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Brazilian Technology Symposium

BTSym 2018: Proceedings of the 4th Brazilian Technology Symposium (BTSym'18) pp 45–54Cite as

A Solution for Dubins Path Problem with Uncertainties Using World Cup Optimization and Chebyshev Polynomials

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Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 140))

Abstract

In this paper, an efficient numerical approach is developed for solving the baseline problem with interval uncertainties. Interval arithmetic is also utilized for developing the proposed method in the presence of uncertainties with only lower and upper bounds of parameters. In the proposed method, the equation of motion, performance index, and boundary conditions are first changed into some algebraic equations. This process converts the problem into an optimization problem. The presented technique is based on an interval extension of Chebyshev polynomials where its coefficients are achieved by world cup optimization algorithm, as a new optimization algorithm. The proposed method approximates the control and state variables as a function of time. The proposed solution is based on state parameterization, such that the state variable is approximated by the proposed interval Chebyshev polynomials with unknown interval coefficients. Finally, by solving the baseline problem in the presence of interval uncertainties, the reliability and effectiveness of the proposed method are demonstrated.

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Author information

Authors and Affiliations

  1. Department of Electrical and Control Engineering, Tafresh University, 39518 79611, Tafresh, Iran

    Navid Razmjooy & Mehdi Ramezani

  2. Departamento de Engenharia de Telecomunicações, Universidade Federal Fluminense, Rio de Janeiro, Brazil

    Vânia Vieira Estrela

Authors
  1. Navid Razmjooy
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  2. Mehdi Ramezani
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  3. Vânia Vieira Estrela
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Corresponding author

Correspondence to Navid Razmjooy .

Editor information

Editors and Affiliations

  1. Faculty of Electrical and Computing Engineering, University of Campinas, Campinas, São Paulo, Brazil

    Yuzo Iano

  2. Faculty of Technology, University of Campinas, Campinas, São Paulo, Brazil

    Rangel Arthur

  3. Divisão de Engenharia Eletrônica, Instituto Tecnológico de Aeronáutica ITA, São José dos Campos, São Paulo, Brazil

    Osamu Saotome

  4. Universidade Federal Fluminense (UFF), Duque de Caxias, Rio de Janeiro, Brazil

    Vânia Vieira Estrela

  5. Faculty of Electrical and Computing Engineering, University of Campinas, Campinas, São Paulo, Brazil

    Hermes José Loschi

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Razmjooy, N., Ramezani, M., Vieira Estrela, V. (2019). A Solution for Dubins Path Problem with Uncertainties Using World Cup Optimization and Chebyshev Polynomials. In: Iano, Y., Arthur, R., Saotome, O., Vieira Estrela, V., Loschi, H. (eds) Proceedings of the 4th Brazilian Technology Symposium (BTSym'18). BTSym 2018. Smart Innovation, Systems and Technologies, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-030-16053-1_5

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  • DOI: https://doi.org/10.1007/978-3-030-16053-1_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-16052-4

  • Online ISBN: 978-3-030-16053-1

  • eBook Packages: EngineeringEngineering (R0)

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