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

Abstract

This paper proposes three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We firstly 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 selfdynamics. 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 concerning 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 which include the vector of gravitational potential forces, an adaptive algorithm is proposed which requires more information about the agent dynamics but can estimate uncertain agent parameters.For each algorithm, a trigger function is proposed to govern the event update times. At each event, the controller is updated, which ensures that the control input is piecewise constant and saves energy resources. We analyse each controllers and trigger function and exclude Zeno behaviour. Extensive simulations show 1) the advantages of our proposed trigger function as compared to those in existing literature, and 2) the effectiveness of our proposed controllers.

Cooperative Event-Based Rigid Formation Control

“…Examples of successful applications of the event-based control strategy on distributed control systems and networked control systems have been reported in e.g. [19]- [21]. We refer the readers to the recent survey papers [22]- [25] which provide comprehensive and excellent reviews on event-based control for networked coordination and multi-agent systems.…”

Distributed event‐triggered tracking control with a dynamic leader for multiple Euler‐Lagrange systems under directed networks

“…In Reference , the synchronization control problem is addressed under directed topologies by utilizing the robust control mechanism, where the requirement on relative velocity measurements is relaxed. In the case of tracking one stationary leader, two model‐independent controllers are proposed in Reference , where the variable‐gain control law is suitable for undirected networks and the constant‐gain control algorithm is applied to directed networks. More recently, an event‐triggered formation‐containment control framework is developed in Reference to improve the simultaneous performance of leaders' formation and followers' containment.…”

Event‐based distributed robust synchronization control for multiple Euler‐Lagrange systems without relative velocity measurements

“…Event‐based distributed leaderless synchronization control problem and containment control problem with multiple stationary leaders have respectively been discussed, where the interaction network associated with all agents and the subgraph among followers are both assumed to be undirected. Later on, a model‐independent variable‐gain control law with undirected topology and a constant‐gain control algorithm under directed network were presented by Liu et al to address the tracking control problem with a dynamic leader, where the choice of event‐triggered functions was also discussed. It is worth noting that only simplified multiple Euler‐Lagrange systems are studied in the aforementioned results, where the effect of gravity and external unknown disturbance are neglected.…”

“…Later on, a model‐independent variable‐gain control law with undirected topology and a constant‐gain control algorithm under directed network were presented by Liu et al to address the tracking control problem with a dynamic leader, where the choice of event‐triggered functions was also discussed. It is worth noting that only simplified multiple Euler‐Lagrange systems are studied in the aforementioned results, where the effect of gravity and external unknown disturbance are neglected. Based on this motivation, a robust tracking control problem with a dynamic leader for multiple Euler‐Lagrange systems in the presence of generalized gravity, friction, and disturbance was investigated by Kumari et al by applying an event‐based sliding mode strategy.…”

“…Besides, the assumption on communication topology is relaxed in that the directed graph contains a directed spanning tree, which is more realistic and less restrictive than being strongly connected . Furthermore, our results can make sure the synchronization errors converge to zero rather than just uniform ultimate boundedness. In contrast to previous work, we focus on the distributed leaderless synchronization control for multiple Euler‐Lagrange systems. Since no leaders' information can be obtained and referred, leaderless synchronization control is more challenging than traditional leader‐follower tracking and containment control in some ways.…”