This paper designs an Optimal Nonlinear Adaptive Excitation Controller (ONAEC) to enhance the stability of multi-machine power systems. First, the nonlinearities, parameter uncertainties, unmodelled dynamics and time-varying external disturbances of the synchronous generator are aggregated into a perturbation, which is estimated by a High-Gain Perturbation Observer (HGPO) in real-time. Then, the estimated perturbation is fully compensated by ONAEC and the optimal control parameters are obtained by Modified Salp Swarm Algorithm (MSSA). In addition, ONAEC has the advantages of simple structure and easy implementation, and it can achieve a globally consistent control performance by measuring only one state, e.g. rotor angle. Finally, two case studies, e.g., the three-phase short-circuit fault with nominal parameter and parameter uncertainties, are undertaken. Simulation results show that compared with Proportional-Integral-Derivative (PID) control and Feedback Linearization Control (FLC), ONAEC can achieve the best dynamic performance under various operational conditions and effectively restore the power system after failure. This work is supported by National Natural Science Foundation of China (No. 61963020).