Stochastic $$H_{2}/H_{\infty }$$ Control for Mean-Field Stochastic Differential Systems with (x, u, v)-Dependent Noise

Infinite Horizon H2/H∞ Control for Discrete-Time Mean-Field Stochastic Systems

“…In recent years, the application of mean-field theory has become increasingly widespread in fields such as power systems and biology. Many researchers have conducted numerous studies in this area [10][11][12][13][14]. For example, the LQ control problems of discretetime stochastic mean-field systems in the finite and infinite horizon are discussed in [10] and [11], respectively.…”

“…Ref. [13] discussed the H 2 /H ∞ control problem of discrete-time mean-field stochastic systems in the finite horizon, while [14] addressed the H 2 /H ∞ control problem of continuous-time systems in the finite horizon. The problem of mean-field games has been studied in [15] to illustrate the feasibility of the mean-field modeling approach used in economics, and a number of issues worthy of further research were mentioned at the end of the article.…”

“…Ref. [14] studied a continuous-time stochastic control problem for mean-field stochastic differential systems with random initial values and diffusion coefficients that depend on the state, control, and disturbance explicitly, together with their expectations. The work first established a mean-field stochastic-bounded real lemma for continuous-time mean field stochastic systems, thereby revealing the equivalence between robust stability and the solvability of two indefinite differential Riccati equations, which provided a theoretical basis for H ∞ control.…”