# Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review
## 3 Neural Network-Based Forecasting Approaches
### ANN-Based Forecasting Approaches
In addition, the output feedback control algorithm was combined with an adaptive neural network, extended state observer, and nonlinear disturbance observer to estimate the unknown nonlinear dynamics, unmeasured states, and external disturbances [180]. In both works, a double-rod hydraulic servo system was chosen to validate the two control schemes' high-performance control effect. The authors also introduced a neuroadaptive learning method for disturbance rejection in constrained nonlinear systems. Moreover, the neural network adaptive control and the extended state observer to estimate endogenous uncertainties and external disturbances in real time and correct them feed-forwardly were presented in [181]. Further, the filtering problems and nonlinearity of the input were accounted for by adding an auxiliary system. Finally, the overall closed-loop stability was precisely ensured, and the accomplished control performance was validated by real-time nonlinear systems application results. Figure 4: Architecture of various neural networks. Another forecasting method known as delay-based ANN for predicting the turbulent flow temporal signals was proposed in [32]. These signals are obtained from a hot wire anemometer at a single point inside the cylinder to detect coherent structures. In [34], the authors presented the RBFNN model for forecasting the time series of the logistic map, Henon map, Mackey-Glass, and Duffing's systems. In [36], the researchers developed the recurrent predictor neural network model for predicting the annual and monthly sunspot time series. The experimental results of the proposed model are better than the Kalman filter and universal learning network in terms of accuracy and RMSE. The authors of [39] developed the KIII-chaotic neural network for forecasting the multistep time series data on a benchmark system. In [40], the researchers presented the RNN for predicting the electricity price of the power system. The work highlights that this approach is equally relevant to Chinese electrical market data. In [43], the authors presented the RBFNN model for forecasting the Henon map, Lorenz map, four real-time series discharge data, and sea-surface temperature anomaly data collected from various rivers. The work remarks that this presented model can also be used for geological time series. In [48], the authors raised the time delay neural network method for predicting the future behavior of the solar activity. In [51], the researchers demonstrated the BPNN to forecast the multistep nonlinear time series of the diode resonator circuit. From the presented work, it is to be noted that the approach can also be used in other chaotic time series. [PERSON] et al. presented the evolving RNN model for the Lorenz series, logistic, Mackey-Glass, and real-world sunspots series [53]. The experimental results of the proposed model showed to be better than the boosted RNN. [PERSON] and [PERSON] proposed an optimal BPNN model for time series of signal deviation in the stock market [55]. The proposed method is based on SVM and AR models. The experimental results of the proposed model showed better performance than the ARMA, RBFNN, and other models in terms of MAD. In [57], the authors developed the NARX neural network model for empirically predicting chaotic laser, variable bit rate, and video traffic time series of real-world datasets. The simulation results of the developed model reliably performed better than the Elman architectures. Further, the work highlights that this model can also be used for electric load forecasting, financial time series, and signal processing tasks. [PERSON] et al. developed an ANN model for predicting the stochastic generating sequences in a chaotic unimodal dynamical system [58]. It is observed that the presented strategy can also be further applicable for applications such as DNA-based groupings, protein structure arrangement, and financial market time series. The authors of [61] proposed an ensemble ANN model for forecasting the turning points in the Mackey-Glass system.