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A numerical algorithm for singular optimal LQ control systems

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés, 28911, Madrid, Spain

    Marina Delgado-Téllez & Alberto Ibort

Authors
  1. Marina Delgado-Téllez
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  2. Alberto Ibort
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Correspondence to Marina Delgado-Téllez.

Additional information

Research partially supported by MEC grant MTM2004-07090-C03-03. SIMUMAT-CM, UC3M-MTM-05-028 and CCG06-UC3M/ESP-0850.

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Delgado-Téllez, M., Ibort, A. A numerical algorithm for singular optimal LQ control systems. Numer Algor 51, 477–500 (2009). https://doi.org/10.1007/s11075-008-9254-z

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