Applied Stochastic Optimal Control for Spacecraft Guidance
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Optimal control theory has been successfully applied to a wide range of a problems in spacecraft trajectory optimization. Historically, the identification and management of uncertainty in spaceflight applications has been a separate endeavor from optimal trajectory design, with the exception of heuristic margins applied on the deterministic optimal trajectory. Following a stochastic optimal control approach, on the other hand, leads to the direct consideration of uncertainty for the design of closed-loop trajectories with probabilistic constraints. Resulting control laws are designed with respect to all possible trajectory and control input realizations, and the performance is evaluated over measures of the aggregate, or expected, state and control trajectories. This dissertation focuses on specific applications of stochastic optimal control for spacecraft guidance, namely: powered descent guidance (PDG), atmospheric entry guidance, and aerocapture guidance. In addition, extensions are developed, which have further applications for spacecraft guidance, to the general theory of applying convex optimization to jointly steer the mean and covariance of stochastic systems, subject to probabilistic constraints. For minimum-fuel PDG, the problem of setting non-conservative thrust margins is addressed by application of minimum-variance, covariance-constrained stochastic optimal control. The resulting closed-loop PDG process does not, with high probability, either saturate thrust commands or deviate too far from the desired landing site. Next, entry guidance in an atmosphere with spatially-dependent random variations in the atmospheric density is posed as a chance-constrained stochastic optimal control problem; the resulting targeting accuracy is shown to be better than the current state-of-the-art Apollo-derived entry guidance. Finally, in order to address the problem of aerocapture guidance around a planet with an unknown atmosphere, a successive convex programming-based method is developed to solve chance-constrained stochastic optimal control problems for systems acting in the presence of a Gaussian random field. In a numerical example of an aerocapture mission with bank angle control, the developed method is used to solve for a control law that explicitly minimizes the 99th percentile of the required Delta-V, subject to constraints on the probability distribution of the closed-loop bank angle during atmospheric flight.