In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N=9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N+5=14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N+4=13 intensity measurements.