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Optimal control of impulsive switched systems with minimum subsystem durations

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Curtin University, Perth, Australia

    Eunice Blanchard, Ryan Loxton & Volker Rehbock

  2. Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China

    Ryan Loxton

Authors
  1. Eunice Blanchard
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  2. Ryan Loxton
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  3. Volker Rehbock
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Corresponding author

Correspondence to Ryan Loxton.

Additional information

R. Loxton is supported by an International Young Scientists Research Fellowship from the National Natural Science Foundation of China (Grant No. 11350110208), and an International Collaboration Grant from the State Key Laboratory of Industrial Control Technology at Zhejiang University, China (Grant No. ICT1301)

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Blanchard, E., Loxton, R. & Rehbock, V. Optimal control of impulsive switched systems with minimum subsystem durations. J Glob Optim 60, 737–750 (2014). https://doi.org/10.1007/s10898-013-0109-3

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  • DOI: https://doi.org/10.1007/s10898-013-0109-3

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