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On a Class of Optimal Control Problems with State Jumps

Author

Listed:
  • Y. Liu

    (Curtin University of Technology)

  • K. L. Teo

    (Curtin University of Technology)

  • L. S. Jennings

    (University of Western Australia)

  • S. Wang

    (Curtin University of Technology)

Abstract

In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of these switching times and a parameter vector representing the state jumps are taken as decision variables. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computational algorithm is proposed. For illustration, a numerical example is included.

Suggested Citation

  • Y. Liu & K. L. Teo & L. S. Jennings & S. Wang, 1998. "On a Class of Optimal Control Problems with State Jumps," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 65-82, July.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:1:d:10.1023_a:1022684730236
    DOI: 10.1023/A:1022684730236
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    Cited by:

    1. Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.
    2. Yu, Run & Leung, PingSun & Bienfang, Paul, 2009. "Modeling partial harvesting in intensive shrimp culture: A network-flow approach," European Journal of Operational Research, Elsevier, vol. 193(1), pages 262-271, February.
    3. Liang, Xiyin & Pei, Yongzhen & Zhu, Meixia & Lv, Yunfei, 2016. "Multiple kinds of optimal impulse control strategies on plant–pest–predator model with eco-epidemiology," Applied Mathematics and Computation, Elsevier, vol. 287, pages 1-11.
    4. Sadana, Utsav & Reddy, Puduru Viswanadha & Zaccour, Georges, 2021. "Nash equilibria in nonzero-sum differential games with impulse control," European Journal of Operational Research, Elsevier, vol. 295(2), pages 792-805.

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