Title :
An iterative algorithm to solve Algebraic Riccati Equations with an indefinite quadratic term
Author :
Lanzon, Alexander ; Yantao Feng ; Anderson, Brian D. O.
Author_Institution :
Control Syst. Centre, Univ. of Manchester, Manchester, UK
Abstract :
In this paper, an iterative algorithm to solve Algebraic Riccati Equations (ARE) arising from, for example, a standard H∞ control problem is proposed. By constructing two sequences of positive semidefinite matrices, we reduce an ARE with an indefinite quadratic term to a series of AREs with a negative semidefinite quadratic term which can be solved more easily by existing iterative methods (e.g. Kleinman algorithm in [2]). We prove that the proposed algorithm is globally convergent and has local quadratic rate of convergence. Numerical examples are provided to show that our algorithm has better numerical reliability when compared with some traditional algorithms (e.g. Schur method in [5]). Some proofs are omitted for brevity and will be published elsewhere.
Keywords :
Riccati equations; iterative methods; matrix algebra; ARE; algebraic Riccati equations; indefinite quadratic term; iterative algorithm; negative semidefinite quadratic term; numerical reliability; positive semidefinite matrices; Australia; Convergence; Iterative methods; Reliability; Riccati equations; Standards; ARE; indefinite quadratic term; iterative;
Conference_Titel :
Control Conference (ECC), 2007 European
Conference_Location :
Kos
Print_ISBN :
978-3-9524173-8-6