Nonlinear optimal missile guidance for stationary target interception with pendulum motion perspective

This study outlines the set of equations constituting the necessary conditions that should be solved to determine the optimal guidance command for a missile to intercept a stationary target along a desired impact direction at a prespecified final time. Unlike the earlier studies on nonlinear optimal guidance problems, the present study formalises the optimal control problem with both final time and final state fixed. The pure control effort quadratic norm is considered as the performance index to be minimised. A noticeable finding from the study of the necessary conditions is that the flight path angle of the optimal trajectory obeys the simple pendulum dynamics. Full characterisation of the exact optimal solution requires numerically solving a set of four nonlinear algebraic equations with respect to four unknowns.