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首页> 外文会议>Computational methods in science and engineering: advances in computational science >Runge-Kutta Discretizations of Infinite Horizon Optimal Control Problems with Steady-State Invariance
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Runge-Kutta Discretizations of Infinite Horizon Optimal Control Problems with Steady-State Invariance

机译：具有稳态不变性的无限视距最优控制问题的Runge-Kutta离散化

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摘要

Direct numerical approximation of a continuous-time infinite horizon control problem, requires to recast the model as a discrete-time, finite-horizon control model. The quality of the optimization results can be heavily degraded if the discretization process does not take into account features of the original model to be preserved. Restricting their attention to optimal growh problems with a steady state, Mercenier and Michel in [1] and [2], studied the conditions to be imposed for ensuring that discrete first-order approximation models have the same steady states as the infinite-horizon continuous-times counterpart. Here we show that Mercenier and Michel scheme is a first order partitioned Runge-Kutta method applied to the state-costate differential system which arises from the Pontryagin maximum principle. The main consequence is that it is possible to consider high order schemes which generalize that algorithm by preserving the steady-growth invariance of the solutions with respect to the discretization process. Numerical examples show the efficiency and accuracy of the proposed methods when applied to the classical Ramsey growth model.
机译：连续时间无限地平线控制问题的直接数值逼近要求将模型重铸为离散时间有限水平控制模型。如果离散化过程未考虑要保留的原始模型的特征，则优化结果的质量可能会严重下降。为了限制他们对稳态的最优增长问题的关注，Mercenier和Michel在[1]和[2]中研究了为确保离散的一阶逼近模型具有与无限水平连续性相同的稳态而必须施加的条件次同行。在这里，我们证明Mercenier和Michel方案是一阶划分的Runge-Kutta方法，该方法适用于从Pontryagin极大原理产生的状态-状态微分系统。主要结果是可以考虑通过保留关于离散化过程的解的稳定增长不变性来推广该算法的高阶方案。数值算例表明了该方法在经典Ramsey增长模型中的有效性和准确性。

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