The generalised discrete algebraic Riccati equation in linear-quadratic optimal control
Abstract
This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the classic infinite-horizon linear quadratic (LQ) control problem. In particular, a geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation and the output-nulling subspaces of the underlying system and the corresponding reachability subspaces. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem, which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil. In establishing the main results of this paper, several ancillary problems on the discrete Lyapunov equation and spectral factorisation are also addressed and solved.
Citation
Source Title
ISSN
Remarks
NOTICE: this is the author’s version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, Vol. 49, No. 2 (2013). DOI: 10.1016/j.automatica.2012.11.006
Collection
Related items
Showing items related by title, author, creator and subject.
-
Ferrante, A.; Ntogramatzidis, Lorenzo (2013)This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati ...
-
Ferrante, A.; Ntogramatzidis, Lorenzo (2013)This paper proposes a reduction technique for the generalized Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalized discrete algebraic Riccati ...
-
Ferrante, A.; Ntogramatzidis, Lorenzo (2012)A geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati equation arising from the classic infinite-horizon linear quadratic (LQ) control problem and the output-nulling ...