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.

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.

In this article, we present a novel federated learning framework to multivariate regression problems, termed evolving Gaussian federated regression (eGauss+$_{\text{FR}}$). 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.

In data stream modeling problems, online active learning plays an important role for reducing model update times and costs (or efforts) associated with measuring and collecting target values, which are typically required for supervised updates in evolving fuzzy models. We propose an online active learning (oAL) approach for evolving error feedback fuzzy models (EEF-FM), which integrate an auto-regressive (AR) based noise correction component on consequent hyper-planes to gain higher robustness of predictions, especially in the case of measurement noise. Thereby, we first propose a multi-innovation based recursive update scheme for the consequent parameters, substituting conventional recursive fuzzily weighted least squares (RFWLS) approach in order to reduce the sub-optimality of consequent parameters in the case of structural changes in a fully single-pass manner$\rightarrow$EEF-FM-MI. Our oAL technique applies a sample selection strategy in a fully single-pass manner to elicit those samples which are expected to be most important for improving the robustness of model parameters and enriching the model structure when being used for model updates. It is based on three criteria: i) maximization of the D-optimality criterion in the consequent space for addressing the problem to best reduce the parameter uncertainty; it relies on the determinant of the Hessian matrix, which is updated and represented in a multi-innovation context, where a threshold for selection is automatically derived by kernel density estimation; ii) overlap degree in the antecedent space for the purpose to ‘sharpen’ the local trends in the transition regions between the hyper-planes; iii) novelty content in the antecedent space for indicating required knowledge expansion through rule evolution. The results on noisy real-world data sets showed i) that multi-innovation RFWLS could significantly outperform conventional RFWLS in all cases, with achieving an even more significant out-performance of classical EFS (not using any AR-based correction component), ii.) that our oAL strategy was able to reduce the measurement effort by up to 90% with a small increase in the error trend lines, and this with about quartering the computation times for model updates.

In this article, we propose a new variant of evolving fuzzy model for regression problems, which is based on error feedback integration in order to compensate measurement noise and to achieve more robust predictions; thus, it is termed as evolving error feedback fuzzy model. Thereby, we define an autoregressive-based noise model, localized per rule for being able to model different possible noise behaviors in different parts of the input space. Its predictions are added to the real fuzzy model predictions for noise correction purposes. This additive aspect leads to an extended version of the recursive fuzzily weighted least squares estimator (RFWLS-N = RFWLS with noise compensation), inheriting all its favorable convergence properties. For rule antecedent learning, we perform an evolving clustering process with the integration of a new forgetting strategy to be able to achieve more flexible updates in order to account for possible drifts. Therefore, a specific sample weighting concept is designed, with which different forgetting types can be achieved, ranging from (slow) logarithmic forgetting to (uniformly) linear forgetting and to (fast) exponential forgetting. The integration of the weights into the updates of rule centers and inverse covariance matrices is underlined with a theoretical analysis of their sample-wise contributions in the updates. Results on several noise-affected real-world datasets and system identification problems showed significantly improved model performances, compared to related evolving fuzzy methods, to the conventional RFWLS estimator and to the recursive correntropy approach. Antecedent forgetting helped us to improve the error trends in the case of abrupt drifts, while it never worsened the trends in the case of no drift.

This article presents a new design of experiment approach based on an evolving neuro-fuzzy model. The input of the process is proposed by a space-filling method that uses a sequence of step functions to maximize the coverage of the antecedent clusters in the input space of the evolving model, which is called the heuristic step sequence (HSS). When the system reaches a steady state, a new rule is added, existing rules are merged based on the similarity of the consequent transfer functions, and a new optimal excitation is calculated. The output error model structure was chosen because it assumes a noise distribution common to real processes and is suitable for identification, while the step function input signal is one of the most commonly used signals in identification and control. A filtered recursive least squares method is used to identify the consequent parameters of the output error models and the optimization filter is adapted based on the the confidence interval of the local model. Evaluations were performed on a Hammerstein type model comparing the HSS method with a staircase excitation and on a real plate heat-exchanger pilot plant. The experiments show that the proposed HSS method outperforms the staircase excitation and can be used to identify nonlinear dynamical systems of Hammerstein–Wiener type.

In this paper, two approaches to fuzzy prediction interval modelling of the processes with scarce output measurements are presented. Many real-world processes exhibit a significant drawback, originating from infrequent and rare measurements of the critical process variables. The idea behind the presented approach is to develop a model that can estimate the unmeasured process variables and find the narrowest possible bands of these variables that contain the prescribed percentage of data, i.e., the lower and upper bounds. In this work, the fuzzy prediction interval models are applied for estimation of the dissolved oxygen content in the steel bath in an electric arc furnace. Each measurement of the dissolved oxygen content imposes an operational delay and an unnecessary loss of energy. The fuzzy prediction interval can be used in the decision-making process to reduce the number of dissolved oxygen measurements required and provide additional information to the process operators. The approaches are implemented using real operational data from the studied electric arc furnace and the effectiveness of the fuzzy prediction interval methods is illustrated.

In this paper, we present an evolving data-based approach to automatically cluster Twitter users according to their behavior. The clustering method is based on the Gaussian probability density distribution combined with a Takagi–Sugeno fuzzy consequent part of order zero (eGauss0). This means that this method can be used as a classifier that is actually a mapping from the feature space to the class label space. The eGauss method is very flexible, is computed recursively, and the most important thing is that it starts learning “from scratch”. The structure adapts to the new data using adding and merging mechanisms. The most important feature of the evolving method is that it can process data from thousands of Twitter profiles in real time, which can be characterized as a Big Data problem. The final clusters yield classes of Twitter profiles, which are represented as different activity levels of each profile. In this way, we could classify each member as ordinary, very active, influential and unusual user. The proposed method was also tested on the Iris and Breast Cancer Wisconsin datasets and compared with other methods. In both cases, the proposed method achieves high classification rates and shows competitive results.

Evolving fuzzy systems (EFS) have received increased attention from the community for the purpose of data stream modeling in an incremental, single-pass and transparent manner. To date, a wide variety of EFS approaches have been developed and successfully used in real-world applications which address structural evolution and parameter adaptation in single EFS models. We propose a specific ensemble scheme of EFS to increase their robustness in predictive performance on new stream samples. Our approach relies on an online variant of bagging in which various EFS ensemble members are generated from online bags, that is, the members are updated based on a specific probabilistic online sampling technique, and this with guaranteed convergence to classical sampling in batch bagging. The autonomous pruning of ensemble members is undertaken to omit undesired members with atypically higher errors than other members. We propose two variants, hard pruning where undesired members are deleted forever from the ensemble, and soft pruning where members receive weights to calculate the overall ensemble prediction, according to their single performance; thus, members who are undesired at a certain point of time may be dynamically recalled at a later stage. The autonomous evolution of new ensemble members is carried out whenever a drift in the stream is detected, based on a significantly worsening performance indicator, measured in terms of the Hoeffding inequality. Newer members typically represent the drifted state better and are thus up-weighed compared to older members within an advanced (weighted) calculation of the overall ensemble prediction. The new approach termed online bagged EFS (OB-EFS) was successfully evaluated and compared with single EFS models and related SoA approaches on four data streams from real-world applications (containing various noise levels, drifts and new operating conditions) and showed significantly lower prediction error trend lines.

This article proposes a hybrid path-planning algorithm, the HE* algorithm, which combines the discrete grid-based E* search and continuous Bernstein-Bézier (BB) motion primitives. Several researchers have addressed the smooth path planning problem and the sample-based integrated path planning techniques. We believe that the main benefits of the proposed approach are: directly drivable path, no additional post-optimization tasks, reduced search branching, low computational complexity, and completeness guarantee. Several examples and comparisons with the state-of-the-art planners are provided to illustrate and evaluate the main advantages of the HE* algorithm. HE* yields a collision-safe and smooth path that is close to spatially optimal (the Euclidean shortest path) with a guaranteed continuity of curvature. Therefore, the path is easily drivable for a wheeled robot without any additional post-optimization and smoothing required. HE* is a two-stage algorithm which uses a direction-guiding heuristics computed by the E* search in the first stage, which improves the quality and reduces the complexity of the hybrid search in the second stage. In each iteration, the search is expanded by a set of BBs, the parameters of which adapt continuously according to the guiding heuristics. Completeness is guaranteed by relying on a complete node mechanism, which also provides an upper bound for the calculated path cost. A remarkable feature of HE* is that it produces good results even at coarse resolutions.

In this paper, an approach to the identification of hybrid systems is discussed. It is based on the incremental fuzzy C-regression clustering. Based on the distance between the current measurement and the hyperplane of the local model, local models are updated. If necessary, a new local model is constructed. To increase the robustness and prevent false local models, the data are kept in the buffer temporarily. The approach produces good results as shown in two examples. The first example can be modelled as a piecewise affine dynamical system and the second one as a switched dynamical system.

This paper presents a new methodology for Prediction Interval (PI) construction based on a modified Takagi-Sugeno fuzzy system trained with a joint Supervision loss function. Given a desired coverage level, this model is capable of providing predictions of the expected value of the system along with the interval bounds. This methodology is tested by simulation experiments using a dataset containing real temperature data from a rural community in southern Chile. The proposed model was compared with a state-of-the-art Takagi-Sugeno Fuzzy Numbers model. It was shown that the Joint Supervision method manages to obtain slightly superior results to the Fuzzy Numbers approach while greatly reducing the complexity of the training loss function. Additionally, since the proposed model was trained using Particle Swarm Optimization, further performance improvements could be made by employing gradient-based optimization algorithms, since they are compatible with the Joint Supervision loss function.

In this paper, a new approach to evolving fuzzy model identification from streaming data is given. The structure of the model is given as a local model network in Takagi–Sugeno form, and the partitioning of the input–output space is based on metrics in which these local models are defined as prototypes of the clusters. This means that the clusters and the local models share the same parameters; therefore, the number of parameters of the evolving system is much lower in comparison to similar systems of comparable complexity, and the problems of parameter identifiability are not a particular issue. The algorithm adds the local models in an incremental fashion and recursively adapts the local model parameters. The proposed algorithm is tested on three examples to demonstrate the main features. The first example is a simple simulated example with intersecting clusters; the second is a very well-known benchmark that treats the Mackey–Glass time series; the third is an example that shows the classification of the data from a laser rangefinder. These examples show the great potential of the proposed approach in certain applications.

Missing values are common in real-world data stream applications. This article proposes a modified evolving granular fuzzy-rule-based model for function approximation and time-series prediction in an online context, where values may be missing. The fuzzy model is equipped with an incremental learning algorithm that simultaneously imputes missing data and adapts model parameters and structure over time. The evolving fuzzy granular predictor (eFGP) handles single and multiple missing values on data samples by developing reduced-term consequent polynomials and utilizing time-varying granules. Missing at random (MAR) and missing completely at random (MCAR) values in nonstationary data streams are approached. Experiments to predict monthly weather conditions, the number of bikes hired on a daily basis, and the sound pressure on an airfoil from incomplete data streams show the usefulness of eFGP models. Results were compared with those of state-of-the-art fuzzy and neuro-fuzzy evolving modeling methods. A statistical hypothesis test shows that eFGP outperforms other evolving intelligent methods in online MAR and MCAR settings, regardless of the application.

We introduce an incremental learning method for the optimal construction of rule-based granular systems from numerical data streams. The method is developed within a multiobjective optimization framework considering the specificity of information, model compactness, and variability and granular coverage of the data. We use α-level sets over Gaussian membership functions to set model granularity and operate with hyperrectangular forms of granules in nonstationary environments. The resulting rule-based systems are formed in a formal and systematic fashion. They can be useful in time series modeling, dynamic system identification, predictive analytics, and adaptive control. Precise estimates and enclosures are given by linear piecewise and inclusion functions related to optimal granular mappings.

In this article, a new dynamic merging approach for incrementally evolving clustering is presented. This means that the cluster partitions are incrementally learned on-line from streams of data. The criterion of merging is based on the comparison between the sum of volumes of two clusters that fulfill the criteria of a minimal number of samples in the cluster and the expected volume of the newly generated merged cluster. The newly generated merged cluster is conducted by using the weighted averaging of cluster centers and the calculation of the joint covariance matrix from the covariance matrices of the clusters. It has been shown that the proposed new evolving algorithm eGAUSS+ together with the new merging concept is very easy to implement, can work on higher-dimensional data sets, can perform all necessary computation on-line, and can produce reliable clusters.

The development of feedback control systems for overhead cranes is of great importance due to many potential applications and advantages over manual operation concerning stability and robustness. We represent the key nonlinear dynamics of cranes in a compact state-space fuzzy model. The fuzzy model assists the design of a fuzzy controller through parallel distributed compensation. A conservative linear-matrix-inequality feasibility problem is formulated so that a solution guarantees closed-loop Lyapunov stability, constrained inputs, quick positioning of the supporting cart and suppression of load oscillations. Due to the nonlinear nature of the fuzzy model and controller, Jacobian linearization at a hyperbolic equilibrium is avoided. The proposed fuzzy controller for cranes has shown to be effective, robust and able to move loads smoothly even after collisions. Constrained and smooth inputs avoid actuator saturation and tend to increase its lifetime.

We introduce an incremental learning method for the optimal construction of rule-based granular models from numerical data streams. We take into account a multiobjective function, the specificity of information, model compactness, and variability and coverage of the data. We use α-level sets over Gaussian membership functions to set model granularity and operate with hyper-rectangular forms of granules in nonstationary environment. Rule-based models are formed in a systematic fashion and can be used for time series prediction and nonlinear function approximation. Precise estimates and enclosures are given by linear piecewise and inclusion functions related to optimal granular mappings. An application example on early detection and monitoring of the severity of the Parkinson's disease shows the usefulness of the method.

In this paper we present an initial investigation of the evolving cloud-based method using partial density calculation for fault detection of HVAC system (Heating, Ventilation and Air Conditioning). Moreover, we investigate different approaches of choosing the most influential components when calculating the partial local density which is further used for evolving the model structure. The method is based on the simplified fuzzy rule- based-system AnYa where the antecedent part is presented by data clouds. The effectiveness of the proposed method is tested on a model of HVAC system and furthermore, different types of faults are investigated. The results were compared with the well established fault detection method DPCA (Dynamic Principal Component Analysis).

In this paper a new approach to the construction of Bluetooth signal path loss models with a fuzzy modelling algorithm - SUHICLUST is presented. By using these models, Bluetooth beacons, a smartphone and proposed localization algorithm a very accurate low-cost localization system was developed. With the SUHICLUST algorithm fuzzy path loss models were constructed for all available beacons installed in our laboratory. The developed localization algorithm is based on the use of improved fingerprinting method and particle swarm optimization which take into account also confidence intervals of fuzzy models. Both methods are computationally efficient, which enables real-time processing and low energy consumption on a smartphone.

Gradual drifts in data streams are usually hard to detect and often do not necessarily trigger the evolution of new fuzzy rules during model adaptation steps in order to represent the new, drifted data distribution(s) appropriately in the fuzzy model. Over time, they thus lead to oversized rules with untypically large local errors (typically also worsening the global model error), as representing joint local data distributions before and after a drift happened likewise. We therefore propose an incremental rule splitting concept for generalized fuzzy rules in order to autonomously compensate these negative effects of gradual drifts. Our splitting condition is based on the local error of rules measured in terms of a weighted contribution to the whole model error and on the size of the rules measured in terms of the volume of the associated clusters. We use the concept of statistical process control in order to omit an extra threshold parameter in our splitting condition. The splitting technique relies on the eigendecomposition of the rule covariance matrix to adequately manipulate the largest eigenvector and eigenvalues in order to retrieve the new centers and contours of the two split rules. Furthermore, we guarantee sufficient flexibility in adapting the shapes and consequents of the split rules to the new drifted situation in the stream by integrating a specific dynamic and smooth forgetting concept of older samples, which formed the original (nonsplit) rules. Robustness against outliers is guaranteed by the realization of a two-layer model building process, where one layer represents the cluster partition and the other layer the rule partition: Only clusters becoming significant over time are accepted as rules in the fuzzy model. The splitting concepts are integrated in the generalized smart evolving learning engine for fuzzy systems (termed as Gen-Smart-EFS) and successfully tested on two real-world application scenarios, engine test benches and rolling mills, the latter including a real-occurring gradual drift (whose position in the data is known). Results show clearly improved error trend lines over time when splitting is applied, compared to the case when it is not applied: reduction of the mean absolute model error by about one third (rolling mills) and about one half (engine test benches).

This article deals with trajectory planning that is suitable for nonholonomic differentially driven wheeled mobile robots. The path is approximated with a spline that consists of multiple Bernstein-Bézier curves that are merged together in a way that continuous curvature of the spline is achieved. The article presents the approach for optimization of velocity profile of Bernstein-Bézier spline subject to velocity and acceleration constraints. For the purpose of optimization, velocity and turning points are introduced. Based on these singularity points, local segments are defined where local velocity profiles are optimized independently of each other. From the locally optimum velocity profiles, the global optimum velocity profile is determined. Since each local velocity profile can be evaluated independently, the algorithm is suitable for concurrent implementation and modification of one part of the curve does not require recalculation of all local velocity profiles. These properties enable efficient implementation of the optimization algorithm. The optimization algorithm is also suitable for the splines that consist of Bernstein-Bézier curves that have substantially different lengths. The proposed optimization approach was experimentally evaluated and validated in simulation environment and on real mobile robots.

In this paper a new approach to indoor localization with Bluetooth beacons is presented. The developed localization algorithm is based on the use of fuzzy path loss models and particle swarm optimization which is the main novelty of this paper. The fuzzy path loss model of each beacon is obtained with a supervised, hierarchical clustering algorithm (SUHICLUST) which accurately describes collected measurements of signal strengths. These are obtained in a very simple way by walking around the area and using the proposed relative localization system, which is based on visual odometry and inertial navigation system. The particle swarm optimization enables computational efficiency of the developed localization algorithm, which is essential for real-time processing and low energy consumption on a smartphone. The results of the testing of the localization algorithm show very high accuracy of localization for a low-cost localization system.

This paper presents robust evolving cloud-based controller (RECCo) for the distributed solar collector field (DSCF). The main issue of the DSCF is that the primary energy source (variable) cannot be manipulated. Beside this, unpredictable changing of environmental conditions (outlet temperature, cloudiness, solar radiation) on the daily basis strongly influence the dynamics of the whole process. According to this, the RECCo controller is robust enough to cope with the high levels of uncertainty present in the DSCF plant. RECCo is a fuzzy rule-based type of controller based on parameter-free premise (IF) part while the PID-type control consequent is used. Algorithm starts with zero fuzzy rules (zero clouds in data space). During operation it evolves its structure (adding new data clouds) and adapts the PID parameters for each data cloud while preforming the control of the plant. This means that no a-priori knowledge of the controlled process is required. Moreover, the ability of the learning is tested on the different operating points which cover the majority of the operating range of the DSCF plant.

This paper presents an improved version and a modification of Robust Evolving Cloud-based Controller (RECCo). The first modification is normalization of data space in RECCo. As a consequence, some of the evolving and adaptation parameters become independent of the range of the process output signal. Thus the controller tuning is simplified which makes the approach more appealing for the use in practical applications. The data space normalization is general and is used with Euclidean norm, but other distance metrics could also be used. Beside the normalization new adaptation scheme of the controller gain is proposed which improves the control performance in the case of a negative initial error in starting phase of the evolving process. At the end, different simulation scenarios are tested and analyzed for further practical implementation of the Cloud-based controller into real environments. For that reason a detail simulation study of a plate heat exchanger is performed and different scenarios were analyzed.

Increasing demands on effluent quality and loads call for an improved control, monitoring, and fault detection of waste-water treatment plants (WWTPs). Improved control and optimization of WWTP lead to increased pollutant removal, a reduced need for chemicals as well as energy savings. An important step toward the optimal functioning of a WWTP is to minimize the influence of sensor faults on the control quality. To achieve this, a fault-detection system should be implemented. In this paper, the idea of using an evolving method as a base for the fault-detection/monitoring system is tested. The system is based on the evolving fuzzy model method. This method allows us to model the nonlinear relations between the variables with the Takagi-Sugeno fuzzy model. The method uses basic evolving mechanisms to add and remove clusters and the adaptation mechanism to adapt the clusters' and local models' parameters. The proposed fault-detection system is tested on measured data from a real WWTP. The results indicate the potential improvement of the WWTP's control during a sensor malfunction.

This paper presents a new approach to design of experiments (DoE), based on an evolving fuzzy model structure and a supervised hierarchical clustering algorithm. DoE is the field that deals with the problem of how to design the most optimal and economic experimentation. The goal is to identify a highly nonlinear and possibly high-dimensional system, together with the minimal experimental effort required. The theory is well developed for linear and polynomial models; however, they are often not suitable for general use. For this reason, a fuzzy model in the form of Takagi-Sugeno (T-S) is used, because it has the properties of a universal approximator. The method works iteratively by sampling the system in the input domain and evolving the fuzzy model. The method is demonstrated with a simulation, which shows the potential of the proposed approach.

This issue marks the first anniversary issue of IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS after it changed its name from IEEE TRANSACTIONS ON NEURAL NETWORKS. I am happy to report that we had a great year! The number of new submissions in a year exceeded 1,000 for the first time in the history of TNN/TNNLS. IEEE TNN had a very successful development for 22 years from 1990 to 2011, and we have good reasons to believe that IEEE TNNLS will have many more years of successful growth.

This paper presents the solving of the petrol sales volume estimation problem given by the Task Force on Competitions, Fuzzy Systems Technical Committee IEEE Computational Intelligence Society. The solution using eTS, SAFIS and eFuMo method is presented. The results are compared to linear ARX model identified using RLS method. Results using static and prediction model are given. The paper also presents parts of new eFuMo method, which is based on recursive Gustafson-Kessel clustering.

This paper presents the solving of the petrol sales volume estimation problem given by the Task Force on Competitions, Fuzzy Systems Technical Committee IEEE Computational Intelligence Society. The solution using eTS, SAFIS and eFuMo method is presented. The results are compared to linear ARX model identified using RLS method. Results using static and prediction model are given. The paper also presents parts of new eFuMo method, which is based on recursive Gustafson-Kessel clustering.

This paper presents a new, supervised, hierarchical clustering algorithm (SUHICLUST) for fuzzy model identification. The presented algorithm solves the problem of global model accuracy, together with the interpretability of local models as valid linearizations of the modeled nonlinear system. The algorithm combines the advantages of supervised, hierarchical algorithms, which are based on heuristic tree-construction algorithms, together with the advantages of fuzzy product space clustering. The high flexibility of the validity functions that is obtained by fuzzy clustering combined with supervised learning results in an efficient partitioning algorithm, which is independent of initialization and results in a parsimonious fuzzy model. Furthermore, the usability of SUHICLUST is very undemanding, because it delivers, in contrast with many other methods, reproducible results. In order to get reasonable results, the user only has to set either a threshold for the maximum number of local models or a value for the maximum allowed global model error as a termination criterion. For fine-tuning, the interpolation smoothness controls the degree of regularization. The performance is illustrated on both analytical examples and benchmark problems from the literature.

This paper deals with the problem of fuzzy nonlinear model identification in the framework of a local model network (LMN). A new iterative identification approach is proposed, where supervised and unsupervised learning are combined to optimize the structure of the LMN. For the purpose of fitting the cluster-centers to the process nonlinearity, the Gustafsson-Kessel (GK) fuzzy clustering, i.e., unsupervised learning, is applied. In combination with the LMN learning procedure, a new incremental method to define the number and the initial locations of the cluster centers for the GK clustering algorithm is proposed. Each data cluster corresponds to a local region of the process and is modeled with a local linear model. Since the validity functions are calculated from the fuzzy covariance matrices of the clusters, they are highly adaptable and thus the process can be described with a very sparse amount of local models, i.e., with a parsimonious LMN model. The proposed method for constructing the LMN is finally tested on a drug absorption spectral process and compared to two other methods, namely, Lolimot and Hilomot. The comparison between the experimental results when using each method shows the usefulness of the proposed identification algorithm.

In this work, we propose a combined approach based on Particle Swarm Optimization (PSO) and Sequential Quadratic Programming (SQP) for solving the real-time optimization problem appearing in the hybrid predictive control of systems with continuous and discrete inputs. The conventional PSO for continuous problems is mixed with binary PSO for handling discrete variables, and after iterations of the algorithm have ended, SQP is applied for refining the continuous variables. This new method (PSO+SQP) is favorably compared with a conventional non-linear optimization techniques (based on Branch and Bound and Explicit Enumeration) and PSO. Also, a multi-objective approach is considered as a tuning method for the population size and number of iterations for PSO. All these algorithms are applied for the temperature control of a Batch Reactor.

In this paper the new algorithm SUHICLUST (supervised hierarchical clustering) is presented. It unifies the strengths of the supervised, incremental construction scheme LOLIMOT with the advantages of product space clustering. The result of this fusion is a powerful structure identification algorithm that enables approximation of processes with axes-oblique partitioning, high flexible validity functions and local polynomial models. The theoretical comparison with LOLIMOT and product space clustering and a demonstration example underline the usefulness of SUHICLUST.

The paper deals with an important aspect of continuous systems modelling and simulation approaches, with possibilities for multi-domain modelling. The traditional approach is based on block oriented schemes in which causal relations play an important role. However this causality is artificially generated in order to fulfil appropriate conditions for simulation on conventional sequential computers. Fortunately new concepts which are based on object oriented approaches, physically oriented connections and algebraic manipulations enable the so called acausal modelling which can efficiently be used for multi-domain modelling. The advantages and disadvantages of traditional and more advanced approaches are discussed. The described multi-domain approach is illustrated with modelling of a laboratory helicopter using a very popular multi-domain modelling environment Dymola with Modelica language. A multivariable controller was designed for a wide operating range. The control signals which drive the main and the tail rotors enable the desired pitch and rotation (azimuth) angles. The multidomain object oriented approach enables an efficient coupling of elements from mechanical libraries and a block library for the implementation of control system.

In the paper, the hybrid predictive control based on a fuzzy model is presented. The identification methodology for a nonlinear system with discrete state-space variables by combining fuzzy clustering and principal component analysis is proposed. The fuzzy model is used for hybrid predictive control design where the optimization problem is solved by the use of genetic algorithms. An illustrative experiment on a hybrid tank system is conducted to present the benefits of the proposed approach.

This paper presents a method of continuous-time model predictive control for nonlinear Wiener-type systems. The system's output nonlinear mapping is approximated by the means of fuzzy systems, and is inherently incorporated in the predictive control scheme; thus, inverting the output function is not necessary. The predictive control law is derived in an analytical form to avoid the problems with non-convex optimization in each time step. A simulation experiment is conducted to present the control quality in the case of a pH-neutralization process with a heavily nonlinear output mapping.

In this paper, we present a new method of interval fuzzy model identification. The method combines a fuzzy identification methodology with some ideas from linear programming theory. We consider a finite set of measured data, and we use an optimality criterion that minimizes the maximum estimation error between the data and the proposed fuzzy model output. The idea is then extended to modeling the optimal lower and upper bound functions that define the band which contains all the measurement values. This results in lower and upper fuzzy models or a fuzzy model with a set of lower and upper parameters. The model is called the interval fuzzy model (INFUMO). We also showed that the proposed structure uniformly approximates the band of any nonlinear function. The interval fuzzy model identification is a methodology to approximate functions by taking into account a finite set of input and output measurements. This approach can also be used to compress information in the case of large amount of data and in the case of robust system identification. The method can be efficiently used in the case of the approximation of the nonlinear functions family. If the family is defined by a band containing the whole measurement set, the interval of parameters is obtained as the result. This is of great importance in the case of nonlinear circuits' modeling, especially when the parameters of the circuits vary within certain tolerance bands.

This correspondence addresses the problem of interval fuzzy model identification and its use in the case of the robust Wiener model. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion which minimizes the maximum estimation error between the data and the proposed fuzzy model output is used. The min-max optimization problem can then be seen as a linear programming problem that is solved to estimate the parameters of the fuzzy model in each fuzzy domain. This results in lower and upper fuzzy models that define the confidence interval of the observed data. The model is called the interval fuzzy model and is used to approximate the static nonlinearity in the case of the Wiener model with uncertainties. The resulting model has the potential to be used in the areas of robust control and fault detection.

Intelligent systems may be viewed as a framework for solving the problems of nonlinear system control. The intelligence of the system in the nonlinear or changing environment is used to recognize in which environment the system currently resides and to service it appropriately. This paper presents a general methodology of adaptive control based on multiple models in fuzzy form to deal with plants with unknown parameters which depend on known plant variables. We introduce a novel model-reference fuzzy adaptive control system which is based on the fuzzy basis function expansion. The generality of the proposed algorithm is substantiated by the Stone-Weierstrass theorem which indicates that any continuous function can be approximated by fuzzy basis function expansion. In the sense of adaptive control this implies the adaptive law with fuzzified adaptive parameters which are obtained using Lyapunov stability criterion. The combination of adaptive control theory based on models obtained by fuzzy basis function expansion results in fuzzy direct model-reference adaptive control which provides higher adaptation ability than basic adaptive-control systems. The proposed control algorithm is the extension of direct model-reference fuzzy adaptive-control to nonlinear plants. The direct fuzzy adaptive controller directly adjusts the parameter of the fuzzy controller to achieve approximate asymptotic tracking of the model-reference input. The main advantage of the proposed approach is simplicity together with high performance, and it has been shown that the closed-loop system using the direct fuzzy adaptive controller is globally stable and the tracking error converges to the residual set which depends on fuzzification properties. The proposed approach can be implemented on a wide range of industrial processes. In the paper the foundation of the proposed algorithm are given and some simulation examples are shown and discussed. © 2002 Wiley Periodicals, Inc.

The implementation of the fuzzy predictive functional control (FPFC) on the magnetic suspension system is presented. The magnetic suspension system is in our case the pilot plant for magnetic bearing and is an open-loop unstable process, therefore a lead compensator is used to stabilize it. The high quality control requirements include a periodical step response and zero steady-state error. Adding the integrator to a feedback causes overshoot. The solution to the problem is a cascade control with fuzzy predictive functional controller in the outer loop. To cope with the unknown model parameters and the nonlinear nature of the magnetic system, a fuzzy identification based on the FNARX model is used. After a successful validation the obtained fuzzy model is used for the controller design. The FPFC is compared with a cascade PID control. The results obtained with the FPFC are very promising and comparable with the conventional control techniques.

In the paper a novel model-reference adaptive control system is introduced, which is based on the fuzzy model of the process. The combination of adaptive control theory based on the models obtained by fuzzy basis function expansion results in fuzzy direct model-reference adaptive control which provides higher adaptation ability than basic adaptive control systems. The main advantage of the proposed approach is simplicity together with high performance. In the paper the basics of the proposed algorithm are given and a simulation example on highly nonlinear process model is shown and discussed.

In this paper, a new method of predictive control is presented. In this approach, a well-known method of predictive functional control is combined with fuzzy model of the process. The prediction is based on fuzzy model given in the form of Takagi-Sugeno type. The proposed fuzzy predictive control has been evaluated by implementation on heat-exchanger plant, which exhibits a strong nonlinear behavior. It has been shown that in the case of nonlinear processes, the approach using fuzzy predictive control gives very promising results. The proposed approach is potentially interesting in the case of batch reactors, heat-exchangers, furnaces, and all the processes that are difficult to model.