This paper is concerned with the open-loop linear quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations (GDREs), the follower first solves a mean-field stochastic LQ optimal control problem. Then the leader turns to solve an optimization problem for a linear mean-field forward-backward stochastic differential equation (MF-FBSDE). By introducing new state and costate variables, we present a sufficient condition for the existence and uniqueness of the Stackelberg strategy in terms of the solvability of some Riccati equations and a convexity condition. Furthermore, it is shown that the open-loop Stackelberg equilibrium admits a feedback representation involving the new state and its mean. Finally, two examples are given to show the effectiveness of the proposed results.

This paper discusses adaptive control problems of high-order stochastic nonlinear time-delay systems. Compared with the existing results, the considered system involves uncertain parameters, intricate stochastic drift terms and unknown time-varying delays. Based on a modified method of adding a power integrator and Lyapunov-Krasoviskii (L-K) functional technique, new controllers are successfully constructed to achieve the objectives of adaptive stabilization and adaptive tracking, respectively. Examples are given to show the effectiveness of the proposed control strategies.