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Euler Discretization and Inexact Restoration for Optimal Control

Author

Listed:
  • C. Y. Kaya

    (University of South Australia
    Universidade Federal do Rio de Janeiro)

  • J. M. Martínez

    (University of Campinas)

Abstract

A computational technique for unconstrained optimal control problems is presented. First, an Euler discretization is carried out to obtain a finite-dimensional approximation of the continuous-time (infinite-dimensional) problem. Then, an inexact restoration (IR) method due to Birgin and Martínez is applied to the discretized problem to find an approximate solution. Convergence of the technique to a solution of the continuous-time problem is facilitated by the convergence of the IR method and the convergence of the discrete (approximate) solution as finer subdivisions are taken. The technique is numerically demonstrated by means of a problem involving the van der Pol system; comprehensive comparisons are made with the Newton and projected Newton methods.

Suggested Citation

  • C. Y. Kaya & J. M. Martínez, 2007. "Euler Discretization and Inexact Restoration for Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 191-206, August.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:2:d:10.1007_s10957-007-9217-x
    DOI: 10.1007/s10957-007-9217-x
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    References listed on IDEAS

    as
    1. C.Y. Kaya & J.L. Noakes, 2003. "Computational Method for Time-Optimal Switching Control," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 69-92, April.
    2. Walter Alt, 2001. "Mesh-Independence of the Lagrange–Newton Method for Nonlinear Optimal Control Problems and their Discretizations," Annals of Operations Research, Springer, vol. 101(1), pages 101-117, January.
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    Cited by:

    1. Nahid Banihashemi & C. Yalçın Kaya, 2013. "Inexact Restoration for Euler Discretization of Box-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 726-760, March.
    2. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    3. Elijah Polak & Seungho Lee & Ismail Bustany & Akshay Madhan, 2016. "Method of Outer Approximations and Adaptive Approximations for a Class of Matrix Games," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 876-899, September.
    4. Regina S. Burachik & Alexander C. Kalloniatis & C. Yalçın Kaya, 2021. "Sparse Network Optimization for Synchronization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 229-251, October.

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