Optimal impact-angle-control guidance law considering a first-order autopilot dynamics

In order to study the optimal guidance law with autopilot dynamics, the missile motion equations were constructed. Aiming at the optimal control problem with terminal state constraints, a generalized expression of the optimal guidance law considering a first-order autopilot dynamics was derived, extending the traditional weighting function to the-nth power form of time-to-go. By setting the object function's terminal-state-weighting-coefficient as infinity values, an optimal impact-angle-control guidance law considering a first-order autopilot dynamics (OIACGL-1) was proposed. Meanwhile, two simplified forms of the OIACGL-1 were discussed. For the OIACGL-1 system with impact angle constraint and initial heading error, performance of the normalized terminal acceleration was analyzed. The analysis results show that for the OIACGL-1 system, the normalized terminal acceleration commands are always equal to exactly zero values when n≥0, while the corresponding terminal acceleration responses are approach to near zero values.