Abstract <p>Currently, there are a large number of tasks to be carried out by aircraft. The complicating factor in this case is incomplete and inaccurate knowledge of the properties of the object under investigation and the conditions in which it operates. In particular, during the flight may arise various abnormal situations such as equipment failures and structural damage that need to be remedied by reconfiguring the control system or controls of the aircraft. The aircraft control system should be able to work effectively in these conditions by rapidly changing the parameters and/or structure of the control laws. Adaptive control techniques allow this requirement to be met. One of the approaches to the synthesis of adaptive laws for dynamic systems control is the application of machine learning methods. The article proposes to use for this purpose one of the variants of the adaptive critic method, namely the J-SNAC scheme. The algorithm implemented by this scheme is considered. A distinctive feature of the proposed J-SNAC variant is the use of sigma-pi network to implement the critic included in this scheme. Data from the computational experiment carried out in relation to the lateral motion of a maneuverable aircraft demonstrates the efficiency and prospects of using sigma-pi-net in J-SNAC.</p>