Sufficient information about system dynamics and inner states is often unavailable to aerospace system controllers, which requires model-free and output feedback control techniques, respectively. This paper presents a novel self-learning control algorithm to deal with these two problems by combining the advantages of heuristic dynamic programming and incremental modeling. The system dynamics is completely unknown and only input/output data can be acquired. The controller identifies the local system models and learns control polices online both by tuning the weights of neural networks. The novel method has been applied to a multi-input multi-output nonlinear satellite attitude tracking control problem. The simulation results demonstrate that, compared with the conventional actor-critic-identifier-based heuristic dynamic programming algorithm with three networks, the proposed adaptive control algorithm improves online identification of the nonlinear system with respect to precision and speed of convergence, while maintaining similar performance compared to the full state feedback situation.