A sum-of-squares approach to consensus of nonlinear leader-follower multi-agent systems based on novel polynomial and fuzzy polynomial models

This paper addresses the consensus problem of leader-follower nonlinear multi-agent systems (MAS) where, nonlinear agents should approach a nonlinear leader. Firstly, the polynomial model is presented to describe the error dynamics. By choosing polynomial Lyapunov function, the consensus conditions are derived and finally they converted to sum-of-squares (SOS) terms. Secondly, a fuzzy polynomial model is proposed for modeling the error dynamics when the nonlinear agents have more complex dynamics and cannot be approximated with polynomial systems and consensus conditions are expressed in SOS terms. In both cases, a polynomial consensus protocol is designed that guarantees the consensus. Thirdly, the H∞ consensus of the nonlinear MASs based on polynomial model and fuzzy polynomial model is solved and the consensus protocol that guarantees the consensus in the presence of external disturbance is designed. Finally simulation results are added to demonstrate the effectiveness of the proposed approach.