Closed-loop optimization of guidance gain for constrained impact

The tightly constrained guidance problem of impact on a stationary target is considered, subject to look-angle and lateral-acceleration limits, as well as final impact-angle and look-angle constraints. Proportional-navigation guidance with a time-varying gain is proposed to address this problem. The problem has been formulated as an optimal-control problem, where the time-varying PN gain is regarded to be the control, subject to nonlinear engagement kinematics and all the inequality and terminal constraints. A successive solution approach is proposed to solve this nonlinear optimal-control problem as a sequence of convex optimal-control problems that can be numerically solved as second-order cone programs. Compared with standard direct-trajectory-optimization approaches based on general nonlinear-programming methods, the proposed method can solve the problem two orders of magnitude faster in terms of computational time. Compared with existing PN guidance approaches, the proposed method provides a more rigorous and systematic guidance approach, and assures the satisfaction of all guidance objectives in highly constrained but feasible scenarios.