GPOPS - II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming
GPOPS - II: A MATLAB Software for Solving Multiple-Phase Optimal Control Problems Using hp-Adaptive Gaussian Quadrature Collocation Methods and Sparse Nonlinear Programming
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DOI：
10.1145/2558904
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发表时间：
2014-10-01
影响因子：
2.7
通讯作者：
Rao, Anil V.
中科院分区：
文献类型：
--
作者：
Patterson, Michael A.;Rao, Anil V.
本文介绍了一个用变阶高斯正交配置法求解多相最优控制问题的通用MATLAB软件程序GPOPS -Ⅱ。该软件采用Legendre-Gauss-Radau正交配置法，将连续时间最优控制问题转化为大型稀疏非线性规划问题（NLP）。自适应网格细化方法的实施，确定网格间隔的数量和在每个网格间隔内的近似多项式的程度，以达到指定的精度。该软件可以与拟牛顿（一阶导数）或牛顿（二阶导数）NLP求解器接口，并且NLP求解器所需的所有导数都使用最优控制问题函数的稀疏有限差分来近似。该软件的关键组成部分进行了详细描述，并证明了该软件的实用程序上的五个不同复杂性的最优控制问题。本文介绍的软件为研究人员提供了一个有用的平台，在此基础上解决各种复杂的约束最优控制问题。
A general-purpose MATLAB software program called GPOPS - II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods. The software employs a Legendre-Gauss-Radau quadrature orthogonal collocation method where the continuous-time optimal control problem is transcribed to a large sparse nonlinear programming problem (NLP). An adaptive mesh refinement method is implemented that determines the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy. The software can be interfaced with either quasi-Newton (first derivative) or Newton (second derivative) NLP solvers, and all derivatives required by the NLP solver are approximated using sparse finite-differencing of the optimal control problem functions. The key components of the software are described in detail and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a useful platform upon which to solve a wide variety of complex constrained optimal control problems.