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An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem

Author

Listed:
  • Bin Li

    (Harbin Institute of Technology
    Curtin University)

  • Chang Jun Yu

    (Curtin University
    Shanghai University)

  • Kok Lay Teo

    (Curtin University)

  • Guang Ren Duan

    (Harbin Institute of Technology)

Abstract

In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous state and control inequality constraints. By using the control parametrization technique and a time scaling transformation, the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints. On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value, any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For illustration, three examples are solved showing the effectiveness and applicability of the approach proposed.

Suggested Citation

  • Bin Li & Chang Jun Yu & Kok Lay Teo & Guang Ren Duan, 2011. "An Exact Penalty Function Method for Continuous Inequality Constrained Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 260-291, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9904-5
    DOI: 10.1007/s10957-011-9904-5
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    References listed on IDEAS

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    1. Gerdts, Matthias, 2008. "A nonsmooth Newton’s method for control-state constrained optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 925-936.
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    Cited by:

    1. K. H. Wong & H. W. J. Lee & C. K. Chan & C. Myburgh, 2013. "Control Parametrization and Finite Element Method for Controlling Multi-species Reactive Transport in an Underground Channel," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 168-187, April.
    2. Chongyang Liu & Changjun Yu & Zhaohua Gong & Huey Tyng Cheong & Kok Lay Teo, 2023. "Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 798-816, May.
    3. M. V. Dolgopolik, 2018. "A Unified Approach to the Global Exactness of Penalty and Augmented Lagrangian Functions II: Extended Exactness," Journal of Optimization Theory and Applications, Springer, vol. 176(3), pages 745-762, March.
    4. Changjun Yu & Bin Li & Ryan Loxton & Kok Teo, 2013. "Optimal discrete-valued control computation," Journal of Global Optimization, Springer, vol. 56(2), pages 503-518, June.

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