## 1 Introduction  
Edge intelligence within the Industrial Internet of Things (IIoT) represents a transformative paradigm that is revolutionizing operational efficiency and fostering innovation [1]. By strategically situating computational capabilities proximate to data sources, edge computing (EC) empowers real-time insights and decision-making processes [2]. This strategic localization is critical to optimizing resource utilization--a key factor in meeting the stringent demands of industrial ecosystems [3]. The integration of edge intelligence allows IIoT systems to transcend conventional limitations, enabling greater adaptability and agility.  
The localized architecture of EC accelerates data processing, thereby reducing latency and enhancing overall system efficiency [4]. Proximity to data sources facilitates rapid analysis, which is indispensable for real-time responsiveness. This positioning expedites processing, minimizes latency, and improves resource utilization [5].  
Efficient task allocation (TA) and controller migration (CM) are essential for optimizing the performance of edge-based IIoT systems [6]. These systems rely on distributed architectures, where tasks are allocated based on computational capacity and workload distribution [7]. CM ensures system adaptability by dynamically reallocating tasks among nodes to maximize resource utilization. The seamless orchestration of TA and CM promotes streamlined operations and significantly enhances productivity within IIoT environments [8]. Together, TA and CM strengthen system resilience and responsiveness--traits that are vital in industrial contexts [9; 10]. CM supports adaptability by redistributing tasks in response to variable workloads and network conditions. The synergy between TA and CM underpins efficient resource utilization, which is crucial for meeting industrial performance requirements [11].  
The integration of machine learning (ML) techniques enhances TA and performance optimization in edge-based IIoT systems [12]. ML algorithms utilize historical and real-time data to refine task allocation strategies, ensuring optimal resource utilization and efficiency [13]. ML facilitates the proactive identification of performance bottlenecks, enabling the continuous improvement of IIoT operations [14]. The convergence of EC, TA, CM, and ML drives productivity and competitiveness in modern industrial IoT systems. ML's integration enables IIoT systems to achieve proactive optimization, anticipating and addressing performance challenges before they impact operations [15; 16]. Through continuous learning and adaptation, IIoT systems evolve dynamically, ensuring sustained performance enhancements and operational efficiency. ML methods further enhance the optimization of TA and performance within edge-based IIoT systems, driving productivity and competitiveness in industrial settings [16; 17]. The importance of adaptive control under uncertain and dynamic conditions has also been demonstrated in other domains such as robotics, where impedance learning has been applied to manage human-guided interaction [18]. The key contributions of this paper are  
* A cross-layer tasking scheme (CLCTS) that coordinates task grouping and controller re-tasking in IIoT systems.
* A dual-phase model combining task similarity grouping and graph-based controller migration.
* A learning mechanism that minimizes task acceptance error and re-tasking delays.
* Experimental validation demonstrating improved performance over existing methods in completion ratio, processing time, and TAE.