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Computation of the stabilizing solution of game theoretic Riccati equation arising in stochastic $$H_\infty$$ control problems. (English) Zbl 1219.93114
Summary: In this paper, the problem of the numerical computation of the stabilizing solution of the game theoretic algebraic Riccati equation is investigated. The Riccati equation under consideration occurs in connection with the solution of the $$H_\infty$$ control problem for a class of stochastic systems affected by state dependent and control dependent white noise. The stabilizing solution of the considered game theoretic Riccati equation is obtained as a limit of a sequence of approximations constructed based on stabilizing solutions of a sequence of algebraic Riccati equations of stochastic control with definite sign of the quadratic part. The efficiency of the proposed algorithm is demonstrated by several numerical experiments.

##### MSC:
 93E03 Stochastic systems in control theory (general) 93B36 $$H^\infty$$-control 93E15 Stochastic stability in control theory 93D21 Adaptive or robust stabilization
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