Adaptive Exponential Consensus With Cooperative Exponential Parameter Identification Over Leaderless Directed Graphs

Due to the complex entanglement between distributed control and distributed estimation, adaptive multiagent dynamics over leaderless directed graphs are yet not completely understood. This happens even when the adaptive dynamics are based on established tools like model reference adaptive control (MRAC). This work starts from the observation that existing MRAC-based leaderless designs stop at asymptotic consensus, lacking of any guarantee for exponential consensus or parameter identification. The main contribution of this work is to show a new design departing from the existing ones in terms of exploiting persistence of excitation (PE): the proposed design is the first one attaining exponential consensus with exponential parameter identification over leaderless directed graphs. In the special case that the unknown parameters are homogeneous, PE can be relaxed to a weaker cooperative PE (C-PE) condition. The design is illustrated and verified alongside the state-of-the-art.