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Comments on direct transcription solution of DAE constrained optimal control problems with two discretization approaches

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Abstract

There have been a number of results in the literature showing that a direct transcription numerical approach to optimal control problems could have a number of surprising and desirable behaviors that were not always predicted by the existing theory especially when differential algebraic equations are involved. Most of these results were developed with an implicit Runge-Kutta (IRK) discretization being used. It is important to know which of these observations hold for direct transcription software using different types of discretizations and which are discretization specific. This paper reexamines several of these questions but using an hp-pseudospectral code. It is seen that while philosophically the results are often similar to the IRK results, there are some differences that should be understood by users solving constrained optimal control problems. This paper also discusses a type of regularization for higher index problems that does not reduce the index.

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Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695-8205, USA

    Stephen L. Campbell

  2. Applied Mathematical Analysis, LLC, P.O. Box 1135, Issaquah, WA, 98027, USA

    John T. Betts

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  1. Stephen L. Campbell
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  2. John T. Betts
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Correspondence to Stephen L. Campbell.

Additional information

Research supported in part by NSF Grant DMS-1209251.

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Campbell, S.L., Betts, J.T. Comments on direct transcription solution of DAE constrained optimal control problems with two discretization approaches. Numer Algor 73, 807–838 (2016). https://doi.org/10.1007/s11075-016-0119-6

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  • DOI: https://doi.org/10.1007/s11075-016-0119-6

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