2014•Acta Automatica SinicaRequires access

Improved Gauss Pseudospectral Method for Solving Nonlinear Optimal Control Problem with Complex Constraints

Yong Sun, Maorui Zhang, Xiaoling Liang

Abstract

摘要: 针对含有复杂约束条件的非线性最优控制问题,提出了一种改进的Gauss伪谱法 (Improved Gauss pseudospectral method, IGPM). 这类问题难以得到解析解,特别是有些问题不存在解析的模型, 一些参数只能通过查表得到,使得传统方法难以求解. 在传统的Gauss伪谱法的基础上,将非线性的终端状态积分约束等价地转化为线性形式,提出了IGPM, 通过协态映射定理可以计算出协态变量,检验最优性,使得IGPM具有间接法一样的精度. 并且给出了初始时刻协态变量和端点时刻控制变量的计算方法. 为了提高解的精度,基于IGPM提出了迭代算法, 最后将该算法应用于求解高超声速飞行器上升段轨迹优化问题,结果表明最优轨迹基本满足路径约束条件和最优性条件. 关键词: 非线性最优控制 / 改进的Gauss伪谱法 / 协态映射 / 路径约束

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Key concepts: Gauss pseudospectral method, Gauss, Pseudospectral optimal control, Nonlinear system, Mathematics, Chebyshev pseudospectral method, Applied mathematics, Pseudo-spectral method