Adaptive observer design based on scaling and neural networks

Some works based on neural networks have been proposed to estimate adaptively the states of uncertain systems. However, they are subject to several conditions such as previous knowledge of upper bounds for the weight and approximation errors, ideal switching, and previous sample data for an off-line learning phase, which difficult their application. In this paper, an adaptive observer for uncertain nonlinear systems in the presence of disturbances is proposed in order to avoid the above mentioned limitations. Based on a neural Luenberger-like observer, scaling and Lyapunov theory, an adaptive scheme is proposed to make ultimately bounded the on-line observer error. Besides, it is shown that the scaling of unknown nonlinearities, previous to the neural approximation, has a positive impact on performance and application of our algorithm, since it allows the residual state error manipulation without any additional linear matrix inequality solution. To validate the theoretical results, the state estimation of the Rössler oscilator system is performed.