IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n357931.html

An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems

Author

Listed:
  • Emran Tohidi
  • Atena Pasban
  • A. Kilicman
  • S. Lotfi Noghabi

Abstract

This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover, the integral form of this multidomain dynamical system is considered. Collocating these constraints at the Legendre Gauss Lobatto (LGL) points together with using the Legendre Gauss Lobatto quadrature rule for approximating the involved integrals enables us to transform the basic OCPs into the associated nonlinear programming problems (NLPs). In all parts of this procedure, the associated control and state functions are approximated by piecewise constants and piecewise polynomials, respectively. An illustrative example is provided for confirming the accuracy and applicability of the proposed idea.

Suggested Citation

  • Emran Tohidi & Atena Pasban & A. Kilicman & S. Lotfi Noghabi, 2013. "An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:357931
    DOI: 10.1155/2013/357931
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/357931
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/357931?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. F. Toutounian & Emran Tohidi & A. Kilicman, 2013. "Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, April.
    2. Emran Tohidi & F. Soleymani & Adem Kilicman, 2013. "Robustness of Operational Matrices of Differentiation for Solving State-Space Analysis and Optimal Control Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, April.
    3. F. Toutounian & Emran Tohidi & A. Kilicman, 2013. "Fourier Operational Matrices of Differentiation and Transmission: Introduction and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Emran Tohidi & F. Soleymani & Adem Kilicman, 2013. "Robustness of Operational Matrices of Differentiation for Solving State‐Space Analysis and Optimal Control Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emran Tohidi & M. M. Ezadkhah & S. Shateyi, 2014. "Numerical Solution of Nonlinear Fractional Volterra Integro‐Differential Equations via Bernoulli Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Guimarães, O. & Labecca, W. & Piqueira, José Roberto C., 2020. "Generalized operational matrices and error bounds for polynomial basis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 258-272.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:357931. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.