Suboptimal guidance laws with terminal jerk constraint

In this paper, a suboptimal guidance law with the terminal constraints on impact angle, acceleration, and time-derivative of acceleration (jerk) is presented. The proposed homing guidance problem is an over-determined problem, i.e., the number of constraints is much larger than the order of system. Since it is difficult to solve the problem by using the conventional optimal control theory, we newly introduce the control input which consists of an additional feed-forward command and the optimal feedback command. The additional feed-forward command is defined as a polynomial function of time-to-go with two degree-of-freedoms. Here, the coefficients of the function in the feed-forward command are determined to satisfy the constraints on terminal acceleration and jerk. The optimal feedback command in consideration of a feed-forward command is determined by Schwartz inequality. The guidance command obtained from the proposed scheme shows a similar form of the biased proportional navigation (BPN) guidance obtained by the optimal control theory. However, the proposed guidance law is less sensitive to the time-to-go estimation error than the BPN law, and it can be easily implemented in the real system. Furthermore, since the coefficients of time-to-go in the feed-forward command remain as design parameters, the proposed guidance law provides more flexibility in application aspect such as trajectory shaping. The characteristics of the proposed guidance law is studied and its performance is also evaluated through numerical simulation.