Feedback Stabilization Using Two-Hidden-Layer Nets

This paper concerns itself with the global stabilization of nonlinear systems by means of state feedback laws which can be implemented using feedforward neural networks. The objective here is not to provide a practical stabilization technique, but rather to explore the capabilities and the ultimate limitations of alternative network architectures. It is shown that, contrary to what might have been expected from the well-known representation theorems, three-layer (also called "single hidden layer") nets are not sufficient for stabilization, but four-layer nets are enough ¿ assuming that threshold processors are used.