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This paper proposes a varying-gain proportional navigation guidance (PNG) law that can serve as the baseline for precise control of impact time. First, a varying-gain PNG law is developed by an inverse design strategy from the explicit time-to-go estimation of the conventional PNG law, which leads to high control efficiency and accurate time-to-go prediction. Next, to show its potential significance, the varying-gain PNG law is augmented with a biased feedback command to obtain an impact time control guidance (ITCG) law. As a step forward in more practical applications considering missile speed variation induced by thrust, drag, and gravity, another ITCG law is derived from an efficient time-to-go prediction method by taking the exact trajectory-to-go as the independent variable. Further, the varying-gain PNG law and the planar ITCG laws are extended to the three-dimensional guidance scenario by steering the missile to fly on an engagement plane. Compared with similar existing results, the proposed ITCG laws based on the varying-gain PNG law do not involve any linearized approximations in the derivation, and thus possess higher impact precision, wider feasible region, and less energy consumption. Finally, several numerical simulations are performed to support the analytical findings.
Dong et al. (Mon,) studied this question.