The finite horizon H2/H∞ control problem of mean-field type for discrete-time systems is considered in this paper. Firstly, we derive a mean-field stochastic bounded real lemma (SBRL). Secondly, a sufficient condition for the solvability of discrete-time mean-field stochastic linear-quadratic (LQ) optimal control is presented. Thirdly, based on SBRL and LQ results, this paper establishes a sufficient condition for the existence of discrete-time stochastic H2/H∞ control of mean-field type via the solvability of coupled matrix-valued equations.

An H ∞ -type control is considered for mean-field stochastic differential equations (SDEs) in this paper. A stochastic bounded real lemma (SBRL) is proved for mean-field stochastic continuous-time systems with state-and disturbance-dependent noise. Based on SBRL, a sufficient condition is given for the existence of a stabilizing H ∞ controller in terms of coupled nonlinear matrix inequalities.

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