This paper formulates an adaptive fuzzy control approach for the overhead-crane positioning and anti-sway problem. The crane is treated as an underactuated nonlinear system with four states, one horizontal force input, and two controlled outputs: trolley position and load swing angle. The introductory part of the paper is extended with a crane-control-oriented literature overview that distinguishes open-loop input shaping and command smoothing, model-based feedback control, fuzzy and LMI-based control, data-driven and model-free adaptive control , reinforcement learning, and machine-learning-based approaches. The control design is then developed from a compact Takagi–Sugeno fuzzy state-space representation of the nonlinear cart–pendulum crane dynamics. The fuzzy model is obtained by sector nonlinearity and local approximation in fuzzy partition spaces, resulting in two local rules scheduled by the load swing angle. A parallel-distributed fuzzy controller is parameterized as a linear-in-the-parameters control law, and its local parameters are adapted online by a teacher-based normalized least-mean-squares (LMS) rule. The adaptive controller learns the control signal of a virtual supervisory fuzzy controller and then remains active as the controller in the test phase. Projection, leakage regularization, force saturation, and a smooth transfer from the supervisory signal to the learned LMS signal are included to obtain an implementation-oriented closed-loop formulation. The proposed approach is intended as a physically interpretable bridge between robust fuzzy crane modeling and data-driven adaptive control.

The black-box domain adaptation (BBDA) topic is developed to address the privacy and security issues where only an application programming interface (API) of the source model is available for domain adaptations. Although the BBDA topic has attracted growing research attentions, existing works mostly target the vision applications and are not directly applicable to the time-series applications possessing unique spatio-temporal characteristics. In addition, none of existing approaches have explored the strength of foundation model for black box time-series domain adaptation (BBTSDA). This paper proposes a concept of Cross-Prompt Foundation Model (CPFM) for the BBTSDA problems. CPFM is constructed under a dual branch network structure where each branch is equipped with a unique prompt to capture different characteristics of data distributions. In the domain adaptation phase, the reconstruction learning phases in the prompt and input levels are developed. All of which are built upon a time-series foundation model to overcome the spatio-temporal dynamic. Our rigorous experiments substantiate the advantage of CPFM achieving improved results with noticeable margins from its competitors in three time-series datasets of different application domains.

Inverse fuzzy model control (IFMC) is an attractive strategy for regulating nonlinear thermal processes, where complex heat-transfer dynamics, disturbances, and actuator constraints challenge conventional control approaches. However, traditional direct and indirect inverse schemes often exhibit limited generalization and sensitivity to noise. This paper presents a data-driven inverse fuzzy control framework for temperature regulation in thermal systems, combining Takagi–Sugeno modeling, functional cancelation feedback, and auxiliary-input optimization. Gaussian antecedents and affine consequents are jointly identified via nonlinear least squares from input–output data generated by the theoretical PHE model. The same theoretical model is used as the numerical plant in all closed-loop simulations, whereas the forward and inverse fuzzy models are constructed only from the generated data and do not use the analytical PHE equations during identification or online inference. The learned inverse model estimates control actions that achieve the desired temperature trajectory while respecting actuator constraints. The method is evaluated in simulation on a plate heat exchanger (PHE) benchmark under tracking and disturbance-rejection scenarios. Results show accurate temperature regulation, smooth actuator behavior, and disturbance rejection in the tested scenarios. Compared with a numerically tuned PI baseline, the proposed approach reduces tracking RMSE by 27.5% and the standard deviation of the primary control current by 9.6% in the reported simulation scenario, indicating improved tracking and smoother primary actuation. In general, the proposed framework provides an interpretable and efficient solution for nonlinear thermal processes, with potential applications in energy systems, heat exchangers, and related thermal engineering technologies.

The paper presents a mechanistic model of an electric arc furnace (EAF), covering thermal, mass-transfer, and chemical processes. It represents a next step in the field of EAF modeling, building on the basis of our previous work; however, it incorporates substantial enhancements, including newly developed modules for heat and mass transfer, melting geometry, radiation, slag behavior, chemical reactions, off-gas dynamics, and arc-slag interactions. These improvements lead to inclusion of more EAF processes, their accurate representation, and higher calculation accuracy, thus resolving several limitations of the previous model. Furthermore, parameterization and validation of the model using EAF measurements have shown that the model prediction errors for bath temperatures are between 10 degrees C and 20 degrees C, the errors for bath and slag chemistry around 20%, while the off-gas composition and temperature errors are below 20%. These measures show that the model describes all crucial mechanisms of the EAF with sufficient detail, and can thus provide a useful tool for either process simulation, monitoring, or optimization.

This paper highlights the relevance of evolving granular fuzzy systems in adaptive control and fuzzy modeling, particularly for learning in dynamic, nonstationary environments. These systems incrementally construct rule-based models-such as predictors and controllers operating in open-or closed-loop configurations-by adapting both structure and parameters from data streams. This provides a flexible and autonomous alternative to tra ditional parametric-adaptive approaches. We consolidate foundational concepts in fuzzy and adaptive control, positioning evolving systems as data-driven extensions of classical schemes. Key challenges are discussed, includ ing safety-aware adaptation to drift, memory mechanisms, interpretability, and principled structural evolution. Building on these foundations, we develop a more mature formulation of the state-space evolving granular mod eling and control framework (SS-EGM/SS-EGC), introducing a decay-rate-oriented treatment that advances the methodology beyond mere LMI feasibility toward online optimality. A compact case study on the chaotic H & eacute;non map illustrates the approach: an online SS-EGM learned from data streams supports SS-EGC synthesis that sta bilizes the map under bounded inputs. One-step prediction accuracy and decay-rate estimates confirm real-time viability. The framework provides a flexible basis that can be further extended in multiple directions to address the identified challenges.

We propose a novel federated learning framework for multivariate regression, called Evolving Gaussian Federated Regression (eFedR), to address challenges in distributed data acquisition and privacy protection. Traditional clustering methods, requiring predefined clusters, struggle in federated settings with Non-IID data. To overcome this, we introduce an evolving approach using the Evolving Gaussian Clustering (eGauss+) algorithm, which dynamically adjusts clusters based on local data distributions. Each client performs local clustering, sharing cluster centers and covariance matrices with a central server, where they are merged using the eGauss+ method for global aggregation while preserving privacy. Experiments on synthetic datasets with nonlinear relationships demonstrate the framework’s high regression performance and effectiveness in privacy-preserving distributed learning.

This article proposes a new closed-loop control method to induce and maintain a desired depth of hypnosis during total intravenous anesthesia. The method utilizes two-degrees-of-freedom control, with propofol infusion rate as the input and bispectral index (BIS) as the output. A target-controlled infusion (TCI) algorithm called STANPUMP is used as the feedforward action to achieve the desired BIS response, and a feedback controller based on a Kalman filter deals with model uncertainties. Adding a TCI algorithm as the feedforward action improves the time-to-target and enhances patient safety. This is because it allows for a seamless transition to open-loop control if needed.

In the complex landscape of multivariate time series forecasting, achieving both accuracy and interpretability remains a significant challenge. This paper introduces the Fuzzy Transformer (Fuzzformer), a novel recurrent neural network architecture combined with multi-head self-attention and fuzzy inference systems to analyze multivariate stock market data and conduct long-term time series forecasting. The method leverages LSTM networks and temporal attention to condense multivariate data into interpretable features suitable for fuzzy inference systems. The resulting architecture offers comparable forecasting performance to conventional models such as ARIMA and LSTM while providing meaningful information flow within the network. The method was examined on the real world stock market index S&P500. Initial results show potential for interpretable forecasting and identify current performance tradeoffs, suggesting practical application in understanding and forecasting stock market behavior.

Evolving fuzzy systems build and adapt fuzzy models - such as predictors and controllers - by incrementally updating their rule-base structure from data streams. On the occasion of the 60-year anniversary of fuzzy set theory, commemorated during the Fuzz-IEEE 2025 event, this brief paper revisits the historical development and core contributions of classical fuzzy and adaptive modeling and control frameworks. It then highlights the emergence and significance of evolving intelligent systems in fuzzy modeling and control, emphasizing their advantages in handling nonstationary environments. Key challenges and future directions are discussed, including safety, interpretability, and principled structural evolution.

Although existing cross-domain continual learning approaches successfully address many streaming tasks having domain shifts, they call for a fully labeled source domain hindering their feasibility in the privacy constrained environments. This paper goes one step ahead with the problem of source-free cross-domain continual learning where the use of source-domain samples are completely prohibited. We propose the idea of rehearsal-free frequency-aware dynamic prompt collaborations (REFEREE) to cope with the absence of labeled source-domain samples in realm of cross-domain continual learning. REFEREE is built upon a synergy between a source-pre-trained model and a large-scale vision-language model, thus overcoming the problem of sub-optimal generalizations when relying only on a source pre-trained model. The domain shift problem between the source domain and the target domain is handled by a frequency-aware prompting technique encouraging low-frequency components while suppressing high-frequency components. This strategy generates frequency-aware augmented samples, robust against noisy pseudo labels. The noisy pseudo-label problem is further addressed with the uncertainty-aware weighting strategy where the mean and covariance matrix are weighted by prediction uncertainties, thus mitigating the adverse effects of the noisy pseudo label. Besides, the issue of catastrophic forgetting (CF) is overcome by kernel linear discriminant analysis (KLDA) where the backbone network is frozen while the classification is performed using the linear discriminant analysis approach guided by the random kernel method. Our rigorous numerical studies confirm the advantage of our approach where it beats prior arts having access to source domain samples with significant margins.

In this study, we present an Evolving Fuzzy System within the context of Federated Learning, which adapts dynamically with the addition of new clusters and therefore does not require the number of clusters to be selected apriori. Unlike traditional methods, Federated Learning allows models to be trained locally on clients' devices, sharing only the model parameters with a central server instead of the data. Our method, implemented using PyTorch, was tested on clustering and classification tasks. The results show that our approach outperforms established classification methods on several well-known UCI datasets. While computationally intensive due to overlap condition calculations, the proposed method demonstrates significant advantages in decentralized data processing.

In this paper, we propose a new measure for detecting overlap in multivariate Gaussian clusters. The aim of online learning from data streams is to create clustering, classification, or regression models that can adapt over time based on the conceptual drift of streaming data. In the case of clustering, this can result in a large number of clusters that may overlap and should be merged. Commonly used distribution dissimilarity measures are not adequate for determining overlapping clusters in the context of online learning from streaming data due to their inability to account for all shapes of clusters and their high computational demands. Our proposed dissimilarity measure is specifically designed to detect overlap rather than dissimilarity and can be computed faster compared to existing measures. Our method is several times faster than compared methods and is capable of detecting overlapping clusters while avoiding the merging of orthogonal clusters.

This paper presents a fuzzy model reference adaptive control method with an evolving structure. The approach builds on existing adaptive fuzzy controllers by enabling on-line addition of membership functions using a clustering-based mechanism. An additional stabilizing term inspired by sliding mode control is introduced to improve robustness. Two variations of this term are tested and compared. Simulation results on a nonlinear multi-tank system show good tracking performance, with the stabilizing term further improving control quality. The method is suitable for systems with changing dynamics and limited prior knowledge. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

In this article, we present a novel federated learning framework to multivariate regression problems, termed evolving Gaussian federated regression (eGauss+(FR)). The need for a federated approach is due to the increasing problem of distributed acquisition of the data and protection for the rights of distributing these data. Regression problems are usually nonlinear and, therefore, strongly connected to the clustering to divide the data space into smaller subspaces where a linear approximation could be applied. Here, we are faced with the main drawback of traditional clustering methods, where a predefined number of clusters are needed. In federated learning problems, where the data are commonly nonidentically distributed between different sources or clients, this represents a significant challenge. This problem can be overcome by introducing an evolving approach, which adds and removes the clusters on-the-fly. The idea in our approach is to use the incremental c-regression or c-varieties clustering methods to define the clusters, which lie close to the lines and describe them with the centers and the covariance matrices. The clustering is done for each data source or client. Due to the restriction and protection of data sharing, only the centers and the covariance matrices of all clients are then transmitted to main server and merged together, which is here done in a way as proposed in eGauss+ method. From merged clusters the auxiliary points are generated, which than serve to approximate the function by using classical fuzzy models. Our proposed method was demonstrated on simple synthetic data, while synthetic and real-world datasets were used to test time complexity and scalability with the number of clients. The results demonstrate the benefits of evolving federated method, which results in high-quality approximation of the function and can be easily extended to high-dimensional problems.

Accurate clustering of time series data is crucial for extracting meaningful insights from streaming sensor data in industrial applications. To address the challenges of dynamic and unlabeled data streams, we introduce Interval ERAL (iERAL), an enhancement of the Error in Aligned Series (ERAL) framework. iERAL is a time series alignment and averaging method designed for online analysis, incorporating an interval band to represent variance in the underlying data. We pair iERAL with an evolving time series clustering algorithm, capable of automatically detecting, adapting to, and merging clusters in real-time. This evolving approach enables the algorithm to dynamically adjust to new patterns, promote or demote clusters based on their relevance, and handle data variability with interval-based analysis. Unlike previous methods, our approach not only computes the time series prototype for each cluster but also provides a variance band for interval-based analysis. We demonstrate the effectiveness of our method by applying it to line pressure measurements in a real-world industrial setting. The algorithm achieves promising results in clustering unlabeled data streams, highlighting its potential for anomaly detection and adaptive monitoring of industrial processes in evolving operating conditions.

Data-driven modeling has become a predominant approach for learning and understanding systems. Models span a wide range of domains, including medical, health informatics, biological, environmental, meteorological, transportation, and economic systems, as well as complex dynamic virtual information, engineering, and hybrid systems. Computational intelligence techniques, including fuzzy systems, neural networks, evolutionary computation, and their hybridizations, are key driving forces in the current data-driven system modeling effort. This paper addresses data-driven fuzzy and neural modeling analytics and analyzes their performance in nonlinear dynamic systems modeling and prediction tasks. Data-driven fuzzy modeling and neural-based analytics are powerful paradigms that compete closely, often outperforming many alternative state-of-the-art methods, such as gradient boosting, kernel ridge regression, and Gaussian processes. In particular, the flexibility and approximation capabilities of data-driven fuzzy models, long-short-term memory, and convolutional neural networks are analyzed in two applications: (i) learning from a data stream produced by a synthetic nonlinear difference equation, and (ii) electricity load time series forecasting. The usefulness of the models is discussed in terms of their prediction accuracy and parametric complexity. In computational experiments, the recursive or incremental level-set fuzzy model provided both accuracy and interpretability with fewer parameters compared to the other methods, making it an attractive option for real-time modeling and forecasting tasks.

In this paper, we propose an unsupervised federated learning approach for evolving data stream clustering. One of the main challenges in federated clustering is selecting the number of clusters, as the data cannot be examined directly, and each client may have a distinct number of data clusters. Furthermore, data distributions in many real-world systems are not static but evolve over time due to changing environmental conditions, shifting processes, or behavioral patterns. To address these challenges, an Evolving Federated Gaussian Clustering (eFedG) method is proposed that adds and merges clusters over time, without assuming a predefined number of clusters. We propose a methodology for incremental clustering from mini-batches, with a merging mechanism that processes multiple cluster pairs simultaneously in a single step. This approach enables the system to handle heterogeneous data, as local clusters are learned independently and aggregated at the server based on overlap. The federated clustering method was examined on synthetic toy datasets, federated streaming clustering, and real network intrusion data.

Recursive least squares (RLS) algorithm assumes persistent excitation; but this condition is rarely fulfilled in closed-loop systems, where control performance has higher priority over persistent excitation. Variable-directional forgetting (VDF) partly mitigates the problem by confining forgetting to a low-dimensional subspace, thereby averting parameter divergence when the excitation is not persistent. Nevertheless, in this paper we argue that the VDF is sub-optimal: (i) it may forget the entire covariance matrix under rank-deficient excitation, and (ii) it introduces an additional tuning parameter that complicates system design.To overcome these drawbacks, a recursive least squares with domain-driven directional forgetting (RLS-3DF) is developed. Instead of minimizing the squared error over discrete samples, RLS-3DF minimizes the expected squared error over an operating region of the input domain, a region where the user wants the model to be accurate. This continuous-domain formulation, inspired by the separation of validity functions and local parameters in Takagi-Sugeno fuzzy models, decouples the influence of sampling distribution from the accuracy requirement. The resulting algorithm retains information along non-excited directions and does not introduce any additional hyper-parameters.The results look promising, as RLS-3DF improves RLS-VDF across the board by at least 20%, even under conditions that satisfy persistent excitation, which is the most surprising and encouraging result.

In an era of increasing system complexity and growing demands for autonomy and efficiency, control systems must continuously adapt to dynamic and uncertain environments. This study presents a comprehensive survey of evolving fuzzy and neuro-fuzzy controllers, with emphasis on data-driven control systems that adapt in real time in both structure and parameters. As the demand for adaptive and flexible control solutions grows alongside the increasing complexity of systems, evolving model-free and model-based fuzzy, neural, and neuro-fuzzy controllers have emerged as robust approaches, allowing models and controllers to integrate new patterns from data streams. Incremental machine learning methods enable control systems to autonomously detect and track new behaviors, improving their effectiveness in time-varying and unknown environments. Based on a rigorous bibliometric analysis using the Web of Science database, 2760 related papers were identified of which 97 were manually selected for detailed review due to their direct relevance to closed-loop evolving fuzzy or neuro-fuzzy control systems. These papers cover a wide range of methods, including basic parameter tuning, adaptive gain scheduling, and structural modifications grounded in constrained optimization and Lyapunov stability analysis. Such advances mark significant progress in the control of unknown, time-varying systems, with the surveyed literature demonstrating promising results in various applications. The abstracted findings reveal an increase in publications since 2013, confirming the relevance of evolving control in engineering. This review provides a comprehensive analysis of methodologies and achievements in the field, highlighting emerging trends, challenges, and research directions within evolving data-driven control. The novelty of this study lies in its focus on the structural evolution of controllers under real-time constraints, consolidating incremental machine learning for partition-based closed-loop architectures.

In industrial real-time process monitoring and fault detection, detecting and clustering machine events from time series data are essential tasks. However, conventional clustering methods often require the number of clusters to be known in advance, which is impractical in dynamic, real-world industrial scenarios. Therefore, online evolving methods are required. Furthermore, many existing methods used to obtain cluster prototypes generate prototypes containing unwanted artifacts. This paper introduces Streaming Error in Aligned Series (sERAL), a novel method for online time series alignment and averaging. sERAL aims to produce cluster prototypes that accurately represent the underlying data shape, a property often overlooked by competing methods. sERAL is integrated into an evolving time series clustering algorithm capable of unsupervised real-time clustering of time series streams. The method enables dynamic adaptation of both individual clusters and the number of clusters through updating and merging mechanisms. The proposed sERAL method is evaluated using sensor data collected from a real-world industrial manufacturing process. Comparison with established alignment and averaging methods reveals that sERAL produces improved cluster prototypes with fewer erroneous shape artifacts, which are common in Dynamic Time Warping-based methods. Complexity analysis shows that sERAL is highly scalable. This work addresses a significant gap in time series clustering for streaming applications, offering a practical and scalable solution for industrial use cases where signal shape is crucial. The sERAL algorithm and the associated clustering method are made available as an open-source Python package to encourage broad use.