Date of Award:

8-2021

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mechanical and Aerospace Engineering

Committee Chair(s)

Matthew W. Harris

Committee

Matthew W. Harris

Committee

David Geller

Committee

Stephen A. Whitmore

Committee

Geordie Richards

Committee

Randy Christensen

Abstract

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.

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