Near-Optimal Feedback Guidance for Low-Thrust Earth Orbit Transfers

This research describes a near-optimal feedback guidance, based on nonlinear orbit control, for low-thrust Earth orbit transfers. Lyapunov stability theory leads to proving that although several equilibria exist, only the desired operational conditions are associated with a stable equilibrium. This ensures quasi-global asymptotic convergence toward the desired final orbit. The dynamical model includes the effect of eclipsing on the available thrust, as well as all the relevant orbit perturbations, such as several harmonics of the geopotential, solar radiation pressure, aerodynamic drag, and gravitational attraction due to the Sun and the Moon. Near-optimality of the feedback guidance comes from careful selection of the control gains. They are identified in two steps. Step (a) is an extensive table search in which the gains are changed in a large interval. Step (b) uses a numerical optimization algorithm that refines the gains found in (a), while minimizing the time of flight. For the numerical simulations, two scenarios are defined: (i) nominal conditions and (ii) nonnominal conditions, which arise from orbit injection errors and stochastic failures of the propulsion system. For case (i), gain optimization leads to obtaining numerical results very close to those corresponding to a known optimal orbit transfer with eclipse arcs. Moreover, for case (ii), extensive Monte Carlo simulations demonstrate that the nonlinear feedback guidance at hand is effective in driving a spacecraft from a low Earth orbit to a geostationary orbit, also in the presence of nonnominal flight conditions.