Fuzzy-Model-Based Leader-Follower Consensus of Nonlinear Multi-Agent Systems with Input Saturation

Abstract

This paper presents a fuzzy-model-based method for solving the consensus problem of a class of nonlinear multi-agent systems (MASs) with input saturation. Since each agent has nonlinear dynamics, the system is not asymptotically null controllable with bounded controls (ANCBC). Therefore, the widely-used low-gain feedback method for designing consensus protocols of MASs with input saturation can no longer work. To this end, the Takagi-Sugeno (T-S) fuzzy model is adopted to formulate the error dynamics of those nonlinear follower agents with input saturation as well as a leader with time-varying states. Accordingly, by using the properties of convex hull, a set of invariance condition in the format of linear matrix inequality (LMI) is designed. Furthermore, by enlarging the shape reference set, the estimation of the attraction domain can be obtained. Simultaneously, by viewing the control gain as an extra free parameter in the LMI optimization procedure, the leader-follower consensus algorithm is proposed, which guarantees that all followers with input saturation can track the leader, and they can asymptotically reach consensus. Finally, numerical experiments validate the effectiveness of the proposed anti-saturation consensus algorithm.