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In previous investigations, the nonlinear hypothesis use the linear bounded maps. Nonlinear hypothesis are described as the combination of the first order terms, and after of the mentioned combination, one bounded map is applied to alter the result. This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis and second order nonlinear hypothesis and their goal is to improve the second order processes modeling. The proposed nonlinear hypothesis are described as the combination of the first order and second order terms. Since the delta parallel robot is a second order process, it is an excellent platform to prove the effectiveness of the two proposed hypothesis. INDEX TERMS Novel nonlinear hypothesis, second order nonlinear hypothesis, nonlinear hypothesis, delta parallel robot.

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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.

In this article, a fuzzy logic model is proposed for more precise hourly electrical power demand modeling in New England. The issue that exists when considering hourly electrical power demand modeling is that these types of plants have a large amount of data. In order to obtain a more precise model of plants with a large amount of data, the main characteristics of the proposed fuzzy logic model are as follows: (1) it is in accordance with the conditions under which a fuzzy logic model and a radial basis mapping model are equivalent to obtain a new scheme, (2) it uses a combination of the descending gradient and the mini-lots approach to avoid applying the descending gradient to all data.

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.

In this research, a proportional integral derivative regulator, a first-order sliding-mode regulator, and a second-order sliding-mode regulator are compared, for the regulation of two different types of mathematical model. A first-order sliding-mode regulator is a method where a sign-mapping checks that the error decays to zero after a convergence time; it has the problem of chattering in the output. A second-order sliding-mode regulator is a smooth method to counteract the chattering effect where the integral of the sign-mapping is used. A second-order sliding-mode regulator is presented as a new class of algorithm where the trajectory is asymptotic and stable; it is shown to greatly improve the convergence time in comparison with other regulators considered. Simulation and experimental results are described in which an electric oven is considered as a stable linear mathematical model, and an inverted pendulum is considered as an asymmetrical unstable non-linear mathematical model.