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求解含复杂约束非线性最优控制问题的改进Gauss伪谱法

DOI: 10.3724/SP.J.1004.2013.00672, PP. 672-678

Keywords: 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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Abstract:

?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(ImprovedGausspseudospectralmethod,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.

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