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An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints

Author

Listed:
  • Canghua Jiang

    (Harbin Institute of Technology)

  • Qun Lin

    (Curtin University)

  • Changjun Yu

    (Curtin 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 with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method.

Suggested Citation

  • Canghua Jiang & Qun Lin & Changjun Yu & Kok Lay Teo & Guang-Ren Duan, 2012. "An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 30-53, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-012-0006-9
    DOI: 10.1007/s10957-012-0006-9
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    Cited by:

    1. Qun Lin & Ryan Loxton & Kok Teo & Yong Wu, 2015. "Optimal control problems with stopping constraints," Journal of Global Optimization, Springer, vol. 63(4), pages 835-861, December.
    2. Jiachen Ju & Qian Liu, 2020. "Convergence properties of a class of exact penalty methods for semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 383-403, June.
    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. Eunice Blanchard & Ryan Loxton & Volker Rehbock, 2014. "Optimal control of impulsive switched systems with minimum subsystem durations," Journal of Global Optimization, Springer, vol. 60(4), pages 737-750, December.

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