In this paper, a Takenaka-Malmquist (TM) basis function based equivalent data-model is established by an adaptive rational decomposition for the finite-time interval trajectory tracking control and real-time control of a class of nonlinear systems in the frequency domain. This data model can adaptively learn and match the control process of nonlinear systems. As a result, the proposed trajectory tracking as well as real-time control method can reflect the feature of adaptive learning in order-by-order decomposition, and the feasibility of the proposed method is guaranteed by the convergence of adaptive decomposition by TM basis function under the maximum selection principle (MSP) in Hardy space $H^{2}(\mathbb {D})$ . Compared with the traditional model-free control method, this data learning model which matches the control process has obvious advantages in the system model expression and control accuracy. Simulation results at the end of this paper show the effectiveness of the proposed method.