*** ABSTRACT 9660604 Mathia This Small Business Innovation Research Phase I project will develop a practical methodology for applying to real world engineering applications new nonlinear adaptive critic principals which incorporate recurrent neural networks. Accurate Automation has recently developed a powerful new theory which guarantees stable adaptive critic control systems. This theory describes certain properties that the subsystems of the adaptive critic algorithm (action, model, critic) and their associated learning algorithms must have to ensure stable control. Recurrent neural networks are a powerful tool which can be applied to realize these properties. We will apply our theory to the development of a theoretical and experimental basis for understanding adaptive critics with recurrent neural network subsystems. The algorithm will learn 'on-line' to control a highly nonlinear system, with stability guaranteed and optimal performance guaranteed in the limit. Phase I will result in prototype of a commercializable software system. In Phase II, we will develop special purpose hardware for sale. The adaptive critic under development in this research will be targeted specifically for application in aircraft, making the aircraft industry the most obvious commercial arena for this technology. Because the adaptive critic algorithm is very general, it will also have applications in any industry requiring good nonlinear controls. Examples of these industries are the chemical industry, the automobile industry, and the photocopier industry. ***