# Edge-Event-Triggered Synchronization for Multi-Agent Systems with Nonlinear Controller Outputs
###### Abstract  
This paper addresses the synchronization problem of multi-agent systems with nonlinear controller outputs via event-triggered control, in which the combined edge state information is utilized, and all controller outputs are nonlinear to describe their inherent nonlinear characteristics and the effects of data transmission in digital communication networks. First, an edge-event-triggered policy is proposed to implement intermittent controller updates without Zeno behavior. Then, an edge-self-triggered solution is further investigated to achieve discontinuous monitoring of sensors. Compared with the previous event-triggered mechanisms, our policy design considers the controller output nonlinearities. Furthermore, the system's inherent nonlinear characteristics and networked data transmission effects are combined in a unified framework. Numerical simulations demonstrate the effectiveness of our theoretical results. multi-agent systems; synchronization; event-  
employing GPS and inertial navigation equipments to obtain its absolute velocity and position information in the given inertial reference frame. For edge-based event-triggered control, it is applicable in the scenarios where the absolute state information is difficult to measure. For instance, in the deep sea or deep space, each AUV or spacecraft employs sonar or LiDAR to measure the relative velocity and position between itself and its neighbors to achieve multi-agent coordination goals. In [39; 45; 46; 47; 54; 55], all relevant edge state information of each agent is acquired and processed together, which is different from the way of asynchronously acquiring and processing edge state information [40; 41; 42; 43; 45]. However, most of the previous results have not considered the controller output nonlinearities. On one hand, the controller device may have inherent nonlinear characteristics that cause the output signals to be distorted. For instance, the nonlinear characteristics of the control circuits may lead to signal output distortion and saturation. On the other hand, the employment of quantizers may also lead to the distortion of controller output information. In this paper, we provide edge-event- and edge-self-triggered control solutions to solve the synchronization problem of Lipschitz nonlinear multi-agent systems with controller output nonlinearities, in which the edge states associated with each individual are processed together. Besides, we take the effects of controller output nonlinearities into account. It does not only include the nonlinear characteristics of controllers, but also the effects of nonlinear coding required for data transmission in digital communication networks. To avoid the requirement for sensor continuous scanning due to continuous monitoring of measurement errors in the proposed event-triggered condition, an edge-self-triggered policy is proposed to save sensor resource consumption. In the designed event-triggered policy, neighboring individuals do not need to employ communication networks to transmit data. However, in the proposed self-triggered policy, a small amount of data communication is necessary, which brings savings in sensor resources. There exists a trade-off between communication resource consumption and sensor resource consumption between the two policies, which are suitable for different application scenarios. Nonlinear dynamic models can be used to describe a large number of actual systems in engineering scenarios, for example, various types of nonlinear circuits, spring-mass-vehicle devices, inverted pendulums, etc. The research of nonlinear multi-agent system coordination control problems can provide solutions for such scenarios. The proposed triggering mechanisms can save resources consumed by interaction, and the considered output nonlinear fluctuation can evaluate the impact of communication transmissions and actuator nonlinearities.