Voltage Regulation in Edge Energy Router System via $H_{\infty}$ Control with Markov Jump

With the increase in the amount of tasks offtoaded to the network edge, the energy supply of edge devices has become a challenge worthy of attention. It is a feasible way to use renewable energy to supply energy for edge devices, but production of renewable energy has certain uncertainty and stochasticity. In order to provide sufficient energy to ensure stable operation of edge devices, energy Internet (EI) provides an idea, that is, different edge devices are connected with distributed small energy supply and storage systems. As the core equipment of energy Internet, energy router (ER) plays an important role in information transmission, energy transmission and system control. In this paper, the concept of edge energy router is proposed, which has the ability of task computing and scheduling similar to edge computing server, as well as the ability of energy transmission and system control of energy router. Each edge energy router is connected with loads, photovoltaic panel (PV), micro turbine (MT) and battery energy storage (BES) to form a self-sufficient microgrid (MG) system. However, there exists a delay in energy transmission and task scheduling between different ERs. Moreover, the DC bus voltage stability of each edge energy router system is negatively affected by internal uncertainty, stochasticity and external interference. Therefore, the system is modeled by Markov jump ODEs with time delay, and robust control of DC bus voltage deviation is discussed in this paper. The linear matrix inequality (LMI) method is used to solve this Markov jump control problem. Finally, numerical simulations show the effectiveness of the proposed method.