On an iterative algorithm to compute the positive stabilizing solution of generalized algebraic Riccati equations

Author

Feng, Yantao ; Anderson, Brian D O

Author_Institution

Res. Sch. of Inf. Sci. & Eng., Australian Nat. Univ., Canberra, ACT, Australia

fYear

2009

fDate

17-19 June 2009

Firstpage

3530

Lastpage

3534

Abstract

An iterative algorithm to solve a kind of generalized algebraic Riccati equations (GARE) in LQ stochastic zero-sum game problems is proposed. In our algorithm, we replace the problem of solving a GARE with an indefinite quadratic term by the problem of solving a sequence of GARE with a negative semidefinite quadratic term which can be solved by existing methods. Under some appropriate conditions, we prove that our algorithm is globally convergent.

Keywords

Riccati equations; algebra; convergence; game theory; iterative methods; stochastic processes; LQ stochastic zero-sum game problems; generalized algebraic Riccati equations; global convergence; indefinite quadratic term; iterative algorithm; negative semidefinite quadratic term; positive stabilizing solution; Australia; Closed loop systems; Control systems; Control theory; Differential algebraic equations; Iterative algorithms; Performance analysis; Riccati equations; Stochastic processes; Stochastic resonance; GARE; Iterative; Stochastic;

fLanguage

English

Publisher

ieee

Conference_Titel

Control and Decision Conference, 2009. CCDC '09. Chinese

Conference_Location

Guilin

Print_ISBN

978-1-4244-2722-2

Electronic_ISBN

978-1-4244-2723-9

Type

conf

DOI

10.1109/CCDC.2009.5192595

Filename

5192595