A Numerical Algorithm for Singular Optimal LQ Control Systems Articles uri icon

publication date

  • August 2009

start page

  • 477

end page

  • 500

issue

  • 4

volume

  • 51

international standard serial number (ISSN)

  • 1017-1398

electronic international standard serial number (EISSN)

  • 1572-9265

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.