Optimal Control and Bifurcation Issues for Lorenz-Rössler Model

• 作者: Abdo M. Al-Mahdi Omalsad H. Odhah Saba M. Alwan
• 来源期刊: 最优化(英文)
• 学科: 数学
• 关键词: Lorenz-Rössler Model BIFURCATION Pontryagin Principle Optimal Control Problem
• 年，卷（期）: 2020,（3）
• 页码范围: 71-85
• 页数: 15页
• 分类号: O17

摘要

Optimal control is one of the most popular decision-making tools recently in many researches and in many areas. The Lorenz-R<span style="FONT-FAMILY:;COLOR: #4f4f4f" font-size:14px;white-space:normal;background-color:#ffffff;?=""><span style="color:#4F4F4F;font-family:"font-size:14px;white-space:normal;background-color:#FFFFFF;">&#246;</span></span>ssler model is one of the interesting models because of the idea of consolidation of the two models<span style="font-family:Verdana;">:</span><span style="font-family:Verdana;"> Lorenz and <span style="white-space:nowrap;"><span style="color:#4F4F4F;font-family:"font-size:14px;white-space:normal;background-color:#FFFFFF;">&#246;</span></span><span style="FONT-FAMILY:;COLOR: #4f4f4f" font-size:14px;white-space:normal;background-color:#ffffff;?=""></span>ssler. This paper discusses the Lorenz-R<span style="FONT-FAMILY:;COLOR: #4f4f4f" font-size:14px;white-space:normal;background-color:#ffffff;?=""><span style="color:#4F4F4F;font-family:"font-size:14px;white-space:normal;background-color:#FFFFFF;">&#246;</span></span>ssler model from the bifurcation phenomena and the optimal control problem (OCP). The bifurcation property at the system equilibrium <img alt="" src="Edit_128925fa-e315-4db4-b9e4-9cd999342cb9.bmp" /> </span><span style="font-family:Verdana;">is studied and it is found that saddle-node and Hopf bifurcations can be holed under some conditions on the parameters. Also, the problem of the optimal control of Lorenz-R<span style="FONT-FAMILY:;COLOR: #4f4f4f" font-size:14px;white-space:normal;background-color:#ffffff;?=""><span style="color:#4F4F4F;font-family:"font-size:14px;white-space:normal;background-color:#FFFFFF;">&#246;</span></span>ssler model is discussed and </span><span style="font-family:Verdana;">it </span><span style="font-family:Verdana;">u</span><span style="font-family:Verdana;">ses</span><span style="font-family:Verdana;"> the Pontryagin’s Maximum Principle (PMP) to derive the optimal control inputs that achieve the optimal trajectory. Numerical