Robust Formation Control for Uncertain Multiagent Systems With an Unknown Control Direction and Disturbances

Abstract

This paper proposes robust formation control laws for uncertain multiagent systems subjected to an unknown control direction and disturbances under the assumption that information about the reference trajectory is only available to some of the agents. Different from the existing results, the proposed control algorithms can enable the agents to converge to the specified points utilizing only local relative measurements, in which no control direction information and upper bounds of external uncertainties are required. To simplify and facilitate the analysis, external disturbances are roughly divided into structured and unstructured uncertainties. To attenuate the errors caused by the structured uncertainties, an adaptive control technique is applied to obtain the estimates of the unknown constant coefficients, and compensating functions with learning ability are developed to eliminate the errors caused by the unstructured uncertainties. A Nussbaum-type function is employed to settle the formation control problem in the presence of unknown signs of the control direction. Formation stability analysis for uncertain nonlinear multiagent systems is performed according to the Lyapunov stability theory. It is proved that the formation errors are bounded within a small desired accuracy by implementing the proposed robust control laws, and the desired formation is then achieved. Finally, two illustrative examples are presented to support the obtained theoretical results.

Keywords

• Robust adaptive formation control
• multiagent systems
• Nussbaum function
• unknown control direction
• disturbances