This paper develops a data-based output feedback control method for a class of nonlinear systems, which have unknown mathematical models. The dynamic model of the system is assumed to be smooth, while the corresponding Jacobian matrices are constant matrices in each sampling period. We employ a zero-order hold and a fast sampling technique to sample and measure the output signal. When these measured data contain white noises, we use the least squares method to estimate the corresponding Jacobian matrices. The feedback gain matrix is calculated and adjusted adaptively in real time according to them. Theoretical analysis on the convergence condition is provided, and simulation results are used to demonstrate the feasibility of this method. methods need some prior knowledge about the system characteristics. There are some typical direct data-based control methods, such as iterative learning control [15][16][17], model-free adaptive control [18,19], virtual reference feedback tuning (VRFT) [20,21], and unfalsified control [22,23]. The iterative learning control method requires the system to perform the same task over a finite time interval repetitively. The model-free adaptive control method is suitable for the nonlinear systems, which have continuous partial derivatives with respect to control inputs, and it needs the systems to satisfy some generalized Lipschitz conditions. The VRFT method is usually applied to control discrete-time SISO systems, whose controller design problem is transformed into a parameter identification problem with the help of a virtual reference signal. The VRFT method assumes that the structure of the controller is known. The unfalsified control method recursively "falsifies" controllers that fail to satisfy a performance specification by using online I/O data.This paper develops a data-based output feedback control method for a class of nonlinear systems, which have unknown mathematical models. The dynamic model of the system is assumed to be smooth, while the corresponding Jacobian matrices are constant matrices in each sampling period. We employ a zero-order hold (ZOH) and a fast sampling technique to sample and measure the output signal. When these measured data contain white noises, we use the least squares method to estimate the corresponding Jacobian matrices. The feedback gain matrix is calculated and adjusted adaptively in real time accordingly. This control method only needs some basic prior knowledge about the system, while requiring no repeatability of the system behaviors. Besides, this method is also applicable to MIMO systems.Moreover, most existing nonlinear adaptive control methods generally fall into two broad categories: methods based on explicit knowledge of mathematical model structures and methods based on intelligent control theory. The first category consists of control methods with special requirements on the model structure [24][25][26], for example, lower triangular structure, nonlinear affine structure with respect to the input, and the structure of controlled pla...