Closed-Form Solution of RTPN Guidance Law using Adomian Decomposition

Closed-form approximate solution of the nonlinear equations of motion of an aerial homing engagement under the realistic true proportional navigation guidance law is derived using the Adomian decomposition method. ADM provides an analytical approximate series solution to nonlinear differential equations, requiring no linearization or direct integration of the nonlinear terms. A novel attempt has been made in considering the autopilot and airframe dynamics in the guidance loop pursuing a constant maneuvering target. Derivation of the Adomian polynomials for the solutions are presented in details and numerical results illustrate the validity of the technique.