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Solving a class of nonlinear optimal control problems via he’s variational iteration method

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Abstract

This paper presents an analytical approximate solution for a class of nonlinear quadratic optimal control problems. The proposed method consists of a Variational Iteration Method (VIM) together with a shooting method like procedure, for solving the extreme conditions obtained from the Pontryagin’s Maximum Principle (PMP). This method is applicable for a large class of nonlinear quadratic optimal control problems. In order to use the proposed method, a control design algorithm with low computational complexity is presented. Through the finite iterations of algorithm, a suboptimal control law is obtained for the nonlinear optimal control problem. Two illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, Iran

    Mohammad Shirazian & Sohrab Effati

Authors
  1. Mohammad Shirazian
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  2. Sohrab Effati
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Correspondence to Mohammad Shirazian.

Additional information

Recommended by Editorial Board member Guang-Hong Yang under the direction of Editor Young Il Lee.

Mohammad Shirazian received his B.S. and M.S. degrees in applied mathematics from Ferdowsi University of Mashhad, in 2007 and 2009 respectively. He is now pursuing a Ph.D. degree in applied mathematics (control and optimization) at Ferdowsi University of Mashhad, Mashhad, Iran. His research interests include optimal control theory and its applications, numerical methods for solving ODEs and PDEs, fuzzy theory, and neural networks.

Sohrab Effati received his B.S. degree in Applied Mathematics from Birjand University, Birjand, Iran, his M.S. degree in Applied Mathematics from Institute of Mathematics at Tarbiat Moallem Tehran University, Tehran, Iran, in 1992 and 1995, respectively. He received his Ph.D. degree in Control Systems from Ferdowsi University of Mashhad, Mashhad, Iran, in April 2000. He is an Associate Professor with the Department of Applied Mathematics at Ferdowsi University of Mashhad in Iran. His research interests include control systems, optimization, fuzzy theory, and neural network models and its applications in optimization problems, ODE and PDE.

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Shirazian, M., Effati, S. Solving a class of nonlinear optimal control problems via he’s variational iteration method. Int. J. Control Autom. Syst. 10, 249–256 (2012). https://doi.org/10.1007/s12555-012-0205-z

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  • DOI: https://doi.org/10.1007/s12555-012-0205-z

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