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An improved method for solving a system of discrete-time generalized Riccati equations. (English) Zbl 1360.93392
Summary: We consider a set of discrete-time generalized Riccati equations that arise in quadratic optimal control of discrete-time stochastic systems subjected to both state-dependent noise and Markovian jumps. The iterative method to compute the maximal and stabilizing solution for a wide class of discrete-time nonlinear equations was derived by V. Dragan et al. [Int. J. Control 83, No. 4, 837–847 (2010; Zbl 1209.93091)]. Here we modify this method and illustrate it in the computation of the maximal solution of a system of discrete-time generalized Riccati equations. Convergence properties of this method are analyzed. Numerical experiments are reported to estimate the effectiveness of this new iterative method.

93C55 Discrete-time control/observation systems
93C15 Control/observation systems governed by ordinary differential equations
49N10 Linear-quadratic optimal control problems
65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
93E20 Optimal stochastic control
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