Numerical Algorithms

, Volume 51, Issue 4, pp 477–500 | Cite as

A numerical algorithm for singular optimal LQ control systems

  • Marina Delgado-Téllez
  • Alberto Ibort
Original Paper


A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear–quadratic optimal control problems is presented. The algorithm is based on the Presymplectic Constraint Algorithm (PCA) by Gotay-Nester (Gotay et al., J Math Phys 19:2388–2399, 1978; Volckaert and Aeyels 1999) that allows to solve presymplectic Hamiltonian systems and that provides a geometrical framework to the Dirac-Bergmann theory of constraints for singular Lagrangian systems (Dirac, Can J Math 2:129–148, 1950). The numerical implementation of the algorithm is based on the singular value decomposition that, on each step, allows to construct a semi-explicit system. Several examples and experiments are discussed, among them a family of arbitrary large singular LQ systems with index 2 and a family of examples of arbitrary large index, all of them exhibiting stable behaviour.


Singular optimal control theory Implicit differential equations Geometrical constraint algorithm Numerical algorithms 

Mathematics Subject Classifications (2000)

49J15 34A09 34K35 65F10 


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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Carlos III de MadridMadridSpain

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