Nonlinear Optimal Guidance for Impact Time Control with Field-of-View Constraint

Abstract: An optimal guidance law for impact time control with field-of-view constraint is presented. The guidance law is derived by first converting the inequality-constrained nonlinear optimal control problem into an equality-constrained one through a saturation function. Based on Pontryagin's maximum principle, a parameterized system satisfying the necessary optimality conditions is established. By propagating this system, a large number of extremal trajectories can be efficiently generated. These trajectories are then used to train a neural network that maps the current state and time-to-go to the optimal guidance command. The trained neural network can generate optimal commands within 0.1 milliseconds while satisfying the field-of-view constraint. Numerical simulations demonstrate that the proposed guidance law outperforms existing methods and achieves nearly optimal performance in terms of control effort.