From Theory towards Flight: Convex Optimization based Approaches for Non-convex, Stochastic, and Realistic Aerospace Missions

Abstract

This dissertation addresses critical gaps between real-world applications and theoretical developments in the field of convex optimization toward future aerospace autonomy. Despite recent advancements in convex optimization theory, applying such techniques in aerospace context often reveals challenges due to the inherent complexities of real-world problems and limitations in existing methods. For instance, many real-world problems are highly non-convex, making them difficult to solve with standard convex optimization techniques (Non-convexity). Additionally, problems must be modeled with sufficient fidelity and all relevant mission constraints to yield practical solutions, but current optimization research often oversimplifies models for the sake of numerical tractability (Realisticity). Furthermore, in future autonomous aerospace applications where stringent safety constraints (e.g., three-sigma guarantees) are crucial, trajectory planners must provide a nominal trajectory that satisfies all mission constraints while keeping deviations within safety margins (Stochasticity). This research bridges these gaps by proposing frameworks that combine rigorous optimization theory, astrodynamics, convex optimization, and stochastic optimization. The dissertation consists of the following key contributions: 1) a framework for over-approximating the reachable set of nonlinear systems, 2) techniques to convexify mixed-integer constraints into deterministic ones with theoretical guarantees, 3) a sequential convex programming-based framework to minimize the terminal state dispersion of a stochastic dynamical system about a specified destination, and 4) a flight-qualified trajectory planner for asteroid reconnaissance under uncertainty.