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Computation of Optimal Trajectories for Delay Systems: An Optimize-Then-Discretize Strategy for General-Purpose NLP Solvers

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Book cover Numerical Methods for Optimal Control Problems

Part of the book series: Springer INdAM Series ((SINDAMS,volume 29))

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Abstract

We propose an “optimize-then-discretize” approach for the numerical solution of optimal control problems for systems with delays in both state and control. We first derive the optimality conditions and an explicit representation of the gradient of the cost functional. Then, we use explicit discretizations of the state/costate equations and employ general-purpose Non-Linear Programming (NLP) solvers, in particular Conjugate Gradient or Quasi-Newton schemes, to easily implement a descent method. Finally, we prove convergence of the algorithm to stationary points of the cost, and present some numerical simulations on model problems, including performance evaluation.

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Acknowledgements

The authors would like to thank anonymous reviewers for helpful comments which improved the presentation.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy

    Simone Cacace & Roberto Ferretti

  2. Department of Mathematics, Yazd University, Yazd, Iran

    Zahra Rafiei

Authors
  1. Simone Cacace
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  2. Roberto Ferretti
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  3. Zahra Rafiei
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Corresponding author

Correspondence to Simone Cacace .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Sapienza University of Rome, Roma, Italy

    Maurizio Falcone

  2. Department of Mathematics & Physics, Roma Tre University, Rome, Italy

    Roberto Ferretti

  3. Mathematical Institut, Universität Bayreuth, Bayreuth, Bayern, Germany

    Lars Grüne

  4. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA

    William M. McEneaney

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Cacace, S., Ferretti, R., Rafiei, Z. (2018). Computation of Optimal Trajectories for Delay Systems: An Optimize-Then-Discretize Strategy for General-Purpose NLP Solvers. In: Falcone, M., Ferretti, R., Grüne, L., McEneaney, W. (eds) Numerical Methods for Optimal Control Problems. Springer INdAM Series, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-01959-4_3

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