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Synchronizing a network of robots in consensus is an important task for cooperative work. Detecting faults in a network of robots in consensus is a much more important task. In considering a formation of Wheeled Mobile Robots (WMRs) in a master–slave architecture modeled by graph theory, the main objective of this study was to detect and isolate a fault that appears on a robot of this formation in order to remove it from the formation and continue the execution of the assigned task. In this context, we exploit the extended Kalman filter (EKF) to estimate the state of each robot, generate a residual, and deduce whether a fault exists. The implementation of this technique was proven using a Matlab simulator.

This work deals with a physical one- and two-dimensional (1D and 2D) parameters estimation of a filtration process of slurry, the second stage of phosphoric acid manufacture. This study focuses on recursive least square and instrumental variable techniques applied to the (1D) and (2D) models. The model of the rotary drum filter is based on different physical laws involved in the filtration phase in order to get a simulator of the filtration process. Besides, many physical parameters rise in the system model and effect enormously the efficiency which should be modelled with precision such as permeability, porosity and viscosity. We use a constructive realization procedure for (2D) systems which may lead to a Fornasini–Marchesini local state-space model to describe the dynamic of the system states.

The presence of faulty valves has been studied in the literature with various machine learning approaches. The impact of using fault data only to train the system could solve the class imbalance problem in the machine learning approach. The data sets used for fault detection contain many independent variables, where the salient ones were selected using stepwise regression and applied to various machine learning techniques. A significant test for the given regression technique was used to validate the outcome. Machine learning techniques, such as decision trees and deep learning, are applied to the given data and the results reveal that the decision tree was able to obtain more than 95% accuracy and performed better than other algorithms when considering the tradeoff between the processing time and accuracy.