Distributed optimization for uncertain nonlinear MASs under event-triggered communication

In this paper, we consider the distributed adaptive optimization problem for nonlinear multi-agent systems (MASs) with unmatched uncertainties under a dynamic event-triggered mechanism (DETM). Unlike the existing distributed optimization results that focus on the linear MASs under static or simple event-triggered communication, more general nonlinear MASs with unmatched uncertainties are considered in this paper, which makes the design of the distributed optimization strategy challenging. To solve this problem, a distributed adaptive optimization algorithm based on the dynamic event-triggered mechanism is first proposed for first-order uncertain nonlinear MASs, which could provide a dynamic agent interaction-based adaptive event sampling. Based on this, a DETM-based distributed adaptive optimization algorithm is designed for high-order uncertain nonlinear MASs by employing the backstepping technique. Specifically, by introducing a high-order filter, an improved distributed optimization algorithm is further proposed, to ensure the existence of high-order derivatives of the local reference, making the application of the backstepping technique easy. Ultimately, a simulation example with comparisons is provided to show the efficacy of the developed algorithm.