Soft Comput DOI 10.1007/s00500-016-2349-x METHODOLOGIES AND APPLICATION Adaptive iterative learning control based on IF–THEN rules and data-driven scheme for a class of nonlinear discrete-time systems Chidentree Treesatayapun 1 © Springer-Verlag Berlin Heidelberg 2016 Abstract An adaptive iterative learning controller (ILC) is designed for a class of nonlinear discrete-time systems based on data driving control (DDC) scheme and adaptive networks called fuzzy rules emulated network (FREN). The proposed control law is derived by using DDC scheme with a com- pact form dynamic linearization for iterative systems. The pseudo-partial derivative of linearization model is estimated by the proposed tuning algorithm and FREN established by human knowledge of controlled plants within the format of IF–THEN rules related on input–output data set. An on-line learning algorithm is proposed to compensate unknown non- linear terms of controlled plant, and the controller allows to change desired trajectories for other iterations. The perfor- mance of control scheme is verified by theoretical analysis under reasonable assumptions which can be held for a general class of practical controlled plants. The experimental system is constructed by a commercial DC motor current control to confirm the effectiveness and applicability. The comparison results are addressed with a general ILC scheme based on DDC. Keywords Iterative learning control · Data-driven control · Discrete-time systems · Adaptive control · DC motor · Neuro-fuzzy Communicated by V. Loia. B Chidentree Treesatayapun treesatayapun@gmail.com; chidentree@cinvestav.edu.mx 1 Department of Robotic and Advanced Manufacturing, CINVESTAV-Saltillo, 25900 RamosArizpe, Mexico 1 Introduction In 1980s, the control algorithm, which can be applied for tracking control problems of a finite time interval repeatable task, has been proposed in Arimoto et al. (1984). This kind of controller has been defined as iterative learning control (ILC). Recently, ILC schemes have been wildly developed for dynamic systems with repetitive operation cycles over a fixed time interval tasks which have been considered in most of the industrial applications (Choi and Lee 2000; Tayebi 2004). Furthermore, all exogenous signals such as references, disturbance and noise have been assumed to be identical from trial to trial for designing ILC schemes. The introduction of additional nonrepeating exogenous signals has been developed for controllers to achieve high perfor- mance (Helfrich et al. 2010) under the accuracy of controlled plant transfer function and mathematical model. Regarding the existing strong nonlinearity and unknown uncertainty of application plants, the accurate model of controlled plants is difficult to be reckoned (Wang et al. 2007). To avoid the requirement of controlled plant mathematical model, the data-driven control (DDC) schemes have been proposed by using only the set of input–output data which can be mea- sured and stored for the historical algorithm (Hou and Wang 2013; Zhu and Hou 2014; Treesatayapun 2015; Hou and Jin 2011). The combination schemes between ILC and DDC have been proposed in Chi et al. (2014) for the practical systems without any requirement of plant’s mathematical model and repeatable exogenous signals. In general, the identical initial condition has been required to design ILC based on DDC Chi et al. (2015) to achieve a perfect tracking performance. Fur- thermore, the accuracy of pseudo-partial derivative (PPD) can effect the performance of control systems; thus, the learning gain for tuning PPD has been developed in Chi 123