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Actuators nonlinearities are unknown external perturbations in robots, which are unwanted because they can severely limit their performance. This research is focused on the stabilization of robots subject to actuators nonlinearities with a regulator containing the sigmoid mapping. Our regulator has the following three main characteristics: a) a sigmoid mapping is used to ensure boundedness of the regulator law terms, b) the chattering is reduced by the usage of the saturation mapping instead of the signum mapping, and c) the stabilization is ensured by the Lyapunov analysis. Finally, we evaluate our regulator for the stabilization of two robots.

The perturbations are the unwanted and unknown inlets in nonlinear plants which can affect the outlets. In this article, an estimator is studied for the variables and perturbations estimation in nonlinear plants. The saturation map is used in our estimator instead of the signum map to decrease the chattering, and we ensure the estimator convergence by the Lyapunov analysis. The conditions required by our estimator gains are found to reach the variables error convergence, and these gains are used for the perturbations estimation. An algorithm is proposed to choose the gains for achieving a satisfactory performance in our estimator. The studied estimator is applied for the variables and perturbations estimation in the gas turbine and gasification plants.

The modified backpropagation algorithm based on the backpropagation with momentum is used for the parameters updating of a radial basis mapping (RBM) network, where it requires of the best hyper-parameters for more precise modeling. Seeking of the best hyper-parameters in a model it is not an easy task. In this article, a genetic algorithm is used to seek of the best hyper-parameters in the modified backpropagation for the parameters updating of a RBM network, and this RBM network is used for more precise electricity consumption modeling in a city. The suggested approach is called genetic algorithm with a RBM network. Additionally, since the genetic algorithm with a RBM network starts from the modified backpropagation, we compare both approaches for the electricity consumption modeling in a city.

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