This paper addresses the problem of enlarging the Domain of Attraction (DA) based on a Generalized Eigenvalue Problem (GEVP) approach. The main contribution is the maximization of the (DA) while characterizing the asymptotic stability region by a Lyapunov Function. Such result is obtained using a Genetic Algorithm (GA). A theoretical proof of the validity of the obtained domain is developed. An illustrative example ends the paper.

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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.