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Determination of Periodic Trajectories of Dynamic Systems Subject to Switching Input Constraints

Author

Listed:
  • Matheus Henrique Marcolino

    (Instituto Tecnológico de Aeronáutica)

  • Roberto Kawakami Harrop Galvão

    (Instituto Tecnológico de Aeronáutica)

  • Karl Heinz Kienitz

    (Instituto Tecnológico de Aeronáutica)

  • Márcio Santos Vieira

    (Embraer)

Abstract

The present paper is concerned with the determination of periodic state trajectories of discrete-time dynamic systems resulting from the application of bidirectional on/off input sequences subject to switching constraints. The main contribution consists of characterizing the feasible input sequences and associated state trajectories in terms of a set of linear constraints involving integer variables. For practical purposes, the resulting solutions obtained by an integer linear solver can be evaluated in terms of engineering criteria such as amplitude or fuel expense in order to choose an appropriate trajectory to be used as target in a control law. A numerical example involving a double-integrator system is presented to illustrate the use of the proposed constraint formulation for the determination of feasible periodic state trajectories.

Suggested Citation

  • Matheus Henrique Marcolino & Roberto Kawakami Harrop Galvão & Karl Heinz Kienitz & Márcio Santos Vieira, 2017. "Determination of Periodic Trajectories of Dynamic Systems Subject to Switching Input Constraints," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 848-864, December.
    • Handle: RePEc:spr:joptap:v:175:y:2017:i:3:d:10.1007_s10957-017-1187-z
    DOI: 10.1007/s10957-017-1187-z
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    References listed on IDEAS

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    1. Xiang Wu & Kanjian Zhang & Changyin Sun, 2013. "Parameter Tuning of Multi-Proportional-Integral-Derivative Controllers Based on Optimal Switching Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 454-472, November.
    2. Chongyang Liu & Ryan Loxton & Kok Lay Teo, 2014. "Switching Time and Parameter Optimization in Nonlinear Switched Systems with Multiple Time-Delays," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 957-988, December.
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