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Optimal Feedback Control for Stochastic Impulsive Linear Systems Subject to Poisson Processes

In: Optimization and Optimal Control

Author

Listed:
  • Zhi Guo Feng

    (Chongqing Normal University)

  • Kok Lay Teo

    (Curtin University of Technology)

Abstract

Summary This chapter considers a class of optimal feedback control problems, where its dynamical system is described by stochastic linear systems subject to Poisson processes and with state jumps. We show that this stochastic impulsive optimal parameter selection problem is equivalent to a deterministic impulsive optimal parameter selection problem, where the times at which the jumps occurred as well as their heights are decision variables. Then, by introducing a time scaling transform, we show that this deterministic impulsive optimal parameter selection problem is transformed into an equivalent deterministic impulsive optimal parameter selection problem with fixed jump times. For the numerical computation, we derive the gradient formulae of the cost function and the constraint functions. On this basis, an efficient computational method is developed and an example is solved for illustration.

Suggested Citation

  • Zhi Guo Feng & Kok Lay Teo, 2010. "Optimal Feedback Control for Stochastic Impulsive Linear Systems Subject to Poisson Processes," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 241-258, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-89496-6_13
    DOI: 10.1007/978-0-387-89496-6_13
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    Cited by:

    1. Chongyang Liu & Ryan Loxton & Kok Teo, 2014. "Optimal parameter selection for nonlinear multistage systems with time-delays," Computational Optimization and Applications, Springer, vol. 59(1), pages 285-306, October.

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