An Iterative Approach for Self‐Triggered Control of Linear Systems Based on a Hierarchical Cooperation Framework

ABSTRACT In this paper, we propose a self‐triggered control mechanism based on a hierarchical strategy for linear systems which can further save computer resources while ensuring the advantages of the traditional self‐triggered strategy. A hierarchical cooperation framework is developed to optimize the control structure in the design of the controller, with the upper layer calculating the inter‐execution intervals and the lower layer computing the control input. To improve the system performance, we introduce an alternating solution strategy for iteratively deriving the next sampling instant and input. The one‐step finite horizon boundary is applied to compute the initial triggering interval. Within each subsequent triggering interval, the control input values are determined by minimizing the specified performance index in the lower controller. These values are then fed back to the upper trigger for the calculation of the next triggering interval, on the premise of ensuring the system's stability. By fostering collaboration between control and triggering mechanisms and facilitating iterative optimization across different levels, the number of system triggers is significantly reduced, and the convergence speed of state trajectory is accelerated. The efficiency and superiority of the proposed method are demonstrated through a numerical simulation example.