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Galerkin Optimal Control

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Abstract

This paper introduces a family of computational methods for solving optimal control problems that calculate optimal trajectories using Galerkin numerical techniques. An important result in the theoretical foundation of these methods is that their associated feasibility and consistency theorems are proved for problems with continuous and/or piecewise continuous controls. In this paper we demonstrate that Galerkin numerical techniques allow for the formulation of optimal control problems in a number of ways that allow for efficiency and/or improved accuracy. The family of Galerkin methods presented can solve a wide range of optimal control problems with a variety of state and control constraints. Numerical formulations using Lagrangian and Legendre test functions are derived. Finally, numerical examples demonstrate the versatile nature of various Galerkin optimal control formulations.

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Acknowledgments

This work was supported in part by the Air Force Office of Scientific Research (AFOSR) and the Naval Research Laboratory (NRL). The work and views expressed in this paper are those of the authors and do not reflect the official policy or position of the Department of the Army, the Department of the Navy, the Department of Defense, or the U.S. Government.

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Authors and Affiliations

  1. Department of Mathematical Sciences, U.S. Military Academy, West Point, NY, USA

    Randy Boucher

  2. Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, USA

    Wei Kang

  3. Department of Applied Mathematics and Statistics, University of California at Santa Cruz, Santa Cruz, CA, USA

    Qi Gong

Authors
  1. Randy Boucher
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  2. Wei Kang
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  3. Qi Gong
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Corresponding author

Correspondence to Wei Kang.

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Boucher, R., Kang, W. & Gong, Q. Galerkin Optimal Control. J Optim Theory Appl 169, 825–847 (2016). https://doi.org/10.1007/s10957-016-0918-x

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  • DOI: https://doi.org/10.1007/s10957-016-0918-x

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