Mean-field stochastic H₂/H_∞ control with delay

Abstract

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 generalised stochastic bounded real lemma (SBRL). Secondly, based on the generalized SBRL and the mean-field anticipated forward-backward stochastic delay differential equations, this paper establishes a sufficient condition for the existence of a solution to delayed stochastic $H_2/H_{\mathrm{\infty }}$ control of mean-field type. Thirdly, optimal state feedback regulators are studied for the case with delays only in control variable and disturbance signal via the solvability of coupled matrix-valued equations. Finally, an example is employed to show the effectiveness of the results obtained.

Keywords:

• Mean-field
• stochastic delay differential equation
• $H_2/H_{\mathrm{\infty }}$ control
• forward backward stochastic differential equation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11701214] and Shandong Provincial Natural Science Foundation, China [grant number ZR2019MA045].