## 1 Introduction  
Iterative learning control (ILC) is a technique used to leverage historical tracking information to refine current control inputs. It can successfully drive the system to track the desired trajectory precisely over a fixed time interval. The roots of ILC trace back to robotics, in which a robotic manipulator attempts to repetitively track a predetermined ideal trajectory [1]. The originality of ILC is that it creates a servomechanism to execute the tracking task by virtue of experience or knowledge. The multi-operation feature enables the ILC mechanism to utilize the observed tracking discrepancy of the current operation, correcting control commands and generating an upgrade control command for subsequent operations. Classical ILC algorithms have a range of different control schemes, including derivative-type (D-type), proportional-type (P-type), proportional-derivative-type (PD-type), and proportional-integral-derivative-type (PID-type) laws, all of which are designed to improve the performance of dynamic systems [2, 3, 4]. Notably, ILC can deal with complicated systems with minimal prior knowledge, thanks to its simple algorithmic structure and independence of accurate systems dynamics. In the past few decades, the effectiveness of tracking performance with various ILC algorithms has been recognized in the aspects of theoretical developments. Benefiting from constructive algorithmic innovations, the ILC technique has been utilized in numerous applications [5, 6, 7, 8, 9, 10]. In particular, with the development of computer science, realization of existing efficacious ILCs has been executed in digital mode. This transition necessitates an effective method for handling the discrete-time ILC system's description and analytical techniques. In this regard, benefiting from the finite sampling instants of the ILC system, the lifting technique has been witnessed as one effective manner. In addition, the 2D method has been acknowledged as a powerful method [11]. With the development of ILC technology, ILC-based advanced control technologies have attracted a lot of attention, yielding a variety of new algorithms. [PERSON] and [PERSON] et al. first introduced the concept of a norm-optimal ILC (NOILC) algorithm based on the lifted model description for a class of linear time-varying systems [12; 13; 14; 15; 16]. The NOILC algorithm minimizes a quadratic objective function that contains the additive norms of the tracking error and adjacent iterative control input increments. Its control input for the next operation induces an optimized ILC updating law in a recursive form. However, the NOILC requires solving the Riccati equation for the compensation gain, which is challenging. To avoid such computation difficulty, [PERSON], [PERSON], and [PERSON] et al. proposed a parameter optimization ILC (POILC) using the lower-dimensional optimization for the linear discrete-time invariant systems while retaining the most important properties of the NOILC. The performance index is formulated using the linear quadratic norms of the tracking error and the learning gain, and the iteration-wise scalar gain of the D-type ILC scheme is assigned in the paper [17]. Additional POILC research has been conducted into optimization techniques for improvement of the convergence rate and robustness [18; 19; 20; 21; 22]. [PERSON] and [PERSON] et al. argued the existence and uniqueness of the optimized iteration time-variable learning-gain vector by sequentially minimizing the sum of the tracking error energy and the learning effort intensity, which is amplified by an iteration-wise tuning factor. In addition, they analyzed the strictly non-conditional monotone convergence of the optimized first-order and higher-order iterative learning control scheme [23]. Recently, with the rapid advancement of internet services and communications technologies, network control systems (NCSs) have been widely applied in smart grids, water/gas distribution, and modern public transportation systems.