Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control |
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Authors: | J Frédéric Bonnans Julien Laurent-Varin |
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Institution: | (1) Projet Sydoco, Inria-Rocquencourt, Domaine de Voluceau BP 105, 78153, Le Chesnay, France;(2) Long-Term Design & System Integration Department, ONERA, and Projet Sydoco, INRIA Rocquencourt, Domaine de Voluceau BP 105, 78153, Le Chesnay, France |
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Abstract: | We derive order conditions for the discretization of (unconstrained) optimal control problems, when the scheme for the state
equation is of Runge-Kutta type. This problem appears to be essentially the one of checking order conditions for symplectic
partitioned Runge-Kutta schemes. We show that the computations using bi-coloured trees are naturally expressed in this case
in terms of oriented free tree. This gives a way to compute them by an appropriate computer program.
This study is supported by CNES and ONERA, in the framework of the CNES fellowship of the second author. |
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Keywords: | 49M25 34M99 65L06 |
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