High order variational integrators in the optimal control of mechanical systems

Abstract : In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are momentum preserving and symplectic. In this article, we develop two high order variational integrators which distinguish themselves in the dimension of the underling space of approximation and we investigate their application to finite-dimensional optimal control problems posed with mechanical systems. The convergence of state and control variables of the approximated problem is shown. Furthermore, by analyzing the adjoint systems of the optimal control problem and its discretized counterpart, we prove that, for these particular integrators, dualization and discretization commute.
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Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 2015, 35 (9), pp.4193 - 4223. 〈10.3934/dcds.2015.35.4193〉
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Dernière modification le : vendredi 16 novembre 2018 - 01:51:51
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Cédric M. Campos, Sina Ober-Blöbaum, Emmanuel Trélat. High order variational integrators in the optimal control of mechanical systems. Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 2015, 35 (9), pp.4193 - 4223. 〈10.3934/dcds.2015.35.4193〉. 〈hal-01122910〉

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