基于高斯伪谱的最优控制求解及其应用

李树荣;韩振宇;于光金

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (8) : 1031-1043.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (8) : 1031-1043. DOI: 10.12341/jssms09241
论文

基于高斯伪谱的最优控制求解及其应用

    李树荣(1), 韩振宇(1), 于光金(2)
作者信息 +

Numerical Algorithm of Optimal Control Based on a Gauss Pseudospectral Method and Its Application

    LI Shurong(1), HAN Zhenyu(1), YU Guangjin(2)
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摘要

研究一种基于高斯伪谱法的具有约束受限的最优控制数值计算问题.方法将状态演化和控制规律用多项式参数化近似,微分方程用正交多项式近似.将最优控制问题求解问题转化为一组有约束的非线性规划求解.详细论述了该种近似方法的有效性.作为该种方法的应用,讨论了一个障碍物环境下的机器人最优路径生成问题.将机器人路径规划问题转化为具有约束条件最优控制问题,然后用基于高斯伪谱的方法求解,并给出了仿真结果.

Abstract

A numerical computation of constrained optimal control problem (OCP) is discussed based on Gauss Pseudospectral Method. The state evolvement and control rules are approximated by using some parameterized polynomials, and the differential equations are approximated by using orthogonal polynomials. After such approximation, the OCP-solving problem can be turned to a nonlinear programming problem (NLP) with inequality constraints. The effectiveness of this approximation is expressed in detail. As an application of this numerical method, the optimal path generating (OPG) problem for a robot in an environment with some obstacles is studied. The OPG is firstly modeled as a constrained OCP, and then solved by using proposed numerical method. Some simulation results are given in the paper.

关键词

最优控制 / 高斯伪谱法 / 非完整移动机器人 / 路径规划.

Key words

Optimal control / Gauss pseudospectral method / nonholonomic robot / path planning.

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李树荣 , 韩振宇 , 于光金. 基于高斯伪谱的最优控制求解及其应用. 系统科学与数学, 2010, 30(8): 1031-1043. https://doi.org/10.12341/jssms09241
LI Shurong , HAN Zhenyu , YU Guangjin. Numerical Algorithm of Optimal Control Based on a Gauss Pseudospectral Method and Its Application. Journal of Systems Science and Mathematical Sciences, 2010, 30(8): 1031-1043 https://doi.org/10.12341/jssms09241
中图分类号： 49J20   
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