Mean-Square $H_\infty $ Consensus Control for a Class of Nonlinear Time-Varying Stochastic Multiagent Systems: The Finite-Horizon Case
针对有限时域内非线性离散时变随机多智能体系统，设计静态输出反馈控制器，同时满足H∞一致性性能和均方一致性性能的预设上界约束，并通过递归矩阵不等式给出控制器存在条件。
This paper deals with the consensus control problem for a class of nonlinear discrete time-varying stochastic multiagent systems (MASs) over a finite horizon via static output feedback. The measurement output available for the controller is not only from the individual agent itself but also from its neighboring ones according to the given topology. The nonlinearities described by statistical means can encompass several classes of well-studied nonlinearities in the literature. A new index of mean-square consensus performance, which quantifies the deviation level from the state of individual agent to the average value of all agents' states, is proposed to reflect the transient consensus behavior of the MAS. The purpose of the addressed problem is to design a time-varying output feedback controller such that: 1) the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> consensus performance defined over a given finite horizon is guaranteed with respect to the additive noises and 2) at each time step, the mean-square consensus performance satisfies the prespecified upper bound constraint. By using a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired control scheme for achieving both H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> and mean-square consensus performance requirements. Finally, a simulation example is utilized to illustrate the usefulness of the proposed control protocol.