An adaptive controller is proposed for unknown nonlinear discrete-time systems when the control direction is unknown and unfixed. Two fuzzy rules emulated networks are utilized to establish a system dynamic model which provides the control-gain and the control direction. The control law is developed according to the control direction including the following advantages: first, the relation between input and output of controlled plant cannot be generally Lipschitz with the zero-change of control effort; and second, the control direction is unfixed for both positive and negative values. Theoretical expressions are manifested to guarantee the convergence of model and tracking performance. The practical-validation is conducted by two experimental systems: first, dc motor current control for the case of fixed control direction and Lipschitz condition, and second, robotic system with opened architecture for the case of unfixed control direction and non-Lipschitz condition at constant input.

An adaptive control scheme based on data-driven controller (DDC) is proposed in this article. Unlike several DDC techniques, the proposed controller is constructed by an adaptive fuzzy rule emulated network (FREN) which is able to include human knowledge based on controlled plant's input–output signals within the format of IF-THEN rules. Regarding to this advantage, an on-line estimation of pseudo partial derivative (PPD) and resetting algorithms, which are commonly used by DDC, can be omitted here. Furthermore, a novel adaptive algorithm is introduced to minimize for both tracking error and control effort with stability analysis for the closed-loop system. The experimental system with brushed DC-motor current control is constructed to validate the performance of the proposed control scheme. Comparative results with conventional DDC and radial basis function (RBF) controllers demonstrate that the proposed controller can provide the less tracking error and minimize the control effort

A parallel structure of data input-output adaptive controllers is developed to control the 7-DOF robotic arm. This robotic system is considered as a class of unknown nonlinear discrete-time systems. The proposed controller is designed by an adaptive