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

  • Simone CacaceEmail author
  • Roberto Ferretti
  • Zahra Rafiei
Part of the Springer INdAM Series book series (SINDAMS, volume 29)


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.


Delay systems Optimality conditions Numerical approximation NLP solvers 



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


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Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità Roma TreRomaItaly
  2. 2.Department of MathematicsYazd UniversityYazdIran

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