This paper presents a constrained optimization-based neuro-adaptive control (CONAC) for nonlinear synchronous machines (SMs) under voltage constraints, which allows to control the completely unknown electrical drive system, after a brief learning phase with very satisfactory control performance. The artificial neural network (ANN) in the proposed neuro-adaptive controller (NAC) learns online and empowers the controller to handle parameter uncertainties. Moreover, it solves a constrained optimization problem which allows to consider the nonlinear voltage constraints as well, by deriving the adaptation laws of the ANN’s weights from the Lagrangian function. Boundedness of tracking error, convergence of the ANN weights, and satisfaction of the constraints are guaranteed by Lyapunov theory. Numerical simulations in combination with a realistic (nonlinear) synchronous machine drive demonstrate the effectiveness and robustness against parameter and modeling uncertainties of the proposed NAC and its very acceptable constraints handling.