Impact Angle and Final Position Constrained Optimal Guidance Law

The paper aims at deriving an optimal guidance law which can satisfy both interception and high impact angle requirements. Using penalty function in the object function instead of final constraint condition, with Euler equation and Lagrange multiplier method, the condition for the minimization of the value of the object function can be derived. An optimal guidance law expressed by two missile states (lateral position and lateral velocity), together with the relative velocity between missile and target and the residual time is obtained. It can be transformed into an implementable optimum guidance law expressed by the line of sight angle and angular rate.