9521673 Lewis This project will investigate investigate neural network, (NN), for control of nonlinear dynamical systems. Its objective is to provide a framework for repeatable design of stable NN controllers for large classes of nonlinear systems. It will use nonlinear stability theory (e.g. input -output stability and passivity notions introduced in the 60's by one of the PIs) to study approximation properties of NN, with emphasis on guaranteeing NN controller performance in terms of small tracking errors and bounded NN weights (implying bounded inputs). Re eatable design algorithms will be given for NN controllers. Without guaranteed for performance and sensible design algorithms, NN controller s will rightfully not be accepted bye the control system community or US industry. NN controllers have the potential to significantly improve manufacturing process control in the US, since they are model-free and do not require explicit dynamics of the plant. The UTA work will be done at the Automation and robotics Research Institute (ARRI), so that technology transfer to industry will occur. The NN controllers developed will be implemented on the Flexibly-Link Systems Testbed, and then installed on the Manufacturing Surface Finishing Station. The ARRI Surface Finishing Consortium has offered matching money to finance the extensive technical work needed for this industrial application. ARRI Manager J. M. Fitzgerald, PE, and Dr. Kai Liu will be assigned on a matching fund basis to supervise this project.