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The finite horizon $H_2/H_\infty$ control problem of mean-field type fordiscrete-time systems is considered in this paper. Firstly, we derive amean-field stochastic bounded real lemma (SBRL). Secondly, a sufficientcondition for the solvability of discrete-time mean-field stochasticlinear-quadratic (LQ) optimal control is presented. Thirdly, based on SBRL andLQ results, this paper establishes a sufficient condition for the existence ofdiscrete-time stochastic $H_2/H_\infty$ control of mean-field type via thesolvability of coupled matrix-valued equations.

Discrete-time Mean-field Stochastic $H_2/H_\infty$ Control