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Costate Computation by an Adaptive Pseudospectral Method for Solving Optimal Control Problems with Piecewise Constant Time Lag

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Abstract

In this paper, we consider nonlinear optimal control problems involving piecewise constant delay functions. A discretization of the Bolza problem by an adaptive Legendre pseudospectral method is considered. The method is based on composite pseudospectral method using the well-known Legendre–Gauss–Lobatto collocation points. In this approach, the main problem is converted into a mathematical optimization problem, whose solution is much more easier than that of the original one. It is shown that, under a simple set of conditions, the operations of discretization and dualization are commutative. The method is used to solve an optimal control problem with continuous variable time lag.

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Acknowledgments

The authors are very grateful to the referee’s useful comments and valuable suggestions which have improved the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran

    Sayyed Mohammad Hoseini & Hamid Reza Marzban

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  1. Sayyed Mohammad Hoseini
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  2. Hamid Reza Marzban
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Correspondence to Sayyed Mohammad Hoseini.

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Hoseini, S.M., Marzban, H.R. Costate Computation by an Adaptive Pseudospectral Method for Solving Optimal Control Problems with Piecewise Constant Time Lag. J Optim Theory Appl 170, 735–755 (2016). https://doi.org/10.1007/s10957-016-0957-3

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  • DOI: https://doi.org/10.1007/s10957-016-0957-3

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