  Extreme Learning Machine (ELM) is an emerging learning paradigm for nonlinear
regression problems and has shown its effectiveness in the machine learning
community. An important feature of ELM is that the learning speed is extremely
fast thanks to its random projection preprocessing step. This feature is taken
advantage of in designing an online parameter estimation algorithm for
nonlinear dynamic systems in this paper. The ELM type random projection and a
nonlinear transformation in the hidden layer and a linear output layer is
considered as a generalized model structure for a given nonlinear system and a
parameter update law is constructed based on Lyapunov principles. Simulation
results on a DC motor and Lorentz oscillator show that the proposed algorithm
is stable and has improved performance over the online-learning ELM algorithm.
