With the rapid development of advanced sensing, communication, and the industrial Internet of Things, it has become much easier to obtain, transmit, and, store a massive amount of real-world data. However, imperfect data is inevitable in real-world systems, such as the existence of outliers, contaminated, incomplete, inaccurate, and even missing information in the data. This phenomenon is called data imperfection, which usually makes traditional datadriven modeling and automation methods either unfeasible or ending at undesired inaccuracies. This has been a wellknown challenge to data-driven methods when applied to real-world systems, such as process industry, manufacturing, energy networks, and transportation systems.

This article proposes a deep learning (DL)-based control algorithm-DL velocity-based model predictive control (VMPC)-for reducing traffic congestion with slowly time-varying traffic signal controls. This control algorithm consists of system identification using DL and traffic signal control using VMPC. For the training process of DL, we established a modeling error entropy loss as the criteria inspired by the theory of stochastic distribution control (SDC) originated by the fourth author. Simulation results show that the proposed algorithm can reduce traffic congestion with a slowly varying traffic signal control input. Results of an ablation study demonstrate that this algorithm compares favorably to other model-based controllers in terms of prediction error, signal varying speed, and control effectiveness.

The inverse calculation of burden distribution matrix (BDM) is one of the most important challenges in the blast furnace iron-making processes. Focusing on this practical challenge, this paper proposes a new burden distribution spatial model in burden charging process, and develops a B-spline approximation-based probability density function (PDF) control algorithm to assign the expected thickness distribution of burden layer and perform the required inverse calculation of BDM. First, a novel method for the thickness distribution of burden layer is given using B-spline model. Then, according to the coexistence of continuous and bounded discrete variables in BDM, a novel hybrid optimization control method by combining integer programming and PDF tracking is further established. Finally, the proposed PDF-based iterative inverse calculation of BDM using B-spline models are tested using industrial data. The simulation results show that the proposed method is well-suited to solve the BDM inverse calculation problem in practice.

This paper studies the traffic delay prediction modeling for multiple signalized intersections along the Ala Moana Boulevard and Nimitz Highway in Hawaii. Several machine learning (ML) based approaches have been studied in the literature, and most of them focused on prediction accuracy rather than the end use of real-time control and implementation. These ML models tend to be very complex and non-linear in nature, making it challenging to achieve fast inferences and are computationally heavy for real-time signal control implementation. In this paper, a simple yet accurate hybrid modeling method is proposed to predict traffic delay one-step ahead with the model made suitable for real-time implementation to control traffic flow. Since real-time road-side measurements are recorded in unstructured form, the paper also discusses other issues related to data extraction and the pre-processing process. Finally, a simple signal control loop is developed to demonstrate the proposed modeling approach, which has shown advantages in model accuracy and computation efficiency compared against several existing modeling methods.

This study proposes a new multi-input multi-output optimal bilinear signal control method in which a bilinear dynamic model approximation is used to capture the nonlinear dynamics of the urban traffic networks. With signal green time splits as the control input and traffic delay changes as the output for each intersections in the network, a bilinear system model was developed, which, on the basis of linear system modeling, takes interactions among traffic delays and signal timing splits into consideration. Based on the bilinear system modeling framework, we conducted two steps in each time interval to derive traffic control strategies: (1) we used the normalized least-squared algorithm to estimate system parameters; and (2) we solved an online optimization problem to obtain the updated traffic control inputs for the signal timing that minimizes future traffic delays. We evaluated the proposed method in a microscopic traffic simulation environment (VISSIM) with a 35-intersection network of Bellevue city in Washington. Two different traffic demand patterns: (1) normal traffic demands; and (2) time-varying traffic demands were simulated to compare the performance of different control strategies. Experimental results show that (1) the proposed bilinear system model can better describe traffic system dynamics than linear-model based methods, such as our previously developed linear-quadratic regulator control; and (2) the proposed method outperforms the state-of-the-art signal control strategies, namely the max-pressure and the self-organizing traffic light control methods. We have also shown that the proposed method is applicable to all other possible network layouts and signal controller phasing structures.

This article proposes a new traffic signal control algorithm to deal with unknown-traffic-system uncertainties and reduce delays in vehicle travel time. Unknown-traffic-system dynamics are approximated using a recurrent neural network (NN). To accurately identify the traffic system model, an online-learning scheme is developed to switch among a set of candidate NNs (i.e., multiple-model NNs) based on their estimation errors. Then, a bank of optimal signal-timing controllers is designed based on the online identification of the traffic system. Simulation studies have been carried out for the obtained control strategies using multiple-model NNs, and the desired results have been obtained. Moreover, compared with the widely used actuated traffic signal control schemes, it is shown that the proposed method can reduce vehicle travel delays and improve traffic system robustness.

The automatic control of blast furnace (BF) ironmaking process has always been an important yet arduous task in metallurgic engineering and automation. In this article, a novel Kalman filter-based robust model-free adaptive predictive control (MFAPC) method is proposed for the direct data-driven control of molten iron quality in BF ironmaking. First, a compact-form dynamic linearization-based extended MFAPC method for multivariable molten iron quality control is proposed by generalizing the existing single-variable MFAPC method to multivariable systems. Based on it, a Kalman filter-based robust MFAPC is further proposed considering the problems of data loss and measurement noise in quality detection. Specifically, the robust mechanism in the robust MFAPC combines a novel dynamic linearization method with a concept termed Pseudo-Jacobian matrix to predict the missing data during data loss. After that, a Kalman filter is constructed based on a prediction model to filter the measurement noise. The stability of the proposed control method is analyzed, and various data experiments using actual industrial data are performed to verify the effectiveness of the proposed methods.Note to Practitioners—The extremely complicated dynamics of blast furnace ironmaking process make the model-based controllers difficult to realize in practice. In this article, a novel robust model-free adaptive predictive control method is proposed for direct data-driven control of multivariate molten iron quality in the ironmaking process. This method directly uses the process input and output data to design the multivariable quality controller online by the compact-form dynamic linearization technology and the internal multilayer prediction mechanism, thus avoids the drawback of model-based controllers in troublesome process modeling. Moreover, the proposed method can effectively avoid the influence of data loss and measurement noise on the controller performance with the designed Kalman filter-based robust mechanism. The superiority and practicability of the proposed method are verified using various experiments against actual industrial data.

A fault isolation, estimation, and fault-tolerant control (FTC) scheme for nonlinear time-varying delay stochastic distribution control systems was presented in this paper. The Takagi-Sugeno fuzzy model was adopted to approach the nonlinear dynamics of time-varying delay systems. According to the output equivalence principle and Laplace transformation, an augmented state vector was given to solve the time-varying delay problem. When multiple actuator faults and interference occur simultaneously, fault detection, isolation and fault estimation was designed to obtained the fault information. To decouple faults and obtain the value and location information of the fault, the system was separated into two parts through the designed multiple conversion matrices, in which one subsystem was only affected by one actuator fault. This has simplified the design of fault isolation and estimation. A adaptive observer for fault estimation was given. Then, fault information such as the time, location, and size was determined. The observer gain matrices were calculated using linear matrix inequality (LMI). When a fault was detected and diagnosed, a FTC algorithm was devised using the proportional-integral control scheme to compensate the fault as much as possible. It has been shown that even if multiple faults actuator occurred simultaneously, the FTC controller still ensured the output probability density function of the system traced the desired probability density function when a fault occurred. Finally, the expected results were obtained through the simulation example, which confirmed the effectiveness of the method.

This work investigated stochastic distribution control theory-based traffic signal optimization to achieve a smooth and uniform flow of vehicles through signalized intersections. In this context, the static and linear dynamic stochastic distribution models were developed to express the relationship between the signal timing and the traffic queue length together with its probability density function. Two stochastic distribution control algorithms were designed to control the signal timing at intersections such that the probability density function of the traffic queue of each intersection road segment is made as narrow and as small as possible. Also, a recursive input-output traffic queue estimation model was proposed, which is data-driven and dynamic in nature, to calculate real-time traffic queue length using traffic signal timings and loop-detector data. The control algorithms were evaluated for a one-signal corridor, two-signal corridor, and$2 \times 2$network of signalized intersections. MATLAB simulation examples are provided to demonstrate the use of the proposed algorithms and comparison to the existing widely-used semi-actuated control has been made. Desired results were obtained.

Traffic signal control is important for intersection safety and efficiency. However, most traffic signal control methods are designed for individual intersections or corridors. Although some adaptive control systems have been developed, the methods used are often proprietary and not published, making it difficult to evaluate their effectiveness. This study proposes an adaptive multi-input and multi-output traffic signal control method that not only can improve network-wide traffic operations in terms of reduced traffic delay and energy consumption, but also is more computationally feasible than existing centralized signal control methods. Considering intersection interactions, a linear dynamic traffic system model was built and adaptively updated to reflect how the signal control input of each intersection affects network-wide vehicle travel delay. Based on the system model, an adaptive linear-quadratic regulator (LQR) was designed to minimize both traffic delay and incremental changes in the control input. The proposed control method was evaluated in a microscopic traffic simulation environment with a 35-intersection network of Bellevue City, Washington. Simulation results show that the proposed method had shorter average traffic delays in the network when compared with the traffic delays controlled by the state-of-the-art max-pressure, self-organizing traffic lights, and independent deep Q network methods.

In this article, a fault-tolerant tracking control strategy is investigated for nonlinear probability density function (PDF) control systems with the actuator fault, uncertainties, unknown disturbance, and random packet losses. The control input signal dropout and measurement signal dropouts are described as the independent Bernoulli distribution. An adaptive fault diagnosis (FD) observer based on the Lyapunov function is given to simultaneously estimate the fault, disturbance, and state with packet losses. Different from the traditional robust fault-tolerant control (FTC), a new active fault-tolerant tracking controller is designed based on the model predictive control framework, which has better adaptive fault-tolerant performance. Finally, the validity of the proposed FTC method has been proved by a simulation study of a papermaking process.

The problem of fault diagnosis (FD) and fault tolerant control for a class of Takagi–Sugeno (T–S) fuzzy stochastic distribution control systems subject to sensor and actuator faults is discussed in this article. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/FD observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.

In this article, the optimal operational control problem is considered for complex industrial processes with stochastic disturbances. The performance index is optimized by set points reselection on the operational control layer together with controllers design on the loop control layer. First, the operational indices are obtained through some optimization algorithms. Second, the controllers are designed in the ideal situation to ensure that the controlled variables can track desired set points. To minimize the performance deterioration caused by non-Gaussian stochastic noises or disturbances, a novel Pareto distribution estimation (Pareto DE)-based intelligent set-points reselection approach is proposed to optimize entropy and expectation simultaneously. In the proposed method, entropy is formulated in a recursive way basing on joint PDFs which are obtained through multivariate kernel density and bandwidth selection. Meanwhile, both the controller structure and controller parameters are fixed for whatever disturbances acting on the system. Finally, simulations are given to illustrate the effectiveness of the proposed strategy.

Pulp is the most important raw material in paper industries, whose fiber length stochastic distribution (FLSD) shaping directly determines the energy consumption and paper quality of the subsequent papermaking processes. However, the mean and variance are insufficient to describe the FLSD shaping, which displays non-Gaussian distributional properties. Therefore, the traditional control method based on the mean and variance of the fiber length is difficult to control the FLSD shaping effectively. In this article, a novel data-driven predictive probability density function (PDF) control method is proposed for the FLSD shaping in the refining process. First, the PDF of FLSD shaping is approximated by a radial basis function neural network (RBF-NN) and the parameters of each RBF basis function are tuned by using an iterative learning law. Second, the random vector functional link network (RVFLN)-based data-driven modeling method is employed to construct the prediction model of the weight vector. Consequently, the predictive controller is designed based on the constructed PDF model of the FLSD shaping in the refining process and the stability issue of the resulted closed-loop system is discussed. The experiments using industrial data are given to illustrate the effectiveness of the proposed method. Note to Practitioners-Pulp quality control in the refining process plays a critical role in the optimization of product quality and energy saving in the pulping and papermaking processes. Different from the conventional control method based on the mean and variance of the fiber length, a novel data-driven predictive PDF control method is proposed for the non-Gaussian stochastic distribution dynamic characteristics of the fiber length, which is used to achieve the desired PDF shaping of fiber length distribution. This kind of novel control method includes the control of the traditional mean and variance of the fiber length in some sense and has applications that are more extensive.

By dealing with robust modeling and online learning together in a unified random vector functional-link networks (RVFLNs) framework, this paper presents a novel robust online sequential RVFLNs for data modeling of dynamic time-varying systems together with its application for a blast furnace (BF) ironmaking process. First, to overcome the difficulties caused by the nonlinear time-varying dynamics of process and to enable the RVFLNs to learn online and to avoid data saturation, an improved online sequential version of RVFLNs (OS-RVFLNs) is presented by sequential learning with forgetting factor. It has been shown that the improved OS-RVFLNs with forgetting factor is not only suitable for the large-scale and real-time data transfer situation but also can adjust the sensitivity of the algorithm to different samples. Second, in order to solve the issue of modeling robustness when the dataset is contaminated with various outliers, a Cauchy distribution function weighted M-estimator is introduced to strengthen the robustness of the improved OS-RVFLNs. The non-Gaussian Cauchy distribution function is used to estimate the weights of different data and thus the corresponding contribution on modeling can be properly distinguished. Experiments using actual industrial data of a large BF ironmaking process have demonstrated that the proposed algorithm produces a much stronger robustness and better estimation accuracy than other algorithms.

As one of the most important unit in the papermaking industry, the high consistency (HC) refining system is confronted with challenges such as improving pulp quality, energy saving, and emissions reduction in its operation processes. In this correspondence, an optimal operation of HC refining system is presented using nonlinear multiobjective model predictive control strategies that aim at set-point tracking objective of pulp quality, economic objective, and specific energy (SE) consumption objective, respectively. First, a set of input and output data at different times are employed to construct the subprocess model of the state process model for the HC refining system, and then the Wiener-type model can be obtained through combining the mechanism model of Canadian Standard Freeness and the state process model that determines their structures based on Akaike information criterion. Second, the multiobjective optimization strategy that optimizes both the set-point tracking objective of pulp quality and SE consumption is proposed simultaneously, which uses NSGA-II approach to obtain the Pareto optimal set. Furthermore, targeting at the set-point tracking objective of pulp quality, economic objective, and SE consumption objective, the sequential quadratic programming method is utilized to produce the optimal predictive controllers. Finally, the simulation results demonstrate that the proposed methods can make the HC refining system provide a better performance of setpoint tracking of pulp quality when these predictive controllers are employed. In addition, while the optimal predictive controllers orienting with comprehensive economic objective and SE consumption objective, it has been shown that they have significantly reduced the energy consumption.

The dynamics of powertrain control systems are complicated and involve both nonlinear plant model and control functionalities, albeit they are well defined and formulated using first principle approaches. This constitutes difficulties in exploring implementable optimal tuning rules for some selected control parameters using vehicle-to-vehicle (V2V) communica- tions. This paper presents a way to use neural networks (NN) to represent the problem of parameter tuning for optimizing fuel consumption. For this purpose, physical modelling and validation have been firstly performed for the closed loop powertrain system of the concerned vehicle for some given driving cycles. This is then followed by the sensitivity analysis that selects most influential control parameters to optimize. Using the data generated from the obtained physical models, an equivalent NN formulation has finally been obtained that gives simple yet unified objectives and constraints ready to be used to solve the optimization problem that produces optimal tuning rules for the selected control parameters to minimize fuel consumption.

Functional brain network (FBN) has become very popular to analyze the interaction between cortical regions in the last decade. But researchers always spend a long time to search the best way to compute FBN for their specific studies. The purpose of this study is to detect the proficiency of operators during their mineral grinding process controlling based on FBN. To save the search time, a novel semi-data-driven method of computing functional brain connection based on stacked autoencoder (BCSAE) is proposed in this paper. This method uses stacked autoencoder (SAE) to encode the multi-channel EEG data into codes and then computes the dissimilarity between the codes from every pair of electrodes to build FBN. The highlight of this method is that the SAE has a multi-layered structure and is semi-supervised, which means it can dig deeper information and generate better features. Then an experiment was performed, the EEG of the operators were collected while they were operating and analyzed to detect their proficiency. The results show that the BCSAE method generated more number of separable features with less redundancy, and the average accuracy of classification (96.18%) is higher than that of the control methods: PLV (92.19%) and PLI (78.39%).

Complex industrial processes are multivariable and generally exhibit strong coupling among their control loops with heavy nonlinear nature. These make it very difficult to obtain an accurate model. As a result, the conventional and data-driven control methods are difficult to apply. Using a twin-tank level control system as an example, a novel multivariable decoupling control algorithm with adaptive neural-fuzzy inference system (ANFIS)-based unmodeled dynamics (UD) compensation is proposed in this paper for a class of complex industrial processes. At first, a nonlinear multivariable decoupling controller with UD compensation is introduced. Different from the existing methods, the decomposition estimation algorithm using ANFIS is employed to estimate the UD, and the desired estimating and decoupling control effects are achieved. Second, the proposed method does not require the complicated switching mechanism which has been commonly used in the literature. This significantly simplifies the obtained decoupling algorithm and its realization. Third, based on some new lemmas and theorems, the conditions on the stability and convergence of the closed-loop system are analyzed to show the uniform boundedness of all the variables. This is then followed by the summary on experimental tests on a heavily coupled nonlinear twin-tank system that demonstrates the effectiveness and the practicability of the proposed method.

Optimal operation of an industrial blast furnace (BF) ironmaking process largely depends on a reliable measurement of molten iron quality (MIQ) indices, which are not feasible using the conventional sensors. This paper proposes a novel data-driven robust modeling method for the online estimation and control of MIQ indices. First, a nonlinear autoregressive exogenous (NARX) model is constructed for the MIQ indices to completely capture the nonlinear dynamics of the BF process. Then, considering that the standard least-squares support vector regression (LS-SVR) cannot directly cope with the multioutput problem, a multitask transfer learning is proposed to design a novel multioutput LS-SVR (M-LS-SVR) for the learning of the NARX model. Furthermore, a novel M-estimator is proposed to reduce the interference of outliers and improve the robustness of the M-LS-SVR model. Since the weights of different outlier data are properly given by the weight function, their corresponding contributions on modeling can properly be distinguished, thus a robust modeling result can be achieved. Finally, a novel multiobjective evaluation index on the modeling performance is developed by comprehensively considering the root-mean-square error of modeling and the correlation coefficient on trend fitting, based on which the nondominated sorting genetic algorithm II is used to globally optimize the model parameters. Both experiments using industrial data and industrial applications illustrate that the proposed method can eliminate the adverse effect caused by the fluctuation of data in BF process efficiently. This indicates its stronger robustness and higher accuracy. Moreover, control testing shows that the developed model can be well applied to realize data-driven control of the BF process.

This paper studies how to control the output of a class of nonlinear discrete-time systems, to completely track any given bounded reference trajectories in finite time. For this problem, we develop two kinds of constructive control methods for the total output case and the partial output case, respectively. For each case, the first kind of methods can design the time instant after which the complete trajectory tracking is accomplished, but cannot guarantee the monotonic decrease of the norm of the tracking error before that time instant; the other kind of methods not only can determine when the output trajectory coincides with the reference trajectory, but also can make the norm of the tracking error decrease monotonically before that time instant. For the partial output case, the proposed control methods can guarantee that the rest part of the system output is bounded for all the time. These control methods are feasible no matter whether the dynamic models of these systems are smooth or nonsmooth. Then, the simulation and experiment results prove the feasibility of the proposed methods.

This paper presents a novel fault-tolerant control method for a class of discrete-time and nonGaussian stochastic systems, where two subsystems are connected in series so as to operate in a collaborative way. For such systems, the output probability density function of the second subsystem is taken as the output of the whole system. The proposed method includes the design of a fault diagnosis (FD) algorithm for the first subsystem and the establishment of a fault-tolerant control algorithm for the second subsystem. At first, linear matrix inequality techniques are used to construct the FD algorithm for the first subsystem. Once the fault is diagnosed, a fault-tolerant control algorithm is designed using the well-known optimal norm-based iterative learning control approach. Different from the existing fault tolerant controller methods, the proposed fault-tolerant control is designed not for the faulty subsystem but for the healthy subsystem. As a result, when a fault occurs in the first subsystem, the reconfigured controller for the healthy second subsystem can accommodate the fault and guarantee that the whole system will still exhibit good operational performance. A simulated example is used to demonstrate the collaborative fault-tolerant control effect and desired results have been obtained.

The whole production line of hematite ore processing is composed of raw ore processing, shaft furnace roasting, grindings, and magnetic separation production phases. Their automation systems consist of the process control part and the operational optimization system. The target of the optimal operational control is to optimize the concerned operational indices, namely, the intermediate product quality, efficiency, and consumptions. The dynamics between the operational indices and the global production indices (i.e., the total concentration grade, metal recovery rate, production rate, beneficiation ratio, and costs) with month, day, and hour time scales changes in line with the variations of production conditions, composition of raw ore together with capability of equipment. These indices are difficult to measure online and as a result it is difficult to model accurately. Moreover, there are characteristics in terms of both interconnections and conflictions among these indices. This leads to isolated operation of individual automation systems for these processes and the optimization of global production indices for whole production line cannot be realized. This paper presents a novel problem description for the integrated optimization of the automation systems of mineral processing. For this purpose, the analysis is made on the difficulty of using the existing optimization methods-based decision making methods to obtain the integrated optimization of the automation systems. The integrated optimization strategy for the automation systems of mineral processes is proposed using our previously established target value optimization of global production indices , two time scales decomposition approach and target value optimization of operational indices. The proposed strategy aims at realizing the optimization of global production indices. Using real data from a mineral processing plant on hematite beneficiation process, relevant simulations, and real industrial experiments have been carried out. The obtained experimental results show the efficiency and effectiveness of the proposed strategy.

The 17 papers in this special section focus on integrated optimization of industrial automation.

In this paper, we propose a sliding-mode-based stochastic distribution control algorithm for nonlinear systems, where the sliding-mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function. Kullback-Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.

In this paper, the challenging issue of estimating virtual unmodeled dynamics is addressed. A novel estimation algorithm based on historical data and the output of low-order approximation models for virtual un-modeled dynamics is presented. In particular, the virtual un-modeled dynamics are decomposed into known and unknown parts, where only the unknown part is to be estimated. The method effectively avoids the need to use the unknown control input directly, and enables the estimation of the un-modeled dynamics with a relatively simple algorithm. Moreover, it is shown that the proposed algorithm overcomes the difficulty in obtaining the control solutions caused by the fact that the controller input is embedded in un-modeled dynamics. Finally, simulation studies are presented to demonstrate the effectiveness of the proposed method.

By representing nonlinear systems as a combination of linear part and unmodeled dynamics, in this paper, an improved estimation algorithm using an adaptive neuro-fuzzy inference system (ANFIS) for unmodeled dynamics is presented. At first, the unmodeled dynamics is divided into two parts using the differential expansion of the control input at the last time instant; then, the two parts are estimated by the ANFIS. It has been shown that the proposed algorithm overcomes the problem that the unknown control input is embedded in unmodeled dynamics, which makes the true value of unmodeled dynamics difficult obtain. Moreover, the method improves the precision of the estimation of unmodeled dynamics. Second, under the assumption that the growth rate of unmodeled dynamics does not exceed its input vector, the “one-to-one mapping” and “regularization technique” are adopted to deal with the input and output data and the unmodeled dynamics, respectively. As a result, the data vector can be guaranteed to lie inside a compact set, which ensures the use of the universal approximation property of the ANFIS. On the other hand, it has been shown that datum of a system can be fully used to obtain the parameters (centers, widths) in membership functions and the network connection weights in the ANFIS by offline training. These parameters are tuned online to improve the estimation convergence rate of the unmodeled dynamics. The effectiveness of the proposed estimation method is illustrated by comparing it with the simulation results that are obtained from the other existing methods. Finally, the proposed estimation method is applied to the nonlinear switching control design. Both simulation and theoretical analysis have confirmed that the nonlinear switching control which adopts the proposed estimation method cannot only guarantee the stability and convergence of the system but can exhibit a desired dynamic performance for the closed-loop system as well.

In this paper, a novel knowledge-based global operation approach is proposed to minimize the effect on the production performance caused by unexpected variations in the operation of a mineral processing plant subjected to uncertainties. For this purpose, a feedback compensation and adaptation signal discovered from process operational data is employed to construct a closed-loop dynamic operation strategy. It uses the signal to regulate the outputs of the existing open-loop and steady-state based system so as to compensate the uncertainty in the steady-state operation at the plant-wide level. The utilization mechanism of operational data through constructing increment association rules is firstly described. Then, a rough set based rule extraction approach is developed to generate the compensation rules. This includes two steps, namely the determination of the variables to be compensated based on the significance of attributes in the rough set theory and the extraction of the compensation rules from process data. Based upon the operational data of the mineral processing plant, relevant rules are obtained. Both simulation and industrial experiments are carried out for the proposed global operation, where the effectiveness of the proposed approach has been clearly justified.

Reducing energy consumption is a major challenge for "energy-intensive" industries such as papermaking. A commercially viable energy saving solution is to employ data-based optimization techniques to obtain a set of "optimized" operational settings that satisfy certain performance indices. The difficulties of this are: 1) the problems of this type are inherently multicriteria in the sense that improving one performance index might result in compromising the other important measures; 2) practical systems often exhibit unknown complex dynamics and several interconnections which make the modeling task difficult; and 3) as the models are acquired from the existing historical data, they are valid only locally and extrapolations incorporate risk of increasing process variability. To overcome these difficulties, this paper presents a new decision support system for robust multiobjective optimization of interconnected processes. The plant is first divided into serially connected units to model the process, product quality, energy consumption, and corresponding uncertainty measures. Then multiobjective gradient descent algorithm is used to solve the problem in line with user's preference information. Finally, the optimization results are visualized for analysis and decision making. In practice, if further iterations of the optimization algorithm are considered, validity of the local models must be checked prior to proceeding to further iterations. The method is implemented by a MATLAB-based interactive tool DataExplorer supporting a range of data analysis, modeling, and multiobjective optimization techniques. The proposed approach was tested in two U.K.-based commercial paper mills where the aim was reducing steam consumption and increasing productivity while maintaining the product quality by optimization of vacuum pressures in forming and press sections. The experimental results demonstrate the effectiveness of the method.

For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.

This paper presents a novel offline modeling for product quality prediction of mineral processing which consists of a number of unit processes in series. The prediction of the product quality of the whole mineral process (i.e., the mixed concentrate grade) plays an important role and the establishment of its predictive model is a key issue for the plantwide optimization. For this purpose, a hybrid modeling approach of the mixed concentrate grade prediction is proposed, which consists of a linear model and a nonlinear model. The least-squares support vector machine is adopted to establish the nonlinear model. The inputs of the predictive model are the performance indices of each unit process, while the output is the mixed concentrate grade. In this paper, the model parameter selection is transformed into the shape control of the probability density function (PDF) of the modeling error. In this context, both the PDF-control-based and minimum-entropy-based model parameter selection approaches are proposed. Indeed, this is the first time that the PDF shape control idea is used to deal with system modeling, where the key idea is to turn model parameters so that either the modeling error PDF is controlled to follow a target PDF or the modeling error entropy is minimized. The experimental results using the real plant data and the comparison of the two approaches are discussed. The results show the effectiveness of the proposed approaches.

The continuous annealing process line (CAPL) of cold rolling is an important unit to improve the mechanical properties of steel strips in steel making. In continuous annealing processes, strip tension is an important factor, which indicates whether the line operates steadily. Abnormal tension profile distribution along the production line can lead to strip break and roll slippage. Therefore, it is essential to estimate the whole tension profile in order to prevent the occurrence of faults. However, in real annealing processes, only a limited number of strip tension sensors are installed along the machine direction. Since the effects of strip temperature, gas flow, bearing friction, strip inertia, and roll eccentricity can lead to nonlinear tension dynamics, it is difficult to apply the first-principles induced model to estimate the tension profile distribution. In this paper, a novel data-based hybrid tension estimation and fault diagnosis method is proposed to estimate the unmeasured tension between two neighboring rolls. The main model is established by an observer-based method using a limited number of measured tensions, speeds, and currents of each roll, where the tension error compensation model is designed by applying neural networks principal component regression. The corresponding tension fault diagnosis method is designed using the estimated tensions. Finally, the proposed tension estimation and fault diagnosis method was applied to a real CAPL in a steel-making company, demonstrating the effectiveness of the proposed method.

This paper presents a novel nonlinear control strategy for a class of uncertain single-input and single-output discrete-time nonlinear systems with unstable zero-dynamics. The proposed method combines adaptive-network-based fuzzy inference system (ANFIS) with multiple models, where a linear robust controller, an ANFIS-based nonlinear controller and a switching mechanism are integrated using multiple models technique. It has been shown that the linear controller can ensure the boundedness of the input and output signals and the nonlinear controller can improve the dynamic performance of the closed loop system. Moreover, it has also been shown that the use of the switching mechanism can simultaneously guarantee the closed loop stability and improve its performance. As a result, the controller has the following three outstanding features compared with existing control strategies. First, this method relaxes the assumption of commonly-used uniform boundedness on the unmodeled dynamics and thus enhances its applicability. Second, since ANFIS is used to estimate and compensate the effect caused by the unmodeled dynamics, the convergence rate of neural network learning has been increased. Third, a "one-to-one mapping" technique is adapted to guarantee the universal approximation property of ANFIS. The proposed controller is applied to a numerical example and a pulverizing process of an alumina sintering system, respectively, where its effectiveness has been justified.

In this paper, an adaptive generalized predictive control method using adaptive-network-based fuzzy-inference system (ANFIS) and multiple models is proposed for a class of uncertain discrete-time nonlinear systems with unstable zero-dynamics. The proposed controller consists of a linear and robust generalized predictive adaptive controller, a nonlinear generalized predictive adaptive controller based on ANFIS, and a switching mechanism. It has been shown that the linear generalized predictive adaptive controller can ensure the boundedness of the input and output signals, and the nonlinear generalized predictive controller can improve the transient performance of the system. By switching between the two earlier described controllers, the switching mechanism can simultaneously improve the performance and ensure the closed-loop stability. Moreover, the method has relaxed the global boundedness assumption of the higher order nonlinear term and established the analysis of stability and convergence of the closed-loop system. In the proposed controller, ANFIS is adopted to estimate and compensate the unmodeled dynamics, which avoids some possible flaws of a backpropagation (BP) neural network. Simulation results have demonstrated the superiority of the proposed method and verified the theoretical analysis.

During the operation of a grinding circuit (GC) in mineral processing plant the main purpose of control and optimal operation is to control the product quality index, namely the product particle size, into its technically desired ranges. Moreover, the grinding production rate needs to be maximized. However, due to the complex dynamic characteristics between the above two indices and the control loops, such control objectives are difficult to achieve using existing control methods. The complexity is reflected by the existence of process heavy nonlinearities, strong coupling and large time variations. As a result, the lower level loop control with human supervision is still widely used in practice. However, since the setpoints to the involved control loops cannot be accurately adjusted under the variations of the boundary conditions, the manual setpoints control cannot ensure that the actual production indices meet with technical requirements all the time. In this paper, an intelligent optimal-setting control (IOSC) approach is developed for a typical two-stage GC so as to optimize the production indices by auto-adjusting on line the setpoints of the control loops in response to the changes in boundary conditions. This IOSC approach integrates case-based reasoning (CBR) pre-setting controlling, neural network (NN)-based soft-sensor and fuzzy adjusting into one efficient control model. Although each control element is well known, their innovative combination can generate better and more reliable performance. Both industrial experiments and applications show the validity and effectiveness of the proposed IOSC approach and its bright application foreground in industrial processes with similar features.

In this paper, a new method for adaptive control of general nonlinear and non-Gaussian unknown stochastic systems has been proposed. The method applies the minimum entropy control scheme to decrease the closed-loop randomness of the output under an iterative learning control (ILC) basis. Both modeling and control of the plant are performed using dynamic neural networks. For this purpose, the whole control horizon is divided into a certain number of time domain subintervals called batches and a pseudo-D-type ILC law is employed to train the plant model and controller parameters so that the entropy of the closed-loop tracking error is made to decrease batch by batch. The method has the advantage of decreasing the output uncertainty versus the advances of batches along the time horizon. The analysis on the proposed ILC convergence is made and a set of demonstrable experiment results is also provided to show the effectiveness of the obtained control algorithm, where encouraging results have been obtained.

This paper presents a new type of control framework for dynamical stochastic systems, called statistic tracking control (STC). The system considered is general and non-Gaussian and the tracking objective is the statistical information of a given target probability density function (pdf), rather than a deterministic signal. The control aims at making the statistical information of the output pdfs to follow those of a target pdf. For such a control framework, a variable structure adaptive tracking control strategy is first established using two-step neural network models. Following the B-spline neural network approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. The dynamic neural network (DNN) is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function. To achieve the required control objective, an adaptive controller based on the proposed DNN is developed so as to track a reference trajectory. Stability analysis for both the identification and tracking errors is developed via the use of Lyapunov stability criterion. Simulations are given to demonstrate the efficiency of the proposed approach.

This study is motivated by the onboard fault detection of gas turbine engines (GTEs), where the computation resources are limited and the disturbance is assumed to be band-limited. A fast Fourier transformation (FFT)-based disturbance frequency estimation approach is proposed and performance indexes are improved by integrating such frequency information. Furthermore, in the left eigenvector assignment, both eigenvalues and free parameters are optimized. As illustrated in the application to the actuator fault detection of a GTE, significant improvements are achieved compared to the existing methods. By combining the frequency estimation and eigenvalue optimization, the main contribution of the paper is the reduction of the computation complexity and the avoidance of the local optimal solution due to fixed eigenvalues.

Stochastic distribution control systems aims at the controller design so as to realize a shape control of the distributions of certain random variables in the process. Once the probability density functions (PDFs) of these variables are used to describe their distributions, the control task is to obtain control signals so that the output PFDs of the system are made to follow their target PDFs. In this paper a survey of the recent developments on the research of stochastic distribution control systems will be made.

In this paper, robust minimum entropy tracking control problem is considered for nonlinear stochastic systems. The controlled systems are described by nonlinear non-Gaussian difference equations with the un-modeled uncertainty and modeling error, as well as time delays. Entropy is adopted to characterize the uncertainty of the tracking error. The nonlinear multi-step-ahead predictive cost function is used and the relationship between the probability density functions of the input and the tracking error via the uncertain mapping is established. With these formulations, the cost function can be bounded as a nonlinear functional of the control input and the known bounds of the errors. Explicit design algorithms are presented for the robust suboptimal controller and further for the stabilization controllers. The Renyi's entropy has also been used to simplify the cost function. Simulations are given to demonstrate the effectiveness of the proposed control algorithm.

In this study, a novel identification technique, that is high-gain observer-based identification approach, is proposed for systems with bounded process and measurement noises. For system parameters with abnormal changes, an adaptive change detection and parameter identification algorithm is next presented. The presented technique and algorithm are finally applied to the parameter identification of the gas turbine engine by using the recorded input data from the engine test-bed. The identified parameters and the response curves are desirable. The simulations have proved the effectiveness of the proposed procedure compared with the previous identification approach.

For systems with both state and input time delays, a novel state and sensor fault observer is proposed in this paper to estimate system states and sensor faults simultaneously. In this design, a descriptor system approach and a linear matrix inequality technique are adopted, where the considered sensor fault may be in any form, even unbounded. Unbounded sensor faults will make the system fail unavoidably; it is indispensable to derive a reliable control scheme against sensor failures. Using the estimated state and sensor fault, a reliable observer-based controller is proposed, which makes the system work well no matter whether sensor faults occur or not. The present approaches are next extended to the case for systems with multiple time delays. Finally, a simulation example of the network of three cascaded reactors is used to illustrate the design procedure and demonstrate the efficiency of the present techniques.

This paper presents a pseudo proportional-integral-derivative (PID) tracking control strategy for general non-Gaussian stochastic systems based on a linear B-spline model for the output probability density functions (PDFs). The objective is to control the conditional PDFs of the system output to follow a given target function. Different from existing methods, the control structure (i.e., the PID) is imposed before the output PDF controller design. Following the linear B-spline approximation on the measured output PDFs, the concerned problem is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be casted into a group of matrix inequalities. Furthermore, an improved controller design procedure based on the convex optimization is proposed which can guarantee the required tracking convergence with an enhanced robustness. Simulations are given to demonstrate the efficiency of the proposed approach and encouraging results have been obtained.

Following the recently developed strategies for the modelling and control for multi-input multi-output (MIMO) distribution control systems, this paper presents a dynamic model for the control of combined probability density function. A multilayer perceptron (MLP) neural network is used to approximate the probability density function (PDF) of the systems and a high-order dynamic nonlinear state-space model is obtained. Then nonlinear principal component analysis (NLPCA) is adopted to reduce the obtained model order and a lower-order time-varying system is achieved. The controller design for the lower-order time-varying system is given. The effectiveness of the result has been demonstrated by two examples in the end.

In this paper a direct adaptive neural-network control strategy for unknown nonlinear systems is presented. The system considered is described by an unknown NARMA model, and a feedforward neural network is used to learn the system. Taking the neural network as a neural model of the system, control signals are directly obtained by minimizing either the instant difference or the cumulative differences between a set point and the output of the neural model. Since the training algorithm guarantees that the output of the neural model approaches that of the actual system, it is shown that the control signals obtained can also make the real system output close to the set point. An application to a flow-rate control system is included to demonstrate the applicability of the proposed method and desired results are obtained.