Guidance algorithm for impact time, angle, and acceleration control under varying velocity condition

A highly constrained guidance algorithm is investigated, which is capable of addressing the constraints on impact time, impact angle, and terminal load factor simultaneously, in particular under a challenging condition where the missile's velocity varies passively with time and cannot be adjusted for impact time control. To develop the guidance, a new flight dynamics is established by treating downrange as the independent variable and flight time as a state variable, and then augmented by putting forward an Additional Maneuvering Acceleration Term (AMAT) for impact time control. Based on the dynamics, an impact-angle-constrained optimal guidance problem is proposed and solved to develop a new guidance formula. Further, the generalized semi-analytical solutions for the guidance command and impact time are derived by putting forward and linearizing a novel engagement model, which takes the heading angle, line-of-sight angle, and flight time as the state variables. Especially, in Appendix A, for a special kind of varying velocity profile, the complete closed-form solutions are developed. Subsequently, for addressing the impact time constraint, the impact-time solution is used to determine the parameters of the AMAT. Finally, to control the terminal load factor, two inequalities are created by applying the kinetic energy theorem, and then used to deduce the limits of some complex integral terms appearing in the generalized semi-analytical solutions. By analyzing these limits, the guidance coefficients making the load factor converge to a pre-specified value can be determined. The superiority of the guidance is demonstrated by conducting a large number of trajectory simulations.