Robust leader-following consensus control of one-sided Lipschitz multi-agent systems over heterogeneous matching uncertainties

Abstract

This paper presents a novel consensus control methodology for the multi-agent systems (MASs) with one-sided Lipschitz (OSL) nonlinearities under heterogeneous matching uncertainties, non-zero input to the leader, and external perturbations. A leader-following consensus control scheme is considered, and a control law is provided to assure that the followers track the leader successfully to deal with the uncertainties. The present work considers heterogeneous matching uncertainties, and a new approach with different Lyapunov function, rather than using Laplacian matrix term in the Lyapunov function, has been considered for complete elimination of the uncertainties. The proposed strategy is extended to the case where exogenous disturbances are also acting (to deal with un-matching uncertainties) on the nonlinear dynamics, and a robust consensus control approach is revealed. To overcome the chattering problem, a continuous-time consensus control law is also presented to guarantee the convergence of the consensus error to a small bounded set in the presence of external disturbance. To the best of the authors’ knowledge, consensus control of a generalized form of OSL agents for the complete elimination of heterogeneous matching uncertainties and for considering non-zero input to the leader has been explored for the first time. The developed treatment is different from the conventional methods on the linear or Lipschitz nonlinear multi-agents under heterogeneous uncertainties. Finally, an application of the proposed methods to moving agents is furnished to illustrate the strength of the resultant consensualization protocol.

Keywords

• Nonlinear multi-agents
• One-sided Lipschitz function
• Consensus control
• Heterogeneous uncertainties
• Robustness