# An Experience Transfer Approach for the Initial Data of Iterative Learning Control
## 1 Introduction  
Iterative learning control (ILC) is a control method that is suitable for the repetitive control processes, such as reciprocating robot manipulator and multi-batch chemical production processes. In each of these tasks, the system is required to perform the same task over and over again. The learning process uses information from previous repetitions to improve the control data for the current repetition. It can efficiently track a desired trajectory for an uncertainty nonlinear dynamic system without requiring the mathematics model of the system. So, ILC is a model-free data-driven control method. Additionally, it has important practical value for high-precision industrial control systems without an accurate mathematic model [1; 2]. After more than 40 years of development, ILC have made many important achievements in theoretical research [3; 4; 5] and practical applications [6; 7; 8]. The premise of ILC is that the parameters, desired trajectory and initial state of the system must remain unchanged for all repetitive periods [9]. However, if the premise cannot be strictly met, methods should be discovered to expand the scope of application of the ILC, or continue to use the control data obtained from the previous iterative learning, and avoid relearning from the beginning; this is the focus of many scholars in this field. For the situations in which the desired trajectory is not strictly consistent or there is an initial state deviation, [PERSON] proposed to use an extended state observer to estimate the non-strict repetitive disturbance and cancel its influence in advance. It made ILC applicable to the system with limited disturbance [10]. [PERSON] proposed an iterative learning algorithm with initial correction effect and final state attraction, which effectively solved the problem of trajectory deviation in the case of fixed deviation between the iterative initial state and the desired initial state [11]. [PERSON] proposed a flexible ILC for systems with similar desired trajectories by means of Cartesian product [12]. [PERSON] proposed gradient-based norm optimal ILC for unmanned aerial vehicles to cope with exogenous disturbances caused by wind gusts [13]. [PERSON] developed a distributed controller to solve the leader-follower consensus of multiple flexible manipulators with uncertain parameters, unknown disturbances, and actuator dead zones, in which iterative learning is used to handle the repeatable disturbances [14]. All the above studies mainly focus on tracking the trajectory with certain deviation or disturbance. There is no pre-adjustment of the ILC experience data according to the deviation or disturbance. In iterative learning control, the initial iteration control data are usually set to zero or a constant. Once the controlled system or the desired trajectory changes, ILC needs to relearn from the beginning. As a result, in many high-precision machining processes, the original ILC experience is no longer applicable in the situations like a component is replaced, or the working environment changes, or the desired trajectory is adjusted. So ILC needs to go through many turns of learning again. In this process, a large amount of waste will be generated, leading to serious loss of time, materials and energy. Therefore, the research of inheriting the learning experience of former ILC in the new working conditions becomes a very necessary problem. Some researches tried to inherit the experience of former ILC as the initial data of new ILC process when the desired trajectory changes. [PERSON] designed a direct learning control method according to the proportional relationship between the new desired trajectory and the former desired trajectory in the amplitude axis and time axis, respectively [15; 16]. After transforming the former ILC control data on the amplitude axis and time axis, it is used as the initial iterative control data of the new desired trajectory.