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Systematic design of stable neural observers for a class of nonlinear systems

In this paper we present a new method to design an intelligent nonlinear observer for a class of systems with a single unknown static nonlinearity. The observer uses a neural network to represent the unknown characteristic of the nonlinearity. We propose an approach to prove stability during learning and parameter convergence for an adaptation law based on Lyapunov's stability theory. This method works even if the system states are not available for measurement, and only the system output is measurable. Therefore we achieve asymptotic tracking of the real state variables and at the same time stable learning of the nonlinearity.