This paper proposes the use of Legendre pseudospectral method (PSM) to obtain the optimal guidance strategy for a two-dimensional interceptor problem. An optimal control problem is formulated that addresses the conflicting objective of minimizing the energy usage, along with minimizing the time taken by missile to capture the target. The PSM-based guidance strategy is compared with other conventional guidance laws such as pure proportional navigation (PPN) guidance law and also evolutionary algorithm inspired differential evolution tuned proportional navigation (DEPN) guidance law. A scheme by which the PSM guidance strategy can be applied online is also included in this paper. The cost function value and the interception time indicates the superiority of the PSM-based guidance strategy.

中文翻译：

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基于伪谱法的现实拦截器时能优化制导策略

本文提出使用勒让德伪谱法（PSM）来获得二维拦截器问题的最优制导策略。制定了一个最优控制问题，该问题解决了最小化能量使用以及最小化导弹捕获目标所花费的时间的冲突目标。将基于 PSM 的制导策略与其他传统制导律进行比较，例如纯比例导航 (PPN) 制导律以及进化算法启发的差分进化调谐比例导航 (DEPN) 制导律。本文还包括一种可以在线应用 PSM 制导策略的方案。成本函数值和拦截时间表明了基于 PSM 的制导策略的优越性。