Stochastic

This paper studies a continuous-time stochastic H 2 / H ∞ control problem for mean-field stochastic differential systems, with random initial value and diffusion coefficients depending explicitly on the state, control and disturbance as well as their expectations. A mean-field stochastic bounded real lemma is first established, characterizing the equivalence between H ∞ robust stability and the solvability of two indefinite differential Riccati equations. Based on this extremely useful result, an equivalent condition for the existence of H 2 / H ∞ controller is proposed by utilizing the solution of two sets of cross-coupled indefinite Riccati equations. Moreover, when an H 2 / H ∞ controller exists, both the optimal control input and the corresponding worst-case disturbance admit linear feedback representations of the state and its mathematical expectation.