Real-Time Computation of Neighboring Optimal Control Laws
Real-Time Computation of Neighboring Optimal Control Laws
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DOI：
10.2514/6.2002-4657
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发表时间：
2002-08
期刊：
影响因子：
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通讯作者：
I. Michael Ross;F. Fahroo;Hui-yan Yan
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文献类型：
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作者：
I. Michael Ross;F. Fahroo;Hui-yan Yan
邻域最优控制问题的反馈解通常是通过求解矩阵Riccati微分方程得到的。本文提出了一种基于实时求解线性代数方程的新方法。我们的方法是基于线性时变边值问题的伪谱离散化，该问题是由最小值原理的应用引起的。我们展示了如何在不需要显式积分、构造转移矩阵或求解矩阵Riccati微分方程的情况下计算反馈控制律。这有利于方案的实时实施以及预测制导和控制律的设计。一个低推力轨道转移问题的数值算例表明了该方法对邻域最优制导的有效性。
Feedback solutions to the neighboring optimal control problem are typically obtained by solving the matrix Riccati differential equation. In this paper, we propose a new approach based on solving linear algebraic equations in real-time. Our method is based on a pseudospectral discretization of the linear time-varying boundary value problem that arises from an application of the Minimum Principle. We show how feedback control laws can be computed without any explicit integration, construction of transition matrices or solving the matrix Riccati differential equation. This facilitates a real-time implementation of the scheme and the design of predictive guidance and control laws. A numerical example of a low thrust orbit transfer problem shows the effectiveness of the method for neighboring optimal guidance.