Solutions for the Linear-Quadratic Control Problem of Markov Jump Linear Systems

J. B. R. Do Val, J. C. Geromel and O. L. V. Costa
Additional contact information
J. B. R. Do Val: University of Campinas
J. C. Geromel: University of Campinas
O. L. V. Costa: University of São Paulo

Journal of Optimization Theory and Applications, 1999, vol. 103, issue 2, No 2, 283-311

Abstract: Abstract The paper is concerned with recursive methods for obtaining the stabilizing solution of coupled algebraic Riccati equations arising in the linear-quadratic control of Markovian jump linear systems by solving at each iteration uncoupled algebraic Riccati equations. It is shown that the new updates carried out at each iteration represent approximations of the original control problem by control problems with receding horizon, for which some sequences of stopping times define the terminal time. Under this approach, unlike previous results, no initialization conditions are required to guarantee the convergence of the algorithms. The methods can be ordered in terms of number of iterations to reach convergence, and comparisons with existing methods in the current literature are also presented. Also, we extend and generalize current results in the literature for the existence of the mean-square stabilizing solution of coupled algebraic Riccati equations.

Keywords: Linear-quadratic control; Markov jump linear systems; nonstandard Riccati equation; stopping time problems (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1023/A:1021748618305 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:103:y:1999:i:2:d:10.1023_a:1021748618305

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1023/A:1021748618305

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().