A Variation Evolving Method for Optimal Control Computation

Sheng Zhang (), En-Mi Yong (), Wei-Qi Qian () and Kai-Feng He ()
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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

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 13, 246-270

Abstract: 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.

Keywords: Optimal control; Dynamics stability; Variation evolution; Evolution partial differential equation; Initial-value problem; 49M05; 49M29; 35B35 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-019-01537-4

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