基于逆最优问题的最优制导律及特性分析

摘要

在典型的能量最优制导律基础上，将制导律的2个特征根从有限的点/线区域扩展到所有可能的正实根区域，进而提出制导律中的逆最优问题。详细讨论了逆最优问题中性能指标加权矩阵的构造过程，给出了加权矩阵和Riccati矩阵的计算公式；将控制权矩阵选为time-to-go的负n次幂的形式，对加权矩阵的求解进行了举例说明。对8组不同的特征根研究结果表明，尽管每一对可能的特征根取值都能找到最优解释，但这并不能保证与其对应的制导律都能达到与典型能量最优制导律类似的制导性能，特征根取值越靠近典型能量最优制导律，则相对应的制导特性也越接近。%Based on the typical energy optimal guidance laws ( TEOGL) ,the two characteristic roots ( CR) of the TEOGL were extended from a limited points/lines area to all the possible positive-real-roots area and the inverse optimal guidance problem was proposed.The construction procedure of the weighting matrices in the performance index of the inverse optimal problem was dis-cussed and the calculation equations of those weighting matrices and Riccati matrix were also present.As an example, the calculation procedure was demonstrated when the control weighting matrix was chosen as -n power of time-to-go. It is concluded that, for the eight pairs of different CR,although every possible pair of CR may have an optimal explanation,it can't guarantee a similar guidance performance with the TEOGL,except a pair of CR which is chosen to be close to the CR of the TEOGL.