A mixed variable variational method for optimal endo-atmospheric ascent guidance

This paper presents a mixed variable variational algorithm to the optimal atmospheric ascent guidance problem of launch vehicles subject to path constraints and final condition constraints. The optimal three-dimension ascent problem is transformed into a Hamiltonian boundary value problem. And the solving algorithm is a symplectic numerical method based on the dual variational principle, which transforms the Hamiltonian boundary value problem into a system of nonlinear algebraic equations, by taking the left costate and the right state as independent variables on every discrete interval. The method owns the features of the direct and indirect methods, meeting the first-order necessary condition of optimal control problem and without precise initial guess. The performance of the proposed algorithm is assessed with open-loop and closed-loop simulation tests. The results show that the proposed algorithm is feasible, and the precision and efficiency of the algorithm are both better than Gauss pseudo-spectral method and the indirect method.