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A Variation Evolving Method for Optimal Control Computation

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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.

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Acknowledgements

In refining the paper, the authors get the help from Prof. K. L. Teo from Curtin University and Prof. H. J. Pesch from University of Bayreuth. Sincere thanks to them. The authors would also like to thank the Editor in Chief, Prof. B. A. Conway, and the anonymous referees for their help that further improves the paper.

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Authors and Affiliations

  1. China Aerodynamics Research and Development Center, Mianyang, 621000, China

    Sheng Zhang, En-Mi Yong, Wei-Qi Qian & Kai-Feng He

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  1. Sheng Zhang
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  2. En-Mi Yong
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Correspondence to Sheng Zhang.

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Communicated by Bruce A. Conway.

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Research supported by the National Defense Key Laboratory Fund of China, Grant Number: 614222003060717.

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Zhang, S., Yong, EM., Qian, WQ. et al. A Variation Evolving Method for Optimal Control Computation. J Optim Theory Appl 183, 246–270 (2019). https://doi.org/10.1007/s10957-019-01537-4

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