Neighboring Optimal Control Laws Based On Radau Pseudospectral Method

This paper develops a feedback control law for regulating nonlinear time variant system about reference trajectories, and it is applied to the guidance for reusable launch vehicles entry. The neighboring optimal feedback controller presented in this paper is based on the two-point boundary value problem on discretization pesudospectral points. The feedback control laws in this paper can be calculated without solving the matrix Ricaati differential equations, construction of transition matrices or any explicit integration. This facilitates neighboring optimal control laws is calculated in real-time. A numerical example of a hypersonic vehicle entry problem demonstrates the effectiveness of neighboring optimal control method.