# Lyapunov-Guided Energy Scheduling and Computation Offloading for Solar-Powered WSN
## 1 Introduction
Since the energy efficiency of wireless transmission is highly dependent on the channel condition, the channel state changes dynamically in different time slots, allowing the task shunt unloading needs to accommodate the randomness of energy arrivals and data arrivals. [PERSON] et al. [19] proposed an offline optimization-inspired sliding-window-based online partial offloading strategy to minimize the system energy consumption under the practical scenarios with random task state information (TSI) and channel state information (CSI) by jointly optimizing energy beamforming and remote task execution at the access side, and local computation and task offloading at the transmit side. [PERSON] et al. [20] proposed an online algorithm based on perturbed Lyapunov optimization by joint optimizing online partial offloading and resource allocation under time-varying fading channels, random energy arrivals, and random ON-OFF states of the main link. [PERSON] et al. [21] proposed a deep neural network-based parallel computing architecture for an online task offloading and resource allocation system under the time-varying channels constraint to reduce computational latency. [PERSON] et al. [22] propose a Lyapunov-based online optimized method to tradeoff energy efficiency and delay under random channel conditions and task arrivals. [PERSON] et al. [23] proposed an online computational offloading algorithm based on Lyapunov optimization and deep reinforcement learning (DRL) to maximize the network data processing capacity under long-term data queue stability and average power constraints with time-varying channels and random tasks arriving in consecutive time frames. All of the above studies rely on stable energy provision from large grids and have poor network flexibility, which is not suitable for IoT applications with a large number of sensors and wide distribution in remote areas, especially remote video monitoring networks in isolated microgrids and high-voltage transmission and transformation systems. With high density, easy deployment, and being clean and sustainable, renewable energy sources, such as solar energy can provide permanent energy to the network. Nevertheless, the research of renewable energy-powered MEC systems is challenging given the stochastic nature of environmental energy. How to efficiently utilize renewable energy and improve energy efficiency in MEC systems is the key to green communication. [PERSON] et al. [24] established an energy transmission optimization model for solar-powered WSN. [PERSON] et al. [25] predicted the energy state for renewable energy-driven MEC systems and developed a corresponding platform. [PERSON] et al. [26] jointly optimize the offloading strategy and power allocation to maximize the network computation for renewable energy-powered MEC systems. In hybrid renewable energy-grid-powered MEC systems, [PERSON] et al. [27] studied minimized multi-node energy consumption and computation under the constraint of QoS. [PERSON] et al. [28] further proposed a joint optimization algorithm for base station transmit power, terminal offload, and transmit power to minimize the total energy consumption considering both ideal and non-ideal channel state information. The above research mainly focuses on optimizing the offloading scheme at the current moment, ignoring the energy coupling between different time slots, without considering both the task delay and energy coupling constraints to obtain the optimal offloading ratio. [PERSON] et al. [29] used the Markov decision process (MDP) and deep learning (DL) to implement dynamic online/offline IoT edge offloading for renewable energy-powered MEC networks under the quality of service (QoS) expectation constraints. However, the computational complexity of MDP-based methods is high due to the large size of the state and action space. As Lyapunov optimization does not depend on state transfer, its computational complexity is usually much smaller than that of MDP-based methods. [PERSON] et al.