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Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation

Author

Listed:
  • R. Pytlak

    (Military University of Technology)

  • R. B. Vinter

    (Imperial College)

Abstract

In this paper, we describe the implementation aspects of an optimization algorithm for optimal control problems with control, state, and terminal constraints presented in our earlier paper. The important aspect of the implementation is that, in the direction-finding subproblems, it is necessary only to impose the state constraint at relatively few points in the time involved. This contributes significantly to the algorithmic efficiency. The algorithm is applied to solve several optimal control problems, including the problem of the abort landing of an aircraft in the presence of windshear.

Suggested Citation

  • R. Pytlak & R. B. Vinter, 1999. "Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 623-649, June.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:3:d:10.1023_a:1021742204850
    DOI: 10.1023/A:1021742204850
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    References listed on IDEAS

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    1. R. Pytlak, 1998. "Runge–Kutta Based Procedure for the Optimal Control of Differential-Algebraic Equations," Journal of Optimization Theory and Applications, Springer, vol. 97(3), pages 675-705, June.
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    Cited by:

    1. Barro, Diana & Canestrelli, Elio, 2005. "Dynamic portfolio optimization: Time decomposition using the Maximum Principle with a scenario approach," European Journal of Operational Research, Elsevier, vol. 163(1), pages 217-229, May.
    2. Diana Barro & Elio Canestrelli, 2011. "Combining stochastic programming and optimal control to solve multistage stochastic optimization problems," Working Papers 2011_24, Department of Economics, University of Venice "Ca' Foscari", revised 2011.
    3. Yuk-Loong Chow & Xiang Yu & Chao Zhou, 2020. "On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 803-818, June.
    4. 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.
    5. Diana Barro & Elio Canestrelli, 2016. "Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 711-742, July.

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