Inexact Newton and quasi-Newton methods for the output feedback pole assignment problem

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• 作者：El-Sayed M. E. Mostafa ; Mohamed A. Tawhid…
• 关键词：The pole assignment problem ; Output feedback control ; Nonlinear programming ; 49N35 ; 49N10 ; 93D52 ; 93D22 ; 65K05
• 刊名：Computational and Applied Mathematics
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：33
• 期：3
• 页码：517-542
• 全文大小：380 KB
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• 作者单位：El-Sayed M. E. Mostafa (1)
  Mohamed A. Tawhid (1) (2)
  Eman R. Elwan (3)
  
  1. Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bey, 21511?, Alexandria, Egypt
  2. Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, V2C 0C8, Canada
  3. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt
  
• ISSN：1807-0302

文摘

The pole assignment problem (PAP) is a special algebraic inverse eigenvalue problem. In this paper, we present two types of algorithms, namely a quasi-Newton method with line search and some variants of the inexact Newton methods to tackle that problem. For a nonmonotone version of inexact Newton–Krylov method, we give local convergence under the assumptions of semismoothness and \(BD\) -regularity at the solution and global convergence under a nonmonotonic backtracking strategy. For a quasi-Newton method with line search, under suitable assumptions, we show local Q-superlinear convergence. Also, we consider a proximal point quasi-Newton algorithm for solving PAP. Moreover, we modify these methods to tackle the PAP where the corresponding control system is with time delay. Numerical results illustrate the performance of the proposed methods.