A numerical algorithm for singular optimal LQ control systems
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 \cite{Go78,Vo99} that allows to solve presymplectic hamiltonian systems and that provides a geometrical framework to the Dirac-Bergmann theory of constraints for singular Lagrangian systems \cite{Di49}. 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 3 and a family of examples of arbitrary large index, all of them exhibiting stable behaviour.
Cite
@article{arxiv.1203.2194,
title = {A numerical algorithm for singular optimal LQ control systems},
author = {M. Delgado-Tellez and A. Ibort},
journal= {arXiv preprint arXiv:1203.2194},
year = {2012}
}
Comments
An old paper (2009) posted for archival purposes