Output-based modeling of catalytic ozonation by differential neural networks with discontinuous learning law

The aim of this study was to develop an adaptive state estimator with discontinuous parameter adjustment law for the catalytic ozonation system. A nonlinear transformation defined an equivalent system presented in chain-of-integrators form with uncertain structure in the dynamics of the last state. A step-by-step state estimator using a sequence of super-twisting algorithms (STAs) estimated the unmeasured states of the uncertain system. A class of differential neural network (DNN) with discontinuous learning law served to estimate the uncertain section of the catalytic process. The learning method was developed by implementing a strong lower-semi-continuous Lyapunov function. The method used to generate the laws that adjusted the weights, also yields the estimation of the parameters included in the catalytic ozonation system. A set of numerical simulations demonstrated the application of the DNN-based state observer to solve the estimation of the non-measurable information in the catalytic ozonation system. The available output signal was the concentration of the ozone gas at the output of the reactor. This was the only information used by the observer. The state estimator with discontinuous learning laws was also evaluated with experimental information obtained by a catalytic ozonation system using NiO as catalyst and phtalic acid as model contaminant. The effect of aggregating the DNN in the observer structure was compared with the observer using only the sequence of STA. The superior performance of the observer developed in this study was confirmed by evaluating the mean square error of the identification error.