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Journal of Applied Mathematics, Statistics and Informatics

The Journal of University of Saint Cyril and Metodius

Editor-in-Chief: Kvasnicka, Vladimír

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An Efficient Legendre Pseudospectral Method for Solving Nonlinear Quasi Bang-Bang Optimal Control Problems

Emran Tohidi / Somayyeh Lotfi Noghabi
  • Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
  • Other articles by this author:
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Published Online: 2013-04-13 | DOI: https://doi.org/10.2478/v10294-012-0016-0


In this paper, an efficient Legendre pseudospectral approach for the accurate solution of nonlinear quasi bang-bang optimal control problems (OCPs) is investigated. In this approach, after linearizing the dynamical system, control and state functions are considered as piecewise constant and piecewise continuous polynomials, respectively, and the switching points are also taken as decision variables. Furthermore, for simplicity in discretization, a integral formulation of the dynamical equations is considered. Thereby, the problem is converted into a mathematical programming problem which can be solved by well-developed parameter optimization algorithms. Through a numerical implementation we show the efficiency of the proposed method via comparing with a classical pseudospectral method and other discretization approaches.

Additional Key Words and Phrases: Quasi Bang-Bang optimal control; Switching point; Numerical methods; Pseudospectral Legendre method

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About the article

Published Online: 2013-04-13

Published in Print: 2012-12-01

Citation Information: Journal of Applied Mathematics, Statistics and Informatics, Volume 8, Issue 2, Pages 73–85, ISSN (Print) 1336-9180, DOI: https://doi.org/10.2478/v10294-012-0016-0.

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