A numerical algorithm for singular optimal LQ control systems |
| |
Authors: | Marina Delgado-Téllez Alberto Ibort |
| |
Institution: | (1) Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés, 28911 Madrid, Spain |
| |
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.
Research partially supported by MEC grant MTM2004-07090-C03-03. SIMUMAT-CM, UC3M-MTM-05-028 and CCG06-UC3M/ESP-0850. |
| |
Keywords: | Singular optimal control theory Implicit differential equations Geometrical constraint algorithm Numerical algorithms |
本文献已被 SpringerLink 等数据库收录! |
|