Event-Triggered Algorithms for Leader–Follower Consensus of Networked Euler–Lagrange Agents

This paper proposes three different distributed event-triggered control algorithms to achieve leader–follower consensus for a network of Euler–Lagrange agents. We first propose two model-independent algorithms for a subclass of Euler–Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work studying event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities, which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information, and bounds on the initial conditions. When the Euler–Lagrange agents have dynamics that include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain parameters associated with the agent self-dynamics. For each algorithm, a trigger function is proposed to govern the event update times. The controller is only updated at each event, which ensures that the control input is piecewise constant and thus saves energy resources. We analyze each controller and trigger function to exclude Zeno behavior.