求解复杂约束条件下最优控制问题的分段低阶Gauss伪谱法

发布时间：2018-01-28 10:52

本文关键词： 最优控制飞行器轨迹规划 Gauss伪谱法　出处：《空军工程大学学报(自然科学版)》2017年05期 　论文类型：期刊论文

【摘要】：针对含有复杂约束条件的最优控制问题,提出分段低阶Gauss伪谱法。以常规Gauss伪谱法为基础,划分时间区间,在子区间上利用低阶Gauss数值积分离散Bolza型性能指标,利用插值型数值积分的性质离散状态微分方程,利用低阶Gauss伪谱法处理复杂约束条件,得到对应的非线性规划。对状态轨线或控制函数较复杂的情形,该方法克服了传统Gauss伪谱法直接在时间区间上配置Gauss点,插值多项式阶数高、数值解不稳定的缺陷,并且数值解局部代数精度高、计算量小。最后将该方法应用于求解飞行器对地打击轨迹规划最优控制问题,结果表明算法有效可行。
[Abstract]:For the optimal control problem with complex constraints, piecewise low order Gauss pseudospectral method is proposed. The conventional Gauss pseudo spectral method based on the division of the time interval, using low order discrete Bolza Gauss numerical integral performance index in the sub interval, discrete state differential equations by using the interpolation properties of numerical integration, the use of low order the Gauss pseudospectral method to deal with complex constraints, nonlinear planning corresponding. The state trajectory control function or more complex, this method overcomes the disadvantages of traditional Gauss pseudospectral method directly in the time interval Gauss, the order of the polynomial interpolation, numerical solution of unstable defects, and the numerical solution of local high algebraic accuracy a small amount of calculation. Finally, the method is applied to solve the aircraft ground attack trajectory planning optimal control problem. The results show that the algorithm is effective and feasible.

【作者单位】：空军工程大学理学院;空军试验训练基地第二试验训练区武器系统总体试验研究所;
【基金】：国家自然科学基金(61631019)
【分类号】：O232
【正文快照】： 引用格式:李炳杰,王磊,马青海.求解复杂约束条件下最优控制问题的分段低阶Gauss伪谱法[J].空军工程大学学报(自然科学版),2017,18(5):92-98.LI Bingjie,WANG Lei,MA Qinghai.The Solution of an Optimal Control Problem under Conditions of Complicated Re-strictions by Us

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