The finite horizon $H_2/H_{\mathrm{\infty }}$ control problem of mean-field type for delayed stochastic systems is considered in this paper. Firstly, we derive a sufficient mean-field generalized stochastic bounded real lemma (SBRL). Then a sufficient condition for the existence of a solution to delayed stochastic $H_2/H_{\mathrm{\infty }}$ control of mean-field type is established. Finally, optimal state feedback regulators are studied for the case with delays in control variable and disturbance signal.

中文翻译：

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时滞平均场随机H 2 / H∞控制

有限的视野 $H_2/H_{\mathrm{\infty }}$考虑了时滞随机系统的平均场类型控制问题。首先，我们推导了足够的平均场广义随机有界实数引理（SBRL）。然后是存在条件的随机延迟解的充分条件$H_2/H_{\mathrm{\infty }}$建立了均场类型的控制。最后，针对具有控制变量和干扰信号延迟的情况，研究了最佳状态反馈调节器。