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

This paper proposes three different distributedevent-triggered control algorithms to achieve leader-followerconsensus for a network of Euler-Lagrange agents. We firstlypropose two model-independent algorithms for a subclass ofEuler-Lagrange agents without the vector of gravitational po-tential forces. By model-independent, we mean that each agentcan execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when thesensing graph is undirected; algorithm parameters are selectedin a fully distributed manner with much greater flexibility com-pared to all previous work concerning event-triggered consensusproblems. When the sensing graph is directed, a constant-gainalgorithm is employed. The control gains must be centrallydesigned to exceed several lower bounding inequalities whichrequire limited knowledge of bounds on the matrices describingthe agent dynamics, bounds on network topology information andbounds on the initial conditions. When the Euler-Lagrange agentshave dynamics which include the vector of gravitational potentialforces, an adaptive algorithm is proposed which requires moreinformation about the agent dynamics but can estimate uncertainagent parameters.For each algorithm, a trigger function is proposed to governthe event update times. At each event, the controller is updated,which ensures that the control input is piecewise constant andsaves energy resources. We analyse each controllers and triggerfunction and exclude Zeno behaviour. Extensive simulations show1) the advantages of our proposed trigger function as comparedto those in existing literature, and 2) the effectiveness of ourproposed controllers.