Consensus Control of Nonlinear Stochastic Multiagent Systems With Unknown and Time-Varying Control Coefficients Based on Novel Nussbaum Functions

This article investigates the distributed control of a group of stochastic high-order nonlinear systems in which the subsystems are with unknown and time-varying control coefficients of unknown signs, inherent nonlinear drift and diffusion terms. To solve the control problem with unknown control directions, where traditional available Nussbaum functions are not applicable for the consensus of stochastic nonlinear systems with unknown and time-varying coefficients of unknown signs, a novel type of Nussbaum function is proposed with a new paradigm of stability analysis in probability. Global consensus control of stochastic multiagent systems is achieved by designing distributed controllers which integrate designed distributed filters and novel Nussbaum functions. In addition, it can be proved that all signals in the closed-loop system are bound in probability, and the transient consensus errors of the followers are bounded by positive constants which can be adjusted arbitrarily small. The effectiveness of the proposed control scheme is demonstrated by simulation results.

I. Introduction

Due to the diverse applications of multiagent systems (MASs), such as group surveillance of unmanned ground vehicles, formation of autonomous aerial vehicles and satellites, the research on consensus control of multiple agents has attracted plenty of attention from researchers and has achieved fruitful research results, such as [1], [2], [3], and [4] and many references therein. The model of agents in the MASs could be linear or nonlinear. In [5], for MASs with higher-order linear dynamics, the consensus control problem is considered. In [6], the output regulation consensus control of linear MASs is studied based on the dynamic distributed control scheme. It is well known that practical systems are always inherently nonlinear. Therefore, it is more significant to investigate the control of nonlinear MASs. The results obtained for nonlinear MASs include [7], [8], [9], [10], [11], [12], [13]. For example, in [11], the output feedback containment control protocol is designed for the MASs with input saturation constraints and switching topologies. A robust adaptive fully distributed consensus control scheme is designed in [12] for a group of nonlinear MASs subjected to unmatched external disturbances. However, it assumes that the nonlinear terms of the agents meet the Lipschitz condition. In [13], the commonly used Lipschitz condition is relaxed. Moreover, finite-time consensus is realized for such high-order mismatched uncertain nonlinear MASs.