Symmetry

This article delves into the fuzzy finite-time adaptive control problem for uncertain nonlinear systems where state measurements are unavailable, nonlinear functions are unknown, and communication is limited. To emulate the unknown nonlinear relationships within the control methodology, we exploit fuzzy logic systems, while also proposing a state observer to address the challenge of unobservable states. To avoid the “complexity explosion” problem intrinsic to conventional backstepping techniques, the controller is developed based on the dynamic surface control methodology, which incorporates first-order filters to successfully alleviate this issue. An event-triggered approach is introduced to alleviate the computational and communication overhead. By leveraging the finite-time control approach, an adaptive finite-time fuzzy control algorithm is constructed using the adaptive backstepping technique. An event-triggered mechanism is designed to reduce communication frequency, while rigorously maintaining closed-loop stability and ensuring a positive minimum inter-event time to avoid Zeno behavior. The proposed finite-time controller achieves finite-time stability of the controlled systems, thereby guaranteeing that all system signals remain bounded within a finite time, despite the presence of unmeasurable states, unknown nonlinear functions, and limited communication constraints. This paper differentiates itself from recent related studies by proposing a co-designed observer–controller framework that rigorously guarantees finite-time stability under an event-triggered communication mechanism, thereby effectively addressing the multiple concurrent challenges of state estimation, rapid convergence, and limited network resources. Simulation examples are conducted to illustrate the effectiveness and feasibility of the derived control algorithm.

Accurate short-term wind power forecasting plays a critical role in maintaining grid stability due to the inherently irregular and fluctuating nature of wind resources. Deep learning models such as LSTM, GRU, and CNN are widely used to learn temporal dynamics; however, their ability to capture or adapt to the underlying symmetries and asymmetries inherent in real-world wind energy data remains insufficiently explored. In this study, we evaluate and compare these models using authentic production and meteorological data from the Tokat Wind Farm in Türkiye. The forecasting scenarios were designed to reflect the temporal structure of the dataset, including seasonal patterns, recurrent behaviors, and the symmetry-breaking effects caused by abrupt changes in wind speed and operational variability. The results demonstrate that the LSTM model most effectively captures the temporal relationships and partial symmetries within the data, yielding the lowest error metrics (RMSE = 0.2355, MAE = 0.1249, MAPE = 25.16%, R² = 0.8199). GRU and CNN offer moderate performance but show reduced sensitivity to asymmetric fluctuations, particularly during periods of high variability. The comparative findings highlight how symmetry-informed model behavior—specifically the ability to learn repeating temporal structures and respond to symmetry-breaking events—can significantly influence forecasting accuracy. This study provides practical insights into the interplay between data symmetries and model performance, supporting the development of more robust deep learning approaches for real-world wind energy forecasting.

The system made by a charged particle interacting with a single electrostatic wave which propagates perpendicularly to the magnetic field, at a frequency larger than the cyclotron one, has been extensively studied in the literature due to its implications for ion heating in magnetized plasmas. It is known that a threshold in the electrostatic potential must be exceeded in order for stochastic particle motion and heating to occur. Regardless of its amplitude, however, the electrostatic wave induces a periodic oscillation in the particle motion. We show, by analytical and numerical arguments, that this dynamic is non-adiabatic, meaning that the particle does not land back in its initial state when the wave is slowly turned off. This way, particle energization (although not rigorous heating) occurs even under sub-threshold conditions.