Pareto Suboptimal Strategy for Uncertain Mean-Field Nonlinear Stochastic Systems

Abstract

In this paper, a static output feedback (SOF) Pareto suboptimal strategy for an uncertain mean-field nonlinear stochastic system is discussed. It is assumed that the nonlinear function in the stochastic system for each player is unknown and constrained by a norm-bounded function. As a preliminary result, the single-player case problem is solved in terms of the guaranteed cost control technique. As a result, it is shown that the necessary conditions satisfying the suboptimality of the upper bound of the cost are established by stochastic coupled-matrix equations (SCMEs). Next, the aforementioned results are applied to a mean-field stochastic system with a large population. Notably, a new necessary condition is described by the solvability condition related to large-scale SCMEs. To avoid the treatment of high-order computation for solving SCMEs, a new reduced-order numerical technique based on the fixed point iteration method is introduced. Consequently, the centralized strategy set is computed, although a large population is considered. Finally, to demonstrate the effectiveness of the proposed scheme, an academic example is solved.