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A Variation Evolving Method for Optimal Control Computation

Author

Listed:
  • Sheng Zhang

    (China Aerodynamics Research and Development Center)

  • En-Mi Yong

    (China Aerodynamics Research and Development Center)

  • Wei-Qi Qian

    (China Aerodynamics Research and Development Center)

  • Kai-Feng He

    (China Aerodynamics Research and Development Center)

Abstract

A new method, which originates from the continuous-time dynamics stability theory in the control field, is proposed for the optimal control computation. By introducing a virtual dimension, the variation time, an infinite-dimensional dynamic system that describes the variation motion of variables is derived from the optimal control problem based on the Lyapunov principle. The optimal solution is its stable equilibrium point and will be obtained in an asymptotically evolving way. Through this method, the intractable optimal control problems are transformed to the initial-value problems and they may be solved with mature ordinary differential equation numerical integration methods. Especially, the deduced dynamic system is globally stable, so any initial value may evolve to an extremal solution ultimately.

Suggested Citation

  • Sheng Zhang & En-Mi Yong & Wei-Qi Qian & Kai-Feng He, 2019. "A Variation Evolving Method for Optimal Control Computation," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 246-270, October.
    • Handle: RePEc:spr:joptap:v:183:y:2019:i:1:d:10.1007_s10957-019-01537-4
    DOI: 10.1007/s10957-019-01537-4
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    References listed on IDEAS

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    1. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
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