Adaptive Nonlinear Observer Design Using Feedforward Neural Networks

This paper concerns the design of a neural state observer for nonlinear dynamic systems with noisy measurement channels and in the presence of small model errors. The proposed observer consists of three feedforward neural parts, two of which are MLP universal approximators, which are being trained off-line and the last one being a Linearly Parameterized Neural Network (LPNN), which is being updated on-line. The off-line trained parts are able to generate state estimations instantly and almost accurately, if there are not catastrophic errors in the mathematical model used. The contribution of the on-line adapting part is to compensate the remainder estimation error due to uncertain parameters and/or unmodeled dynamics. A time delay term is also added to compensate the arising differential effects in the observer. The proposed observer can learn the noise cancellation property by using noise corrupted data sets in the MLP's off-line training. Simulation results in two case studies show the high effectiveness of the proposed state observing method.