Minimum-Effort Impact-Time Control Guidance Using Quadratic Kinematics Approximation

A guidance law for intercepting a stationary target is derived based on solving the minimum effort optimal control problem with fixed terminal time and a quadratic approximation of the kinematic equations. It is proven that this optimal control problem has, in general, a unique solution. Based on this solution, a guidance law is proposed that is shown to be implementable based on typically available sensor data, using a semi-analytic procedure. Numerical simulations show that the solution based on the quadratic kinematics approximation matches closely the solution based on the original nonlinear kinematics that can only be obtained by numerical optimization.