In this paper, a neural-network (NN) observer-based optimal control solution for unknown nonlinear systems with control constraints using adaptive dynamic programming (ADP) is considered. First, to confront the unknown system, a NN observer is designed to estimate system states. Second, to deal with the control constraints, a quasi-norm performance index function is introduced. Third, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In the design, two NNs are used: a feedforward NN to constitute the NN observer which is applied to obtain the states, and a critic NN to approximate the value function. Finally, by using Lyapunov's direct method, uniform ultimate boundedness (UUB) stability of the NN observer-based control system is proved.