A Mixed Variable Variational Method for Optimal Control Problems with Applications in Aerospace Control
求解最优控制问题的混合变量变分方法及其航天控制应用

The nonlinear optimal control problem is transformed into the Hamiltonian two point boundary value problem (TPBVP), and a numerical method is proposed based on the dual variational principle. The nonlinear Hamiltonian TPBVP is transformed into a system of nonlinear equations by using the dual variational principle and by taking the left costate and the right state as independent variables. The proposed algorithm has the feature of both "direct method" and "indirect method" for solving optimal control problem, i.e., it satisfies the first-order necessary condition of optimal control theory, and it needs no precise initial guess for costate variables and avoids the solving of large scale nonlinear programming problem. The accuracy and efficiency of the proposed method are discussed by numerical simulations in aerospace control. Comparison between the proposed algorithm and the famous Gauss pseudo-spectral method in aeronautics and astronautics control shows that the proposed algorithm has obvious advantages on accuracy and efficiency.