Liouville fractional integral operator;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=wavelet method&option=203" rel="nofollow">wavelet method;</a> </p> <div class="translation"> 机译：Caputo衍生物;分数最优控制问题;数值解决方案;riemann-liouville分数积分运算符;小波法; 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(3D-DCT) AND DISCRETE FRACTIONAL RANDOM TRANSFORM (DFRNT) AND AN APPARATUS THEREOF, ESPECIALLY FOR INSERTING A FORENSIC MARK GENERATED IN A FORENSIC MARK GENERATOR INTO THE DUAL FREQUENCY DOMAINS AND A DFRTN TRANSFORM PLANE THROUGH A QUANTIZATION METHOD</a> <b>[P]</b> . <span> 外国专利：  KR20130098535A </span> <span> . 2013-09-05</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：使用二维离散小波变换（2D-DWT）和三维离散余弦变换（3D-DCT）和离散分数阶随机变换（DFRNT）的二维域进行视频取证标记的方法及其前瞻性在法证生成器中通过量化方法进入双频域和DFRTN变换平面 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130411429961.html">D2D FFR SIGNALING FOR FRACTIONAL FREQUENCY REUSE FFR FOR D2D COMMUNICATIONS</a> <b>[P]</b> . <span> 外国专利：  KR20160127029A </span> <span> . 2016-11-02</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于分数频率重用的D2D FFR信号重用于D2D通信的FFR </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130409482559.html">Apparatus for post processing of the images of cutting of 2D cross section defining a set of data volume of 3D image; graphical user interface; the method of post processing images of cutting cross section 2D; medical system for post processing of the images of CO Tens of 2D cross section; element of computer program for controlling a device; and executable mediaBy computer.</a> <b>[P]</b> . <span> 外国专利：  BR112014008461A2 </span> <span> . 2017-04-11</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于对2D横截面的切割图像进行后处理的设备，其定义了一组3D图像的数据量;图形用户界面;切割截面2D图像的后处理方法;用于对二维横截面的CO Tens图像进行后处理的医疗系统;用于控制设备的计算机程序的元素;和可执行媒体通过计算机。 </span> </p> </li> </ul> </div> </div> </div> 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