Date of Award:
Doctor of Philosophy (PhD)
Mechanical and Aerospace Engineering
Matthew W. Harris
Matthew W. Harris
Stephen A. Whitmore
The focus of this dissertation is in the development and application of relaxation techniques that enable efficient and real-time solution of complex computational guidance problems. Relaxations transform a non-convex constraint into a convex constraint and provides proof that the optimal solutions to the relaxed problem are optimal for the original problem. Unique contributions of this work include: 1) a relaxation technique for solving fixed final time problems between fixed points, 2) a performance analysis on the application of computational guidance for the Mars Ascent Vehicle, and 3) establishment of sufficient conditions for non-singularity of optimal control for problems on a smooth manifold with mixed constraints. The first result states that for annularly constrained linear systems, controllability is a sufficient condition for the problem to be solvable as a sequence of convex programs. The second result applies relaxations to an ascent problem. The third result is the most general result to date for problems with mixed constraints. It uses a minimum principle on manifolds with mixed constraints to analyze the problem in a geometric framework, and shows that strong observability of the dual system is sufficient for non-singularity.
Kunhippurayil, Sheril Avikkal, "Exact and Approximate Relaxation Techniques for Computational Guidance" (2021). All Graduate Theses and Dissertations. 8172.
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