Adaptive event-triggered distributed optimisation for second-order nonlinear multi-agent systems with external disturbance

In this paper, an unconstrained distributed optimisation problem for a class of second-order uncertain nonlinear systems subject to external disturbances is considered. In order to achieve optimal consensus and save communication resources, a novel distributed adaptive event-triggered control algorithm is proposed. Each agent updates its own state only at event-triggering instants without the requirement for global topology information. To effectively counteract the external disturbances and guide the states of all agents toward an optimal consensus point, the controller is designed based on gradient descent and the internal model principle. Furthermore, with Lyapunov stability theory, the designed controller can be proved to achieve asymptotic stability without time-varying parameters and the Zeno-behaviour is effectively excluded. Finally, a simulation example is provided to illustrate the validness of the designed control strategies.