Adaptive fully-distributed sign-consensus control approach for nonlinear multi-agent systems over a signed graph

In this paper, the notion of sign-consensus for the Lipschitz nonlinear multi-agents over a signed graph is introduced and controller design conditions are provided for realizing consensus among signs of states of agents. The previous works on sign-consensus are limited to the linear systems only. The attainment of sign-consensus for the nonlinear multi-agent systems is a non-trivial control problem, for which Lipschitz nonlinear dynamics are reformulated using the linear parameter varying (LPV) transformation. To guarantee the sign-consensus in a network of multiple agents, fully-distributed adaptive protocol is applied using reformulated Lipschitz nonlinear dynamics, and two design conditions are provided based on the Lipschitz constant oriented and LPV-based approaches. The first approach is comparatively less computationally complex while LPV approach holds significance for developing less conservative sign-consensus control scheme. To the best of our knowledge, distributed sign consensus methods for Lipschitz systems, based on LPV formulation, have been analyzed for the first time. The proposed approach is adaptive and can be regarded as fully-distributed, as it does not require the central knowledge of graph properties. Further, results are extended for nonlinear systems undergoing disturbances and ultimate boundedness of sign-consensus error is guaranteed. Numerical simulations on groups of Chua’s circuits and mechanical oscillators are presented to validate the results.