Pseudospectral Feedback Control: Foundations, Examples and Experimental Results
Ross, I. Michael
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Suppose optimal open-loop controls could be computed in real time. This implies optimal feedback control. These controls are, typically, nonsmooth. Nonsmooth controls raise fundamental theoretical problems on the existence and uniqueness of feedback solutions. A simple, yet powerful, approach to address these theoretical issues is the concept of a on fourth- solution that is closely linked to the practical implementation of zero-order-hold control sampling. In other words, even traditional feedback controls involve open-loop controls through the process of sampling. In this paper, we advance the notion of Caratheodory-_ solutions that use the sampling intervals to compute optimal open-loop controls. A sampling theorem is developed which indicates that the Lipschitz constant of the dynamics is a fundamental sampling frequency. This places computation at the level of first principles in describing the foundations for achieving feedback. We obtain these controls by way of Pseudospectral (PS) methods as these techniques can generate optimal open-loop controls within fractions of a second even when implemented in a MATLAB environment running on legacy computer hardware. In order to facilitate an exposition of the proposed ideas to a wide audience, we introduce the core principles only while relegating the intricate details to numerous recent references. These principles are then applied to generate PS feedback controls for the slew maneuvering of NPSAT1, a spacecraft conceived, designed and built at the Naval Postgraduate School and scheduled to be launched in Fall 2007.
The article of record as published may be located at http://dx.doi.org/10.2514/6.2006-6354Approved for public display, distribution unlimitedProceedings of AIAA-Guidance, Navigation, and Control Conference and Exhibit ; Paper no. AIAA 2006-6354, Keystone, Colorado, Aug. 21-24, 2006
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