In recent years, wind speed forecasting is considered as a challenging task required for the prediction of wind energy resources. As a highly varying data, wind speed time series requires highly nonlinear temporal features for the prediction tasks. However, most forecasting approaches apply shallow supervised features extracted using architectures with few nonlinear hidden layers. Moreover, the exact features captured in such methodologies cannot decrease the wind data uncertainties. In this paper, an interval probability distribution learning (IPDL) model is proposed based on Restricted Boltzmann Machines and Rough Set Theory to capture unsupervised temporal features from the wind speed data. The proposed model contains a set of interval latent variables tuned to capture the probability distribution of wind speed time series data using contrastive divergence with Gibbs sampling. A real-valued interval deep belief network (IDBN) is further designed employing a stack of IPDLs with a fuzzy type II inference system (FT2IS) for the supervised regression of future wind speed values. In order to automatically learn meaningful unsupervised features from the underlying wind speed data, real-valued input units are designed inside IDBN to better approximate the wind speed probability distribution function compared to classic DBNs. The high generalization capability of our unsupervised feature learning model incorporated with the robustness of IPDLs and FT2IS leads to accurate predictions. Simulation results on the Western Wind Dataset reveal significant performance improvement in 1-hr up to 24-hr ahead predictions compared to single-model approaches including both shallow and deep architectures, as well as recently proposed hybrid methodologies.

In this paper, a novel approach is proposed for adjusting the position of a magnetic levitation system using projection recurrent neural network-based adaptive backstepping control (PRNN-ABC). The principles of designing magnetic levitation systems have widespread applications in the industry, including in the production of magnetic bearings and in maglev trains. Levitating a ball in space is carried out via the surrounding attracting or repelling magnetic forces. In such systems, the permissible range of the actuator is significant, especially in practical applications. In the proposed scheme, the procedure of designing the backstepping control laws based on the nonlinear state-space model is carried out first. Then, a constrained optimization problem is formed by defining a performance index and taking into account the control limits. To formulate the recurrent neural network (RNN), the optimization problem is first converted into a constrained quadratic programming (QP). Then, the dynamic model of the RNN is derived based on the Karush-Kuhn-Tucker (KKT) optimization conditions and the variational inequality theory. The convergence analysis of the neural network and the stability analysis of the closed-loop system are performed using the Lyapunov stability theory. The performance of the closed-loop system is assessed with respect to tracking error and control feasibility.