Optimal guidance method based on conjugate gradient method and pseudospectral method

This paper aims to propose a method to solve the nonlinear optimal guidance problems with various performance indexes. First, the conjugate gradient method is derived based on the performance indexes of general form and specified form, and the execution steps of the optimal guidance method are obtained. Secondly, the pseudospectral collocation scheme is used to solve some intermediate variables in the algorithm, and the differential equations are transformed into algebraic equations, so as to improve the computational efficiency. Finally, the proposed method is applied to the air-to-ground missile guidance problem. By comparing with the simulation results of GPOPS-II, the optimality of the proposed method is verified. Additionally, the high computational efficiency of the algorithm is also verified.