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A neural network (NN) implementation of an adaptive optimal stochastic output feedback control is developed to stabilize the resistive wall mode (RWM), a critically important instability in fusion machines like tokamaks. The design of an adaptive optimal stochastic output feedback control was discussed and reported earlier by Sun, Sen, and Longman. The system dynamics is experimentally determined via the extended least square method with an exponential forgetting factor and covariance resetting. The optimal output feedback controller is redesigned periodically online based on the system identification. The output measurements and past control inputs are used to construct new control inputs. These are achieved by an architecture of NNs consisting of a pool of sequentially linked Hopfield networks and implemented in hardware with digital NN processors made by the Accurate Automation Corporation. The simulations have shown that the NN adaptive output controller can stabilize the time-dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of the inverse of the nonlinear growth rate, which is the time scale of the development of the possibly dangerous levels of fluctuations. This stabilization is similar to that of the simulation with a C++ implementation. It is expected that significant gains can be achieved for the systems of a higher order, which are to be found in future fusion devices.