## 1 Introduction
[20] focused on aperiodic detection with a communication delay for the application of multiple two-wheeled mobile robots. Other than control, the realization of consensus depends on the effectiveness of the communication system [14; 30]. Issues like time delays [31; 32], disturbances [33; 34] and limited resources [35; 36] have been discussed. [PERSON] et al. [32] solved the time delay problem using the parametric algebraic Riccati equation, whereas [PERSON] et al. [37] proposed a heuristic dynamic programming method. For disturbances in communication transmission, [PERSON] et al. [38] solved the issue of hybrid multi-agent systems with unknown disturbances, whereas [PERSON] et al. [39] proposed a solution for unknown external disturbances in the tracking system. Due to the limitations of communication resources embedded in the multi-agent controller, event-based control has been applied to solve the communication issue during the consensus process [35; 36; 40; 41]. The idea of having an event-triggered control was proposed in order to reduce the frequency of sampling when the agent receives the input signal from the sensor to be sent to the controller. By reducing the transmission of the signal, the computation and communication resources can be reduced to guarantee the practicality of the controller [28; 33; 34; 42; 43; 44]. Due to the significance of event-triggering in multi-agent consensus systems, event-based control has been integrated into consensus control systems by means of sliding mode control (SMC) [45], a fuzzy logic and back stepping technique [46], model predictive control (MPC) [47], distributed control [20; 37; 48; 49; 50; 51; 52]and dynamic role assignment [53]. Not only could this save communication resources, it could also save energy. As the multi-agent robot is normally embedded with the digital microcontroller, which has limited resources, the research on reducing energy usage resulting from communication [54; 55], actuators [56] and trajectory [57] have become recent hot topics in multi-agent research, and this area is also known as \"energy aware\" [58] or \"energy efficient\" [12; 59] research. Motivated by the aforementioned works, this study was carried out to solve the homogenous agent communication issues when finding a consensus for rendezvous applications in the broadcast and communication environment. Although a few stochastic controllers have been applied to finding a consensus for this application, the issue of communication has not been taken into consideration. Therefore, in this study, we propose an integration of an event-triggered system into the simultaneous perturbation stochastic algorithm (SPSA) and a distributed controller to obtain the minimum utilization of the channel, as well as preserving agent performances. This study can be considered an advancement in the existing method, aiming to highlight the importance of reducing energy resources from communication, which will guarantee the practicality of controllers. The effectiveness of the proposed controller was evaluated and observed in terms of trajectory, time, iteration, and number of channels taken to reach consensus for rendezvous purposes. In addition, a conventional sampling system, known as the time-triggered system, was applied in this case study as a benchmark for comparison to the event-triggered system. The obtained results are compared with traditional sampling systems in terms of channel utilization and agent performances to show the effectiveness and robustness of the proposed consensus controller. The rest of this article is structured as follows. In Section 2, the formulation of the problem is explained. Section 3 describes the system, including the global and local consensus controller designs and the proposed theorems. In Section 4, results from the simulation setup are presented and discussed, whereas Section 5 concludes this paper.