This paper proposes a two-stage optimization approach for aerocapture guidance. In classical entry guidance systems, deterministic optimization is used. Large-scale and short-scale density perturbations may strongly affect the performance of the guidance system, and variations in those are usually not accounted for when computing the command. In this work, perturbations that affect the trajectory at future time-steps are taken into consideration when computing the commanded bank angle. The chosen command is optimal based on a set of possible future perturbations, after the observation of which, a correction can be made. Both two-stage stochastic and two-stage robust optimization are proposed as a solution. In a Monte Carlo analysis consisting of 50 runs, the two-stage robust optimization guidance outperforms an optimal, deterministic, numeric predictor-corrector guidance. Excluding one outlier, also the two-stage stochastic optimization makes the guidance perform better than an optimal deterministic numeric predictor-corrector. With either approach, the computational demands are increased by about thirty times compared to an optimal numeric predictor-corrector. Much of the computation time increase may be reduced by parallelization. On the other hand, the extensive tuning required for the optimal numeric predictor-corrector is not needed for the two-stage optimization guidance, making this approach conceptually more robust. Better modeling of the environment may help further improve the performance. Finally, an approximation to the two-stage robust optimization approach is developed. The guidance has computational requirements only four times larger than those of the optimal numeric predictor-corrector guidance, but can be parallelized into two threads, and, except for two outliers, it offers improved performance.@en

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent’s objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect information, that is, where the agent’s true objective function is not contained in the search space of candidate objectives, where the agent suffers from bounded rationality or implementation errors, or where the observed signal-response pairs are corrupted by measurement noise. We formalize this inverse optimization problem as a distributionally robust program minimizing the worst-case risk that the predicted decision (i.e., the decision implied by a particular candidate objective) differs from the agent’s actual response to a random signal. We show that our framework offers rigorous out-of-sample guarantees for different loss functions used to measure prediction errors and that the emerging inverse optimization problems can be exactly reformulated as (or safely approximated by) tractable convex programs when a new suboptimality loss function is used. We show through extensive numerical tests that the proposed distributionally robust approach to inverse optimization attains often better out-of-sample performance than the state-of-the-art approaches.

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