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Optimal discrete-valued control computation

Author

Listed:
  • Changjun Yu
  • Bin Li
  • Ryan Loxton
  • Kok Teo

Abstract

In this paper, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent problem subject to additional linear and quadratic constraints. The feasible region defined by these additional constraints is disconnected, and thus standard optimization methods struggle to handle these constraints. We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective. This leads to an approximate optimal control problem that can be solved using standard software packages such as MISER. Convergence results show that when the penalty parameter is sufficiently large, any local solution of the approximate problem is also a local solution of the original problem. We conclude the paper with some numerical results for two difficult train control problems. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:503-518
    DOI: 10.1007/s10898-012-9858-7
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Changjun Yu & Qun Lin & Ryan Loxton & Kok Lay Teo & Guoqiang Wang, 2016. "A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 876-901, June.

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