The paper presents complex adaptive non-linear systems with one input and one output which are based on dynamic inversion. Linear dynamic compensator makes the stabilization command of the linearised system using as input the difference between closed loop system's output and the reference model's output (command filter). The state vector of the linear dynamic compensator, the output and other state variables of the control system are used for adaptive control law's obtaining; this law is modeled by a neural network. The aim of the adaptive command is to compensate the dynamic inversion error. Thus, the command law has two components: the command given by the linear dynamic compensator and the adaptive command given by the neural network. For estimation the dynamic compensator's state, the non-linear adaptive controller may have a linear reduced order observer. As control system one chooses the non-linear model of helicopter's dynamics in longitudinal plain. The reference model is linear. One obtains the structure of the adaptive control system of the pitch angle and Matlab/Simulink models of the adaptive command system's subsystems. Using these, some characteristics families are obtained. These describe the adaptive command system's dynamics with linear or non-linear actuator.