Analytical optimal impact angle control guidance law considering time-varying velocity

When the missile velocity is time-varying, the assumption of constant velocity leads to a deviation in the prediction of impact angle. This deviation requires additional control effort to nullify the error, leading to decreased terminal velocity and reduced impact effectiveness. To design an impact angle control guidance (IACG) law considering time-varying velocity, analytical solutions of the missile states for an unpowered missile in a dense atmospheric environment are derived, enabling accurate prediction of the missile states under time-varying velocity. However, the missile states are highly nonlinear due to the complex interactions of aerodynamic forces, gravity, and other factors, causing the derivation of analytical solutions challenging. To simplify the solution process, the analytical solutions are divided into two parts: zero attack of angle (AOA) and AOA increment, where zero AOA is adopted as the nominal control. To construct precise perturbation equations, a backpropagation neural network is developed to fit the time-varying drag and velocity under zero AOA. Subsequently, analytical solutions for arbitrary AOA profiles are obtained using the perturbation method. Moreover, to maximize terminal velocity for enhancing impact effectiveness while minimizing control effort, a linear pseudospectral algorithm based on analytical solutions is applied to design an optimal IACG law. Since the terminal impact angle deviations are obtained through the precise analytical solutions, the optimal IACG law generates the optimal command within a very short time. Simulation results validate the accuracy and computational efficiency of the proposed IACG law, and demonstrate its robustness in maintaining performance even under significant dispersions and uncertainties.