Implementable Nonlinear Optimal Guidance Based on Convertibility Among Optimal Trajectories

Optimal guidance is a classical problem and Proportional Navigation Guidance (PNG) is a recognized solution to it. PNG has been widely used and studied, because of its engineering applicability and optimality. PNG is optimal under the small leading angle assumption and linear guidance model. We propose a nonlinear optimal guidance law to improve the performance of PNG under large leading angles and nonlinear conditions. Firstly, we analyze the nonlinear optimal guidance problem and prove the similarity and convertibility among different optimal trajectories. Besides, we construct a particular solution of an existing optimal guidance case through the inverse dynamics of optimal guidance. Then, we generalize this particular solution based on the transformability among the optimal solutions to design the nonlinear optimal guidance, which turns out to be PNG with a variable navigation coefficient. Finally, we take some numerical tests to verify the effectiveness of the proposed guidance law. The result shows that the algorithm performs better than PNG, which verifies the nonlinear optimality of the proposed guidance law.