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

A nonlinear optimal guidance law for impact-time control with field-of-view constraints is presented. The guidance problem is formulated as a pure state-constrained nonlinear optimal control problem, and necessary conditions for optimality are derived using the indirect adjoining approach within the framework of Pontryagin’s minimum principle. By analyzing the necessary conditions, we obtain two structural properties of the optimal solution: 1) the terminal costates lie on a straight line if the field-of-view constraint is active on the optimal trajectory, and 2) the optimal control is continuous along the optimal trajectory. From the geometric point of view, an additional optimality condition is derived. Building on these results, we construct a parameterized impulsive system so that a simple propagation of the impulsive system leads to a large number of optimal trajectories, which not only satisfy the traditional necessary conditions but also meet the additional optimality condition established in the paper. A lightweight neural network trained on the optimal trajectories can then approximate the optimal feedback control in real time. Numerical simulations demonstrate that the proposed guidance law outperforms representative existing methods and achieves nearly optimal performance in terms of control effort.