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首页> 外文期刊>Discrete and continuous dynamical systems >HIGH ORDER VARIATIONAL INTEGRATORS IN THE OPTIMAL CONTROL OF MECHANICAL SYSTEMS
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HIGH ORDER VARIATIONAL INTEGRATORS IN THE OPTIMAL CONTROL OF MECHANICAL SYSTEMS

机译：机械系统最优控制中的高阶变积分

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摘要

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.
机译：近年来，已经在设计用于机械系统的仿真和优化的数值方法方面付出了很多努力，这些方案已被用于保存结构的方案中。一类是变分积分器，它是动量保持且辛的。在本文中，我们开发了两个高阶变分积分器，它们在近似基础空间的维数上有独到之处，并研究了它们在机械系统带来的有限维最优控制问题中的应用。显示了近似问题的状态和控制变量的收敛性。此外，通过分析最优控制问题的伴随系统及其离散化对应物，我们证明了，对于这些特定的积分器，对偶化和离散化是通勤的。

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