A process and neural network architecture for on-line adjustment of the weights of the neural network in a manner that corrects errors made by a nonlinear controller designed based on a model for the dynamics of a process under control. A computer system is provided for controlling the dynamic output response signal of a nonlinear physical process, where the physical process is represented by a fixed model of the process. The computer system includes a controlled device for responding to the output response signal of the system. The computer system also includes a linear controller for providing a pseudo control signal that is based on the fixed model for the process and provides a second controller, connected to the linear controller, for receiving the pseudo control signal and for providing a modified pseudo control signal to correct for the errors made in modeling the nonlinearities in the process. A response network is also included as part of the computer system. The response network receives the modified pseudo control signal and provides the output response signal to the controlled device. The second controller preferably is a neural network. The computer system may include a plurality of neural networks with each neural network designated to control a selected variable or degree of freedom within the system.