WELL-CONDITIONED PSEUDOSPECTRAL OPTIMAL CONTROL METHODS AND THEIR APPLICATIONS
Koeppen, Nicholas R.
Ross, I. Michael
Proulx, Ronald J.
Wilcox, Lucas C.
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Pseudospectral optimal control is an established discipline with flight-proven results. Aerospace applications have included the implementation of minimum-time and zero-propellant maneuvers on high-value space assets. Standard pseudospectral methods have been sufficient for these and other applications that do not require more than approximately 250 nodes. Currently, pseudospectral optimal control uses the Lagrange differential operator, D, which is ill-conditioned such that the condition number grows as O(n2) for first-order systems. Thus, applications in need of higher temporal resolution—such as satellite maneuver and collection planning—have relied upon suboptimal heuristics, inefficient algorithms, or optimal control via domain decomposition. In this thesis, well-conditioned pseudospectral optimal control methods are established, which use the Birkhoff integral operator that exhibits condition number stability of O(1). By forming a well-conditioned system, these methods expand the applicability of optimal control. For satellite maneuver planning, this means the ability to optimize long-duration, low-thrust orbital maneuvers. Satellite collection planning can also be solved with optimal control formulations based on nonsmooth calculus. These high-resolution applications require many more nodes than ill-conditioned methods allow. Even low-resolution optimal control problems can see improvements in computation time through stability.
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