A Pseudospectral Approach to High Index DAE Optimal Control Problems
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Authors
Marsh, Harleigh
Karpenko, Mark
Gong, Qi
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Date of Issue
2018
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Abstract
Historically, solving optimal control problems with high index differential algebraic equations (DAEs) has been considered extremely hard. Computa- tional experience with Runge-Kutta (RK) methods confirms the difficulties. High index DAE problems occur quite naturally in many practical engineering applications. Over the last two decades, a vast number of real-world prob- lems have been solved routinely using pseudospectral (PS) optimal control techniques. In view of this, we solve a “provably hard,” index-three problem using the PS method implemented in DIDO⃝c , a state-of-the-art MATLAB-optimal control toolbox. In contrast to RK-type solution techniques, no la- borious index-reduction process was used to generate the PS solution. The PS solution is independently verified and validated using standard industry practices. It turns out that proper PS methods can indeed be used to “di- rectly” solve high index DAE optimal control problems. In view of this, it is proposed that a new theory of difficulty for DAEs be put forth.
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Article
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Mechanical and Aerospace Engineering (MAE)
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Naval Postgraduate School (U.S.)
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14 p.
Citation
Marsh, Harleigh C., Mark Karpenko, and Qi Gong. "A Pseudospectral Approach to High Index DAE Optimal Control Problems." (2018)
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.