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Optimal control of impulsive switched systems with minimum subsystem durations

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  • Eunice Blanchard
  • Ryan Loxton
  • Volker Rehbock

Abstract

This paper presents a new computational approach for solving optimal control problems governed by impulsive switched systems. Such systems consist of multiple subsystems operating in succession, with possible instantaneous state jumps occurring when the system switches from one subsystem to another. The control variables are the subsystem durations and a set of system parameters influencing the state jumps. In contrast with most other papers on the control of impulsive switched systems, we do not require every potential subsystem to be active during the time horizon (it may be optimal to delete certain subsystems, especially when the optimal number of switches is unknown). However, any active subsystem must be active for a minimum non-negligible duration of time. This restriction leads to a disjoint feasible region for the subsystem durations. The problem of choosing the subsystem durations and the system parameters to minimize a given cost function is a non-standard optimal control problem that cannot be solved using conventional techniques. By combining a time-scaling transformation and an exact penalty method, we develop a computational algorithm for solving this problem. We then demonstrate the effectiveness of this algorithm by considering a numerical example on the optimization of shrimp harvesting operations. Copyright Springer Science+Business Media New York 2014

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  • 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.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:4:p:737-750
    DOI: 10.1007/s10898-013-0109-3
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    References listed on IDEAS

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    1. 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.
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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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