Closed-Loop Guidance with Final Velocity Constraint Using Time-Varying Weighting Coefficient for Shaping of Commanded Acceleration

In this paper, a closed-loop optimal guidance with final position and velocity constraints is obtained by applying time-varying weighting coefficient in the performance index in order to shape the commanded acceleration. The control system is assumed to be linear, time-varying, and of arbitrary order with a throttleable engine. The acceleration due to drag is also modeled as a linear function with respect to velocity vector multiplied by a given function of time. In addition, different weighting functions are suggested for different acceleration constraints, such as maximum dynamic pressure, separation of stages, and zero acceleration at the final time. Finally, the performance of the guidance law for a combined weighting function is evaluated and discussed.