On approximate NN realization of an unknown dynamic system from its input-output history

This paper considers the problem of using input/output data to realize the dynamic equation for a continuous time nonlinear system. The issue is of paramount importance in control theory, particularly for adaptive output feedback control of unknown plants, when the measurement equation and its derivatives, due to uncertain dynamics, are unknown. Using the universal approximation property of Rumelhart-Hinton-Williams´ neural networks, theorems are proved establishing the “memory window length” for input(s) and output(s) for both SISO and MIMO systems, needed for approximate realization. This result can be used to solve output feedback problems for a class of nonlinear systems without the need for a state observer