Pareto-based guaranteed cost control of the uncertain mean-field stochastic systems in infinite horizon

Pareto-based guaranteed cost control (GCC) problem of uncertain mean-field stochastic systems is investigated in infinite horizon. Firstly, the Pareto game of nominal mean-field stochastic systems is studied. Applying the convexity of the cost functionals, it is shown that all Pareto efficient solutions can be obtained by solving a weighted sum optimal control problem, based on which, Pareto-based GCC problem is solved by the GCC of the weighted sum objective functional. Secondly, applying the Karush-Kuhn-Tucker (KKT) conditions, the necessary conditions for the existence of the Pareto-based guaranteed cost controllers are derived. In particular, it turns out that all controllers are expressed as linear feedback forms involving the state and its mean based on the solutions of the cross-coupled generalized algebraic Riccati equations (CGAREs). Thirdly, this paper presents an LMI-based approach to reduce greatly the computational complexity in the controller design. Finally, two examples are given to show the effectiveness of the proposed results.