Iterative algorithms for stabilizing solutions of game theoretic Riccati equations of stochastic control

We propose two iterative procedures for the computation of the stabilizing solution of coupled generalized algebraic Riccati equations with indefinite quadratic term such equations appear in the solution of stochastic H∞ control problems. The method used in this paper is a generalization of the defect correction method introduced in [17] and extends to this framework the algorithm derived in [16] for game-theoretic (deterministic) algebraic Riccati equations. ∗Institute of Mathematics ”Simion Stoilow” of the Romanian Academy, P.O.Box. 1-764, RO014700, Bucharest, Romania, [email protected] †Department of Mathematics, University Duisburg-Essen, Campus Duisburg, D-47048 Duisburg, Germany,e-mail: [email protected] ‡Institute of Mathematics ”Simion Stoilow” of the Romanian Academy, P.O.Box. 1-764, RO014700, Bucharest, Romania, [email protected] §Faculty of Aerospace Engineering, University ”Politehnica” of Bucharest, Romania, e-mail: [email protected]