State estimation based on projection observers applied to sequential treatment based on ozonation and aerobic biodegradation: Application for phenolic wastewaters

The adaptive linearization of dynamic nonlinear systems remains, in general, as an open problem due the complexities associated to the method required to derive the linear or quasi-linear model. The problem is even more difficult if the system is uncertain, that is, when the formal description of the plant is almost unknown considering that number of states is available. This chapter discusses an adaptive linearization method for perturbed nonlinear uncertain systems based on the application of special artificial neural networks. The proposal is based on no-parametric identifier and its convergence is analyzed using the second method of Lyapunov. The suggested structure preserves some inherited structural properties like controllability. The scheme was tested using three different set of activation functions: sigmoid, wavelets and Chevyshev polynomials. The proposed method shows a good transient performance and the identification goals are fulfilled. A distillation column was used to show how the identifier works.