Optimal deterministic guidance for bounded-thrust spacecrafts

The minimum-propellant deterministic guidance law for bounded-thrust, constant jetexhaust velocity, spacecrafts is developed using the neighboring extremal theory. Minimization of the first-order variation in cost between a multi-burn nominal extremal and the perturbed trajectory eliminates all correction strategies except small changes in the nominal thrust-on, thrust-off times and small rotations of the thrust vector. Optimal values of these corrective controls for fixed values of initial state deviations, δx₀, are found by minimizing the second variation in cost subject to the variational state and adjoint equations - an accessory minimum problem. The solution takes the linear feedback form δu=A^-1₂₂A₂₁δx₀, where the matrices A₂₂ and A₂₁ are functions only of transition matrices calculated along the nominal trajectory. The solution is applied to a three-burn Earth-Mars transfer.