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A modified pseudospectral method for solving trajectory optimization problems with singular arc
Author(s) -
Foroozandeh Zahra,
Shamsi Mostafa,
Azhmyakov Vadim,
Shafiee Masoud
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4097
Subject(s) - pseudospectral optimal control , gauss pseudospectral method , legendre polynomials , mathematics , pseudo spectral method , a priori and a posteriori , chebyshev pseudospectral method , optimal control , mathematical optimization , legendre wavelet , scheme (mathematics) , trajectory optimization , nonlinear programming , nonlinear system , computer science , mathematical analysis , orthogonal polynomials , wavelet , fourier analysis , philosophy , chebyshev equation , artificial intelligence , wavelet transform , fourier transform , classical orthogonal polynomials , epistemology , discrete wavelet transform , quantum mechanics , physics
This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.