Optimal Control of Spacecraft Orbital Maneuvers by the Hamilton-Jacobi Theory

Seeking the optimal control of spacecraft orbital maneuvers with non-smooth control logic in feedback sense, we extend our recently developed technique based on the Hamilton-Jacobi theory. Specifically we propose a new methodology stemming from the direct use of generating functions for solving optimal feedback control problem. Starting from the Hamilton-Jacobi equation for generating functions representing a two point boundary value problem, we derive a set of 1st order quasilinear partial differential equations with the associated initial condition, which forms the well-known Cauchy problem. These equations can also be derived by applying the invariant imbedding method to the two point boundary value problem. The solution to this Cauchy problem is utilized for determining the optimal control logic of spacecraft orbital maneuvers with hard and soft constraint boundary conditions. Illustrative examples demonstrate that this approach is, in contrast to the direct use of generating functions, promising for solving problems with non-smooth control logic usually caused by imposing control constraints.