## 1 Introduction  
With the global pursuit of renewable energy and carbon neutrality, microgrid systems are receiving more and more attention as an efficient and flexible energy distribution solution [1]. The hydrogen-based microgrid system is a potential energy transformation solution because it can realize the storage and distribution of clean energy, thus providing new possibilities for the sustainable development of the energy system [2]. However, the control and management of such systems face many challenges, such as intelligent control on the demand side and distributed control of the system, it is essential to ensure proper design and operation [3]. The development of microgrid control algorithms is a challenge that can integrate multiple methods and requires consideration of many aspects [4]. Existing research has made many attempts at this, such as applying heuristic algorithms to microgrid control in an attempt to obtain a better control method in a shorter time [5]. In order to deal with the uncertain status and parameters of the system, stochastic control algorithms from ref. [6] are introduced into microgrid control. In order to deal with nonlinear problems in microgrid control algorithms, optimal control algorithms such as adaptive optimization algorithms and neural networks are also used [7, 8]. In the microgrid control problem, the prediction of power generation, the load of the power grid, and the required energy cost are issues that cannot be ignored. Therefore, it is necessary to develop relevant control algorithms in a targeted manner from the perspective of demand-side control. The system control method that has been widely studied is the island DC microgrid energy management system (EMS) based on hierarchical state machine control algorithm [9]. At the same time, the EMS system can be used to achieve real-time power supply management for power suppliers and demanders in the PV+Wind mode [10]. On this basis, there is also a two-level EMS control method that applies EMS to multiple control levels [11]. As for the demand-side control of hybrid power generation systems, ref. [12] discussed the feasibility of applying dual-mode distributed economic control algorithms. Ref. [13] provides a comprehensive and referenceable process for the design, modeling, and control of DC microgrids. Based on the above aspects, it is necessary to consider the prediction of power generation and load of microgrids based on the demand side and the required energy costs. If each control node is understood as multiple agents, the multinode power grid control can be transformed into multiagent control with multiple constraints [14], and the model predictive control (MPC) and hierarchical control [15; 16], which are widely used in the multiagent field, can be introduced because these can not only combine the above two requirements and consider them together but are also reliable methods to predict and solve the optimal control. And Lyapunov theory can be introduced to prove the feasibility of the control method [17]. There are currently many related research algorithms based on MPC. For example, refs. [18; 19], respectively, studied distributed and centralized MPC control methods for renewable energy power generation networks. Refs. [20; 21] apply MPC control to hierarchical distributed control. Ref. [22] presented a distributed MPC framework that is suitable for controlling large-scale networked systems such as power systems. However, while MPC has the above advantages, it also has some disadvantages. For example, because it needs to predict control inputs for many steps in the future, it will inevitably increase the computing cost and communication cost of the system [23; 24]. In order to reduce the communication and computing burden of the system, event-triggered and self-triggered controls are widely used [25; 26]. Self-triggering control can significantly reduce computing costs because it does not need to detect and control the system status at all times [27; 28].