Three-dimensional minimum energy guidance

Using the exact nonlinear equations of motion, an optimal guidance law (OGL) for a vehicle intercepting a maneuvering target in the three dimensional space is derived. It is assumed that a complete knowledge of the motion of the target is available to the interceptor. The guidance law minimizes a weighted linear combination of the time of capture and the expended maneuvering energy. It is proven that the optimal interceptor trajectory is confined to one plane. The planar case solution, in terms of elliptic integrals, is extended to the three dimensional case. Numerical results are presented to compare the OGL with the pure proportional navigation guidance (PPNG).>