ELMAN Neural Network with Modified Grey Wolf Optimizer for Enhanced Wind Speed Forecasting

The scope of this paper is to forecast wind speed. Wind speed, temperature, wind direction, relative humidity, precipitation of water content and air pressure are the main factors make the wind speed forecasting as a complex problem and neural network performance is mainly influenced by proper hidden layer neuron units. This paper proposes new criteria for appropriate hidden layer neuron unit’s determination and attempts a novel hybrid method in order to achieve enhanced wind speed forecasting. This paper proposes the following two main innovative contributions 1) both either over fitting or under fitting issues are avoided by means of the proposed new criteria based hidden layer neuron unit’s estimation. 2) ELMAN neural network is optimized through Modified Grey Wolf Optimizer (MGWO). The proposed hybrid method (ELMAN-MGWO) performance, effectiveness is confirmed by means of the comparison between Grey Wolf Optimizer (GWO), Adaptive Gbest-guided Gravitational Search Algorithm (GGSA), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Cuckoo Search (CS), Particle Swarm Optimization (PSO), Evolution Strategy (ES), Genetic Algorithm (GA) algorithms, meanwhile proposed new criteria effectiveness and precise are verified comparison with other existing selection criteria. Three real-time wind data sets are utilized in order to analysis the performance of the proposed approach. Simulation results demonstrate that the proposed hybrid method (ELMAN-MGWO) achieve the mean square error AVG ± STD of 4.1379e-11 ± 1.0567e-15, 6.3073e-11 ± 3.5708e-15 and 7.5840e-11 ± 1.1613e-14 respectively for evaluation on three real-time data sets. Hence, the proposed hybrid method is superior, precise, enhance wind speed forecasting than that of other existing methods and robust.

Fuzzy adaptive tracking control within the full envelope for an unmanned aerial vehicle

Motivated by the autopilot of an unmanned aerial vehicle（UAV） with a wide flight envelope span experiencing large parametric variations in the presence of uncertainties, a fuzzy adaptive tracking controller（FATC） is proposed. The controller consists of a fuzzy baseline controller and an adaptive increment, and the main highlight is that the fuzzy baseline controller and adaptation laws are both based on the fuzzy multiple Lyapunov function approach, which helps to reduce the conservatism for the large envelope and guarantees satisfactory tracking performances with strong robustness simultaneously within the whole envelope. The constraint condition of the fuzzy baseline controller is provided in the form of linear matrix inequality（LMI）, and it specifies the satisfactory tracking performances in the absence of uncertainties. The adaptive increment ensures the uniformly ultimately bounded（UUB） predication errors to recover satisfactory responses in the presence of uncertainties. Simulation results show that the proposed controller helps to achieve high-accuracy tracking of airspeed and altitude desirable commands with strong robustness to uncertainties throughout the entire flight envelope.

Lower estimation of approximation rate for neural networks

Let SFd and ∏φ,n,d ={∑j^n=1bjφ（wj.x＋θj）：bj,θj∈R,wj∈R^d} be the set of periodic and Lebesgue＇s square-integrable functions and the set of feedforward neural network （FNN） functions, respectively. Denote by dist （SFd , ∏φ,n,d） the deviation of the set SFd from the set ∏φ,n,d. A main purpose of this paper is to estimate the deviation. In particular, based on the Fourier transforms and the theory of approximation, a lower estimation for dist （SFd and ∏φ,n,d） is proved. That is, dist（SFd and ∏φ,n,d） ≥C/（nlog2n）1/2. The obtained estimation depends only on the number of neuron in the hidden layer, and is independent of the approximated target functions and dimensional number of input. This estimation also reveals the relationship between the approximation rate of FNNs and the topology structure of hidden layer.