This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.
Extracting maximum energy from photovoltaic (PV) systems at varying conditions is crucial. It represents a problem that is being addressed by researchers who are using several techniques to obtain optimal outcomes in real-life scenarios. Among the many techniques, Maximum Power Point Tracking (MPPT) is one category that is not extensively researched upon. MPPT uses mathematical models to achieve gradient optimisation in the context of PV panels. This study proposes an enhanced maximisation problem based on gradient optimisation techniques to achieve better performance. In the context of MPPT in photovoltaic panels, an equality restriction applies, which is solved by employing the Dual Lagrangian expression. Considering this dual problem and its mathematical form, the Nesterov Accelerated Gradient (NAG) framework is used. Additionally, since it is challenging to ascertain the step size, its approximate value is taken using the Adadelta approach. A basic MPPT framework, along with a DC-to-DC convertor, was simulated to validate the results.
International audienceIn this paper, a dynamic model of the PEMFC(polyelectrolyte membrane fuel cell) based on physical principles is built, in the form of a nonlinear statespace model. The Fuel Cell System (FCS) is a nonlinear system which is characterized by multiple variables and a strong coupling with profound dynamics. Therefore, it is difficult to apply control theory methods. For this reason, we have approximated the model of FCS by a Takagi-Sugeno Fuzzy model with fuzzy defined regions where the nonlinear system is locally linearized. The dynamics considered are: air compressor, supply and return manifold, anode and cathode flow, humidifier, cooler and stack voltage. Simulation results show that nonlinear system of PEM fuel cell can be approximated by a TS fuzzy model based on nonlinear sectors. The simulations show also that the supply and return manifold pressures and temperatures have significant effects on the dynamics of the PEMFC
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