An optimal midcourse guidance method for dual pulse air-to-air missiles using linear Gauss pseudospectral model predictive control method

This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles, which is based on the framework of the linear Gauss pseudospectral model predictive control method. Firstly, a multistage optimal control problem with unspecified terminal time is formulated. Secondly, the control and terminal time update formulas are derived analytically. In contrast to previous work, the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time, which is coupled with control, state, and costate. On the assumption of small perturbation, a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time. Also, using Gauss pseudospectral collocation, error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations. Furthermore, analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control. Even with their mathematical complexity, these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters. Finally, several numerical simulations, comparisons with typical methods, and Monte Carlo simulations have been done to verify its optimality, high convergence rate, great stability and robustness.