###### Abstract  
As technology evolves, more complex non-affine systems are created. These complex systems are hard to model, whereas most controllers require information on systems to be designed. This information is hard to obtain for systems with varying control directions. Therefore, this study introduces a novel data-driven estimator and controller tailored for single-input single-output non-affine discrete-time systems. This approach focuses on cases when the control direction varies over time and the mathematical model of the system is completely unknown. The estimator and controller are constructed using a Multiple-input Fuzzy Rules Emulated Network framework. The weight vectors are updated through the gradient descent optimization method, which employs a unique cost function that multiplies the error by a hyperbolic tangent. The stability analyses demonstrate that both the estimator and controller converge to uniformly ultimately bounded (UUB) functions of Lyapunov. To validate the results, we show experimental tests of force control that were executed on the z-axis of a drive-controlled 3D scanning robot. This system has a varying control direction, and we also provide comparison results with a state-of-the-art controller. The results show a mean absolute percentage tracking error smaller than one percent on the steady state and the expected variation in the system's control direction. m 2024 7 38 2024 2024 2024 2024 202  
results for systems with varying control directions. Hybrid methods have the popular iterative learning control (ILC) [13; 14] that is commonly used for systems with repetitive tasks. This method has the advantage of decreasing error in each cycle but requires a bit of prior knowledge of the system. These types of controllers have a common disadvantage: they need to know the control direction of the system. In 1983, [PERSON] [15] proposed a solution of adaptive control for systems where the control direction is unknown. His proposed controller could deal with the unknown control direction by adapting a control gain. The proposed function slowly adapts to the unknown control directions. It has been used to solve different problems such as those pertaining to non-affine systems [16; 17], non-linear systems [18], switched systems [19], reducing the computational cost [20; 21], industrial applications [22; 23], and time-varying control gain with no change in the sign [24]. Unfortunately, to the authors' knowledge, only a very few articles address the problem of systems with varying control directions (control gain with sign change) [25; 26]. Both articles use a Nussbaum-type function alongside fuzzy observers and controllers. Their focus is on affine non-linear systems; they only report simulation results to validate their theoretical analysis, and one of them does not present a graph of the control-related parameter estimation. Unlike affine systems, non-affine systems have a non-linear relation with the system output regarding the control input [27; 28; 29]. This property of the non-affine systems makes it very difficult to find an exact solution for them. Non-affine systems have countless applications such as active magnetic bearings, aircraft dynamics, biochemical processes, dynamic models in pendulum control, underwater vehicles, and so on [30; 31]. The common approach to controlling non-affine systems is adaptive control, which mostly involves neural networks where the control direction is either known or estimated with the Nussbaum gain [32; 33; 34]. Some of these systems also show time-varying sign behavior when we talk about the correlation between the output of the system and the control input. Therefore, our focus is the development of an adaptive controller for non-affine systems with time-varying control direction behavior. This work presents two significant contributions. First, we introduce a novel controller capable of effectively managing non-affine, non-linear discrete-time systems with varying control directions.