Two ASRE approaches with application to spacecraft coulomb formations

Suboptimal solutions of nonlinear optimal control problems are addressed in the present work. These suboptimal approaches are known as Approximating Sequence of Riccati Equations (ASRE) methods. In the ASRE methods, the nonlinear problem is reduced to a sequence of linear-quadratic and time-varying approximating problems. For this purpose, the nonlinear equations are written in State Dependent Coefficient (SDC) factorization form. Two different ASRE approaches are discussed and their implementation procedures will be explained. To implement and compare these two techniques, spacecraft Coulomb formations are considered. Suboptimal trajectories of formation attitude and relative position of a two-craft formation utilizing coulomb forces as well as thrusters is discussed. The effectiveness of the approaches as well as their comparison is demonstrated through numerical simulations.