Tensor-based feedback control for locally structured high-dimensional streaming data under limited control capability

Structured high-dimensional streaming data offers abundant information that is crucial for process feedback control. Nevertheless, traditional control models predominantly emphasize the global patterns of spatiotemporal correlation within responses, often neglecting the local correlation structure. This oversight can be problematic in applications where local correlations play a significant role, such as temperature control of composite plates. Additionally, these models typically fail to incorporate local patterns within the spatial influence of control variables, an essential aspect considering the location-sensitive nature of control impact. Moreover, in practice, the suboptimal uniform placement of control variables can significantly impact the effectiveness of control strategies under insufficient control resources. To address these issues, we propose a tensor-based feedback control model for locally structured high-dimensional streaming data under limited control capabilities. For system modeling, we employ kernel distributions to capture the local structure within (i) the response autocorrelation and (ii) the spatial impact of location-sensitive control variables. For online control, we develop a dynamic control strategy to optimize controller placement, enhancing control efficiency despite resource constraints. Finally, we validate the effectiveness of our proposed framework through simulations and a case study.