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 considers quadratic stabilizability and H_∞ feedback control for stochastic discrete-time uncertain systems with state- and control-dependent noise. Specifically, the uncertain parameters considered are norm-bounded and external disturbance is an l²-square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.

This paper mainly investigates the stochastic finite-time annular domain stability and asynchronous H _∞ control for nonlinear stochastic switching Markov jump systems. Firstly, the criterion of stochastic finite-time annular domain stability of the system is given by the modedependent average dwell time method, and two results, which consider particular cases with no switching signal and no Markov jump, are obtained. Secondly, when there are asynchronous phenomena in both deterministic switching and Markov jump, the asynchronous H _∞ controller is given to make the nonlinear switching Markov jump system finite-time annular domain bounded with a prescribed disturbance attenuation level. In addition, two degradation results with no deterministic asynchrony and no stochastic asynchrony are derived, respectively. As a special case, the corresponding result of linear switching Markov jump systems is obtained. Finally, an example is given to illustrate the results.

This article presents results on designing the Pareto-optimal strategy under H∞ constraint for the linear mean-field stochastic systems disturbed by external disturbances. First, combining the stochastic H∞ control theory with the stochastic mean-field theory, we derive the stochastic bounded real lemma (SBRL) of our considered linear mean-field stochastic systems with the stochastic initial condition. Second, we use the mean-field forward-backward stochastic differential equation to solve the mean-field linear quadratic Pareto-optimal problem with indefinite cost functionals. It is proved that the existence of a closed-loop Pareto-optimal strategy is equivalent to the solvability of the coupled generalized differential Riccati equations when some conditions are satisfied. Finally, a necessary and sufficient condition for the Pareto-optimal strategy under the H∞ constraint is researched by four-coupled matrix-valued equations. Besides, we also obtain the Pareto frontier for the mean-field stochastic system with only state-dependent noise. A practical example is presented to show the effectiveness of our main results.