Multivariable time series forecasting is an important topic of machine learning, and it frequently involves a complex mix of inputs, including static covariates and exogenous time series input. A targeted investigation of this input data is critical for improving prediction performance. In this paper, we propose the fusion transformer (FusFormer), a transformer-based model for forecasting time series data, whose framework fuses various computation modules for time series input and static covariates. To be more precise, the model calculation consists of two parallel stages. First, it employs a temporal encoder–decoder framework for extracting dynamic temporal features from time series data input, which analyzes and integrates the relative position information of sequence elements into the attention mechanism. Simultaneously, the static covariates are fed to the static enrichment module, which is inspired by gated linear units, to suppress irrelevant information and control the extent of nonlinear processing. Finally, the prediction results are calculated by fusing the outputs of the above two stages. Using Mooney viscosity forecasting as a case study, we demonstrate considerable forecasting performance improvements over existing methodologies and verify the effectiveness of each component of FusFormer via ablation analysis, and an interpretability use case is conducted to visualize temporal patterns of time series. The experimental results prove that FusFormer can achieve accurate Mooney viscosity prediction and improve the efficiency of the tire production process.

Model-free adaptive controller (MFAC) is a novel data-driven control methodology that relies only on input/output (I/O) measurement data instead of classic mathematical models of actual controlled plants. The single-input single-output (SISO) compact-form MFAC (SISO-CFMFAC) is a promising method for controlling SISO nonlinear time-varying systems. The parameters in SISO-CFMFAC must be carefully tuned before use, as inappropriate parameters may lead to poor control performance. However, up to now, parameter tuning has been a time-consuming and laborious task. In this paper, a new approach called SISO-CFMFAC-LSTM is proposed for parameter self-tuning of SISO-CFMFAC based on long short-term memory (LSTM) neural network. To evaluate the performance of the proposed methodology, qualitative and quantitative comparisons with other existing control algorithms are carried out. Six individual performance indices, namely, the root mean square error (RMSE), the integral absolute error (IAE), the integral time-weighted absolute error (ITAE), the integral absolute variation of the control signal (IAVU), the maximum overshoot (MO), and the imprecise control ratio (ICR), are introduced for quantitative comparison. The experimental results demonstrate that the proposed SISO-CFMFAC-LSTM achieves the best performance in all indices, indicating that it is an effective control method for SISO nonlinear time-varying systems.

This article investigates the partial-form model-free adaptive control (MFAC) issue for a class of discrete-time nonlinear systems. An improved partial-form MFAC design named IPFMFAC-NN is proposed, where neural networks are introduced to enhance the control performance. With the excellent approximation ability of radial basis function (RBF) neural networks, the pseudo gradient (PG) values of control method can be directly approximated online using the measured input and output data of the controlled system. Besides, long short-term memory (LSTM) neural networks are used to tune the essential parameters of the control method online with system error set and gradient information set. Finally, the effectiveness and applicability are verified by SISO discrete nonlinear system simulation and three-tank system simulation, and experimental results demonstrate that the proposed method achieves the best control performance in all five indices. Especially compared with the partial-form MFAC, the proposed method reduces the RMSE index by 43.83% and 6.39%, respectively in two simulations, making it a promising control method for discrete-time nonlinear systems.

This study focuses on the full-form model-free adaptive controller (FFMFAC) for SISO discrete-time nonlinear systems, and proposes enhanced FFMFAC. The proposed technique design incorporates long short-term memory neural networks (LSTMs) and fuzzy neural networks (FNNs). To be more precise, LSTMs are utilized to adjust vital parameters of the FFMFAC online. Additionally, due to the high nonlinear approximation capabilities of FNNs, pseudo gradient (PG) values of the controller are estimated online. EFFMFAC is characterized by utilizing the measured I/O data for the online training of all introduced neural networks and does not involve offline training and specific models of the controlled system. Finally, the rationality and superiority are verified by two simulations and a supporting ablation analysis. Five individual performance indices are given, and the experimental findings show that EFFMFAC outperforms all other methods. Especially compared with the FFMFAC, EFFMFAC reduces the $RMSE$ by 21.69% and 11.21%, respectively, proving it to be applicable for SISO discrete-time nonlinear systems.