Process gases play a crucial role in steelmaking, but various production factors limit their efficiency. Accurate and real-time forecasting of process gas flow is essential for recycling low-caloric gases, minimizing flaring, and enhancing overall energy efficiency. However, traditional forecasting models, such as recurrent statistical approaches, fail to capture the intricate spatiotemporal dependencies of process gases, leading to inaccurate predictions and excessive gas flaring. To address these challenges, we propose a constrained intelligent forecasting framework based on a novel Factorised Dilated Temporal Convolutional Network (FD-TCN). While classical TCNs leverage dilated convolution layers for capturing spatial–temporal information, they suffer from a fixed, task-independent dilation factor that skips important local dynamics of steelmaking processes. FD-TCN mitigates this issue by introducing a factorised dilation mechanism, enabling the efficient expression of diverse temporal patterns. Additionally, existing intelligent gas flow forecasting models seldom enforce system constraints on numerical flow rates, which often produce unrealistic predictions. Our approach integrates domain-specific constraints into the training process, eliminating out-of-range forecasts and improving reliability. We validated FD-TCN across single-variate and multi-variate gas flow forecasting tasks and generalised the method into gas production, gas in manufacturing consumption, and mixed gas recycling. The model achieved the lowest forecasting error and computation usage among the tested architectures. Compared to state-of-the-art deep learning models in process gases utilization, including long-short-term-memory (LSTM) and standard TCN, our constrained FD-TCN method demonstrated 39.7 % higher prediction accuracy in the challenging experiment and achieved a 7.5 × faster prediction time. Constrained FD-TCN presents an efficient, accurate and generalisable gas forecasting solution for energy-efficient industrial processes.

This paper investigates the voltage regulation problems in DC microgrids (DC-MGs) with nonlinear ZIP loads under malicious cyber-physical attacks, proposing an adaptive decentralized fully-actuated two-step control strategy rooted in the fully actuated system (FAS) approach. At first, a unified fully actuated distributed generation unit (FA-DGU) model is developed, integrating nonlinear load dynamics, renewable energy intermittency, attack-induced disturbances, and power line coupling into a lumped uncertainty framework. Then, a decentralized controller is designed using Radial Basis Function neural networks (RBFNNs) to adaptively approximate unknown ZIP load characteristics and attack-generated perturbations, eliminating dependence on communication networks while enabling plug-and-play (PnP) operations through purely local measurements. Following this, Lyapunov stability analysis rigorously proves the asymptotic convergence of voltage regulation errors at the point-of-common-coupling (PCC) under heterogeneous uncertainties. Finally, various uncertain scenarios in DC-MGs are simulated using MATLAB/Simulink, thereby verifying the feasibility and effectiveness of the proposed control method.

Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which significantly hinder accurate long-term forecasting. As a result, understanding long-term statistical behavior is far more valuable than focusing on short-term accuracy. While autoregressive deep sequence models have been applied to capture long-term behavior, they often lead to exponentially increasing errors in learned dynamics. To address this, we shift the focus from simple prediction errors to preserving an invariant measure in dissipative chaotic systems. These systems have attractors, where trajectories settle, and the invariant measure is the probability distribution on attractors that remains unchanged under dynamics. Existing methods generate long trajectories of dissipative chaotic systems by aligning invariant measures, but it is not always possible to obtain invariant measures for arbitrary datasets. We propose the Poincaré Flow Neural Network (PFNN), a novel operator learning framework designed to capture behaviors of chaotic systems without any explicit knowledge of the invariant measure. PFNN employs an auto-encoder to map the chaotic system to a finite-dimensional feature space, effectively linearizing the chaotic evolution. It then learns the linear evolution operators to match the physical dynamics by addressing two critical properties in dissipative chaotic systems: (1) contraction, the system’s convergence toward its attractors, and (2) measure invariance, trajectories on the attractors following a probability distribution invariant to the dynamics. Our experiments on a variety of chaotic systems, including Lorenz systems, Kuramoto-Sivashinsky equation and Navier–Stokes equation, demonstrate that PFNN has more accurate predictions and physical statistics compared to competitive baselines including the Fourier Neural Operator and the Markov Neural Operator.

Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property — ergodicity on their attractors, which makes long-term prediction possible. State-of-the-art methods address ergodicity by preserving statistical properties using optimal transport techniques. However, these methods face scalability challenges due to the curse of dimensionality when matching distributions. To overcome this bottleneck, we propose a scalable transformer-based framework capable of stably generating long-term high-dimensional and high-resolution chaotic dynamics while preserving ergodicity. Our method is grounded in a physical perspective, revisiting the Von Neumann mean ergodic theorem to ensure the preservation of long-term statistics in the $\mathcal{L}^2$ space. We introduce novel modifications to the attention mechanism, making the transformer architecture well-suited for learning large-scale chaotic systems. Compared to operator-based and transformer-based methods, our model achieves better performances across five metrics, from short-term prediction accuracy to long-term statistics. In addition to our methodological contributions, we introduce new chaotic system benchmarks: a machine learning dataset of 140$k$ snapshots of turbulent channel flow and a processed high-dimensional Kolmogorov Flow dataset, along with various evaluation metrics for both short- and long-term performances. Both are well-suited for machine learning research on chaotic systems.

Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it faces high computational costs in complex nonlinear systems and depends on imperfect state-observation mappings. Deep learning (DL) offers more expressive approximators, while integrating DL models into 4D-Var is challenging due to their nonlinearities and lack of theoretical guarantees in assimilation results. In this paper, we propose \textit{Tensor-Var}, a novel framework that integrates kernel conditional mean embedding (CME) with 4D-Var to linearize nonlinear dynamics, achieving convex optimization in a learned feature space. Moreover, our method provides a new perspective for solving 4D-Var in a linear way, offering theoretical guarantees of consistent assimilation results between the original and feature spaces. To handle large-scale problems, we propose a method to learn deep features (DFs) using neural networks within the Tensor-Var framework. Experiments on chaotic systems and global weather prediction with real-time observations show that Tensor-Var outperforms conventional and DL hybrid 4D-Var baselines in accuracy while achieving a 10- to 20-fold speed improvement.

This article investigates the observer-based adaptive decentralized control problem for a class of uncertain interconnected nonlinear fully actuated systems (FAS), considering nonsmooth actuator dynamics including actuator failures and unknown control gains. Based on the dynamic gain scaling technique, a dynamic state observer is constructed. By utilizing the high-order FAS (HOFAS) approach, an adaptive decentralized output feedback controller is designed and a closed-loop structure of the fully actuated subsystems is derived. This structure takes actuator loss of effectiveness, unknown control gains, and unstructured uncertainties into account in the interconnected time-delay subsystems. By selecting suitable Lyapunov-Krasovskii (L-K) functionals, the time-delay terms can be removed, ensuring that all signals of the overall closed-loop system converge to a bounded region. Finally, two simulation examples validate the efficacy of the proposed strategy.

Coupling, as an important characteristic of cyber-physical systems (CPS), brings opportunities and challenges to the control and application of industrial systems. This article mainly analyses the role of the cyber layer in the process of controlling the physical layer and gives a security state assessment method for the CPS after the Denial-of-Service (DoS) attack. First, we develop an advanced CPS coupling model that intricately captures the interactions between the physical and cyber layers, emphasizing both data and topology coupling. Unlike existing models that often overlook these aspects, our model offers a more comprehensive understanding of the complex interdependencies within CPS. Second, we propose a unique method for partitioning network layer nodes based on the physical layer's control requirements. Unlike traditional approaches that treat network layer nodes as homogeneous, our method categorizes nodes into sensor, controller, and actuator areas, each with distinct roles in the control process. This differentiation ensures that data flow within the network layer follows a fixed and logical direction, enhancing the overall system efficiency and reliability. Third, we introduce a security state evaluation factor that leverages the network layer partitioning to assess the system's resilience under cyber-attacks. This evaluation provides a detailed analysis of the system's security status, ensuring that potential vulnerabilities are identified and mitigated. Together, these innovations contribute to a more robust and practical framework for CPS design and analysis, with significant implications for enhancing system security and performance in real-world applications.