In modern realities, the principle of adaptability becomes an absolute necessity for the normal functioning of complex technical systems. To achieve adaptability, controller synthesis can be based both on the classical theory of automatic control and using various approximate methods of intelligent control. This paper analyzes publications from 2014 to 2024 on new approaches to the design of adaptive control systems for various moving objects with a drive actuator. The first part of the review is devoted to classical methods, including the adaptive controller with a reference model, and its new areas of application in technology (control of a vibration machine and a Stuart platform). The similarities between classical adaptive control and machine learning are noted. The second part presents the results of research based on the joint use of a classical controller and various intelligent methods, such as fuzzy logic, neural networks and machine learning, forming complex multi-component control structures. The results show that the use of such an integrated approach can significantly improve the performance of the main controller, expanding its adaptive capabilities with respect to uncertainties and parameter changes, disturbances and the effects of nonlinearities.