Event-triggered adaptive iterative learning control for two-dimensional Fornasini–Marchesini model systems

Although some existing studies have addressed event-triggered iterative learning control–related problems, most of them focus on one-dimensional systems or investigate control systems with the aid of certain two-dimensional analytical methods. This article explores the problem of event-triggered adaptive iterative learning control design for two-dimensional linear discrete-time systems described by the Fornasini–Marchesini model. First, an improved event-triggering condition that only requires the system state and tracking error is devised. Second, by introducing the event-triggered control into the iterative domain, an adaptive parameter law is designed. Then, a novel two-dimensional event-triggered adaptive iterative learning control scheme is developed, which can effectively reduce the updating number of control inputs, alleviate the computational burden on the controller, and save network communication resources. A rigorous theoretical analysis is conducted on the developed two-dimensional event-triggered adaptive iterative learning control scheme using a composite energy function, and the results show that the developed scheme can ensure the convergence of tracking errors. Finally, a simulation example is given to demonstrate the effectiveness of the proposed two-dimensional event-triggered adaptive iterative learning control scheme.