Paper Info
Title
Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon
Abstract
This paper studies a stochastic linear quadratic (LQ) control problem in the infinite time horizon with Markovian jumps in parameter values. In contrast to the deterministic case, the cost weighting matrices of the state and control are allowed to be indinifite here. When the generator matrix of the jump process – which is assumed to be a Markov chain – is known and time-invariant, the well-posedness of the indefinite stochastic LQ problem is shown to be equivalent to the solvability of a system of coupled generalized algebraic Riccati equations (CGAREs) that involves equality and inequality constraints. To analyze the CGAREs, linear matrix inequalities (LMIs) are utilized, and the equivalence between the feasibility of the LMIs and the solvability of the CGAREs is established. Finally, an LMI-based algorithm is devised to slove the CGAREs via a semidefinite programming, and numerical results are presented to illustrate the proposed algorithm.
Year
DOI
Venue
2003
10.1023/A:1024887007165
J. Global Optimization
Keywords
Field
DocType
Stochastic LQ control,coupled generalized algebraic Riccati equations,linear matrix inequality,semidefinite programming,mean-square stability
Second-order cone programming,Mathematical optimization,Quadratically constrained quadratic program,Linear-quadratic-Gaussian control,Mathematical analysis,Algebraic Riccati equation,Linear-quadratic regulator,Linear matrix inequality,Semidefinite programming,Mathematics,Jump process
Journal
Volume
Issue
ISSN
27
2-3
1573-2916
Citations 
PageRank 
References 
24
2.47
8
Authors
3
Name
Order
Citations
PageRank
Xun Li11379.90
Xun Yu Zhou2886212.57
Mustapha Ait Rami314310.15