# Lyapunov-Guided Energy Scheduling and Computation Offloading for Solar-Powered WSN
## 1 Introduction  
With the booming development of computation-intensive applications, such as high-definition video monitoring and face recognition, in the ubiquitous power IoT and vehicular network, intelligent terminal devices need to frequently perform communication and computation operations to provide real-time data support for system intelligence decisions, which makes the network energy consumption, communication traffic, and computation data volume explode [1; 2]. This is especially the case for remote video monitoring networks of isolated microgrids and high-voltage transmission and transformation systems, where sensors are tiny, computationally weak, energy-limited, and supplied inconveniently, making it difficult to realize online remote intelligent inspection based on video image analysis, as it can neither accurately identify defects in video images nor meet a large number of real-time computing, communication, and energy requirements [3; 4]. Cloud computing requires devices to upload data to the remote cloud server with strong computing capacity, increasing more load pressure, delay, and energy consumption [5]. Multi-access edge computing (MEC) transfers task processing to nearby servers at the edge of the network near the terminal side, which can offload heavy load tasks, such as image recognition, to the edge server for computing, effectively relieving the load on the cloud, shortening terminal transmission latency, reducing terminal energy consumption, ensuring the security for stored data, and meeting high computing capacity requirements for equipment fault identification and diagnosis in the remote video inspection scenario [6; 7; 8]. Traditional MEC research has focused on offloading decisions and resource allocation under fixed energy or constant power provision [9]. [PERSON] et al. [10] studied task offloading strategies and resource allocation to minimize network energy consumption under the constraints of terminal energy and network QoS requirements. [PERSON] et al. [11]performed edge offloading based on Markov decision and deployed lightweight reinforcement learning techniques at the terminal to reduce computational complexity and energy consumption. In a wireless-powered MEC system, [PERSON] et al. [12] committed to maximizing computational utility and minimizing grid energy consumption under the offloading delay constraint, by jointly controlling the wireless power allocation at the base station, the offloading data quantity, and power allocation at the terminals. [PERSON] et al. [13] minimized the transmit power of HAP by jointly optimizing the time allocation ratio and computational mode selection under energy causality and computation rate constraints. Considering the energy-signal duality of RF signals, the SWIPT technique can significantly improve network energy efficiency by transmitting wireless information and energy simultaneously. [PERSON] et al. [14] achieved the minimization of total system energy consumption under data transmission rate and transmit power constraints by jointly optimizing power allocation, local computation frequency, offloading factor, and energy harvesting factor in a SWIPT-based MEC network. [PERSON] et al. [15] introduced UAV-assisted mobile edge computing to reduce the network energy consumption and extend the network lifetime while improving stability and scalability for the network coverage. [PERSON] et al. [16] investigated partial offloading and resource allocation in a UAV-enabled wireless-powered MEC system to maximize the computation rate under the energy and mobility constraints of the edge server. [PERSON] et al. [17] jointly optimized the offloading strategy, computational resources, and transmit power to minimize the total weighted energy consumption for the multi-UAV-assisted MEC system with NOMA. [PERSON] et al. [18] further proposed an efficient task-offloading algorithm based on deep reinforcement learning to minimize the system cost by jointly optimizing task offloading, load balancing, and resource allocation.