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This paper focuses on expanding the estimation of the domain of attraction (DOA) for discrete-time positive nonlinear systems subject to input saturation and parameter uncertainties. To facilitate analysis and design, the interval type-2 (IT2) polynomial fuzzy model is used to represent the nonlinear plant and capture uncertainties. Combining with the IT2 polynomial fuzzy controller, the discrete-time positive IT2 polynomial fuzzy-model-based (PIT2PFMB) control system is formed to facilitate analysis. To enlarge the estimation of DOA of the discrete-time PIT2PFMB system, polyhedron is used to characterize the DOA with the help of linear copositive Lyapunov function (LCLF). Referring to the non-convex conditions derived by LCLF, an effective convexification method is proposed in this paper. For comparison purposes, the saturation-dependent-Lyapunov-function-based method is extended to the PIT2PFMB control system by adding the corresponding positivity conditions. In addition, this paper attempts to enlarge the estimation of the DOA by improving the IT2 membership-function-dependent (IT2MFD) method and extending it to all conditions including the stability conditions and the DOA estimation conditions. Finally, an example with simulation results is given to verify the effectiveness of all the methods proposed in this paper for expanding the estimation of the DOA.

Block pulse functions (BPFs) are piecewise constant and not sufficiently smooth. Therefore, their accuracy is limited when it comes to identifying the parameters of fractional order systems (FOSs). This in turn means that BPFs are incapable of offering highly accurate parameter identification results. However, using a great number of BPFs would significantly increase the dimension of the operational matrix and thereby adds to the computational complexity and burden. To overcome this problem, we present here a hybrid function method for identifying FOSs. The method utilizes a hybrid of Bernoulli polynomials and block pulse functions (HBPBPFs) as the base functions to approximate input and output signals. The fractional integral operational matrix of HBPBPFs is derived and used to convert an FOS to an algebraic system. The parameters of the FOS are successfully identified by minimizing the mean square error between the output of the true system and that of the algebraic representation of the FOS. The simulation experiment verifies that our proposed HBPBPFs method is effective and can generate more accurate identification results than existing BPFs methods.

As a position servo system to isolate disturbance from its carrier, stabilized platform requires high-precision and high-adaptability control. However, conventional integer-order PID (IOPID) control fails to meet that requirement. In this paper, a new controller design scheme is proposed for stabilized platform based on fractional calculus. The designed controller is called fractional-order PID (FOPID) controller, which has two extra parameters compared to conventional PID controller. On one hand, it provides more degrees of freedom to design FOPID controller. On the other hand, its differential order and integral order provides more flexibility to tune the controller performance. Therefore, a design method of FOPID controller based on dynamic software modeling is presented. To obtain the ideal controller's parameters, the particle swarm optimization (PSO) bionic algorithm is used to optimize an objective function. In addition, software simulation platform and hardware experiment system are built to design and test the FOPID controller. Finally, the results of simulation and experiment are included to show the effectiveness of the new control method.

The imperialist competitive algorithm (ICA), inspired by sociopolitical behavior in the real world, is a new optimization algorithm. The ICA shows great potential to solve complex optimization problems. In order to improve the ICA's exploration ability and speed up its convergence, two improved schemes are proposed in this paper. The first scheme presents a new possession probability in the imperialistic competition phase. Inspired by geopolitics, not only the power of the empire but also the distance between the imperialists are taken into account in calculating the new possession probability. The second scheme introduces the wavelet mutation operator into the original ICA so as to improve its exploration ability. The improved ICAs (IICAs) are tested on several benchmark functions and then used to design the optimum parameters of tuned mass damper and tune the parameters of a fractional order PID controller of an automatic voltage regulator (AVR) system. Results show that the IICAs outperform the original ICA in terms of solution quality and convergence speed.

To improve the segmentation performance of thresholding methods, a novel strategy of integrating the spatial information between pixel's is proposed in this paper. The proposed strategy utilizes pixel's gray level and its local entropy within a neighborhood to construct a novel 2-D histogram, called gray level-local entropy (GLLE) histogram. The local entropy can effectively reflect the homogeneity of a pixel's gray level in a neighborhood. Based on the GLLE histogram, an ideal thresholding vector is obtained by maximizing the total Tsallis entropy of background and objects. The proposed method is validated through segmenting several real images. Experimental results show that the proposed method outperforms many existing thresholding methods.

In this paper, an online identification method is proposed for nonlinear system identification based on extreme learning machine (ELM)–Hammerstein model. The ELM–Hammerstein model comprises an ELM neural network followed by a linear dynamic subsystem. This model is linear in parameters and nonlinear in the input. To speed up the convergence and meanwhile improve identification accuracy, a changing forgetting factor recursive least squares (CFF-RLS) method is proposed as online learning algorithm. The algorithm can identify the parameters of linear dynamic subsystem and the weights of ELM neural network simultaneously. Simulation results verify the effectiveness of the proposed method.

Automatic voltage regulator (AVR) system is an important equipment in power system for maintaining the terminal voltage of the generator at a specific level. Recently, fractional order PID controller has been designed for AVR system. However, many fractional order PID controller designing methods need to calculate various performance indices in time domain and frequency domain in the process of parameter tuning, which is a tedious and complex process and satisfactory performance can not be obtained. In this paper, a new fractional order PID controller designing method is proposed AVR system based on Bodes reference model. The optimal parameters of FOPID controller is obtained through minimizing the integrated absolute error (IAE) between the output of the Bodes ideal reference model and that of the plant. Particle swarm optimization (PSO) is responsible to search the solution of the IAE criterion, i.e., the parameters of FOPID controller. Extensive simulations and comparisons show that the designed FOPID controller has more excellent performance. Meanwhile, PSO algorithm is effective for searching the optimal FOPID controller parameters.

Extreme Learning Machine (ELM), a competitive machine learning technique for single-hidden-layer feedforward neural networks (SLFNNs), has proven to be efficient and effective algorithm for regression and classification problems. However, traditional ELM involves a large number of hidden nodes for complex real world regression and classification problems which increasing the computation burden. In this paper, a decomposition based fast ELM (DFELM) algorithm is proposed to effectively reduce the computational burden for large number of hidden nodes condition. Compared with ELM algorithm, DFELM algorithm has faster training time with a large number of hidden nodes maintaining the same accuracy performance. Experiment on three regression problems, six classification problems and a complex blast furnace modeling problem are carried out to verify the performance of DFELM algorithm. Moreover, the decomposition method can be extended to other modified ELM algorithms to further reduce the training time.

As a highly complex multi-input and multi-output system, blast furnace plays an important role in industrial development. Although much research has been done in the past few decades, there still exist many problems to be solved, such as the modeling problem. This paper adopts support vector regression (SVR) to construct the prediction model of blast furnace silicon content. To ensure a good generalization performance for the given datasets, it is important to select proper parameters for SVR. In view of this problem, a new particle swarm optimizer called DMS-PSO-CLS is presented to optimize the parameters of SVR. In DMS-PSO-CLS, a new cooperative learning strategy is hybridized with DMS-PSO, which makes particle information be used more effectively for generating better-quality solutions. DMS-PSO-CLS takes merits of the DMS-PSO and the cooperative learning strategy so that both the convergence speed and the convergence precision can be improved. Experimental results show that DMS-PSO-CLS can find the optimal parameters of SVR with high speed and the SVR model optimized by DMS-PSO-CLS can achieve a good regression precision on the predictive problem of blast furnace.

Graphical abstractDisplay Omitted HighlightsA new cooperative learning strategy is hybridized with DMS-PSO.Information can be exchanged among sub-swarms before the regrouping process.Experimental results show that DMS-PSO-CLS has a superior performance. In this article, the dynamic multi-swarm particle swarm optimizer (DMS-PSO) and a new cooperative learning strategy (CLS) are hybridized to obtain DMS-PSO-CLS. DMS-PSO is a recently developed multi-swarm optimization algorithm and has strong exploration ability for the use of a novel randomly regrouping schedule. However, the frequently regrouping operation of DMS-PSO results in the deficiency of the exploitation ability. In order to achieve a good balance between the exploration and exploitation abilities, the cooperative learning strategy is hybridized to DMS-PSO, which makes information be used more effectively to generate better quality solutions. In the proposed strategy, for each sub-swarm, each dimension of the two worst particles learns from the better particle of two randomly selected sub-swarms using tournament selection strategy, so that particles can have more excellent exemplars to learn and can find the global optimum more easily. Experiments are conducted on some well-known benchmarks and the results show that DMS-PSO-CLS has a superior performance in comparison with DMS-PSO and several other popular PSO variants.

Blast furnace gas is a significant energy resource in steel industry. Keeping stable of blast furnace gas flow is an important task for the furnace itself and the application of byproduct gas. However, owing to fluctuation and noisy of gas flow, echo state network is usually ill-posed in the prediction and it is very difficult to accurately predict the amount of gas. In this paper, in order to increase the accuracy of prediction in ill-posed echo state network model, L-curve method is used to compute the regularization parameter, which can alleviate the influence of ill-condition for ESN. Finally, to verify the effectiveness of the proposed method, the real data from blast furnace is employed in the experiments. Compared with two parameter regularization methods and four types of prediction methods, the results demonstrate that the proposed method exhibits a higher prediction accuracy for gas prediction.

Thresholding is a popular method of image segmentation. Many thresholding methods utilize only the gray level information of pixels in the image, which may lead to poor segmentation performance because the spatial correlation information between pixels is ignored. To improve the performance of thresolding methods, a novel two-dimensional histogram—called gray level-local variance (GLLV) histogram—is proposed in this paper as an entropic thresholding method to segment images with bimodal histograms. The GLLV histogram is constructed by using the gray level information of pixels and its local variance in a neighborhood. Local variance measures the dispersion of gray level distribution of pixels in a neighborhood. If a pixel’s gray level is close to its neighboring pixels, its local variance is small, and vice versa. Therefore, local variance can reflect the spatial information between pixels. The GLLV histogram takes not only the gray level, but also the spatial information into consideration. Experimental results show that an entropic thresholding method based on the GLLV histogram can achieve better segmentation performance.

In this paper, a new method for nonlinear system identification via extreme learning machine neural network based Hammerstein model (ELM-Hammerstein) is proposed. The ELM-Hammerstein model consists of static ELM neural network followed by a linear dynamic subsystem. The identification of nonlinear system is achieved by determining the structure of ELM-Hammerstein model and estimating its parameters. Lipschitz quotient criterion is adopted to determine the structure of ELM-Hammerstein model from input–output data. A generalized ELM algorithm is proposed to estimate the parameters of ELM-Hammerstein model, where the parameters of linear dynamic part and the output weights of ELM neural network are estimated simultaneously. The proposed method can obtain more accurate identification results with less computation complexity. Three simulation examples demonstrate its effectiveness.

A deficiency of KH is analyzed.Why KH cannot achieve the excellent balance between exploration and exploitation in optimization processing is explained.To overcome the defect, an improved KH with linear decreasing step (KHLD) is proposed. Krill herd (KH) inspired by the herding behavior of the krill individuals is a new swarm intelligent algorithm which is proved to perform better than other swarm intelligent algorithms. However, there are some weak points yet. In this paper, we analyze a deficiency of KH which cannot achieve the excellent balance between exploration and exploitation in optimization processing and proposed an improved KH-krill herd with linear decreasing step (KHLD). Twenty benchmark functions are used to verify the effectiveness of these improvements and it is illustrated that, in most cases, the performance of KHLD is superior to the standard KH.

Antilock braking system (ABS) is a highly nonlinear system including variation and uncertainties in the parameters due to changes in vehicle loadings, road condition, etc. It is a difficult task to design an ideal controller for ABS. In this paper, a novel robust controller named fractional order sliding mode controller (FOSMC) is proposed for ABS to regulate the slip to a desired value. The proposed FOSMC combines sliding mode controller (SMC) with fractional order dynamics, in which fractional order proportional-derivative (FOPD) sliding surface is adopted. FOSMC can not only deal with the uncertainties in ABS system but also track the desired slip faster than conventional integer order SMC with proportional or proportional-derivative sliding surface. Experimental results demonstrate the effectiveness of the proposed method.

Image super-resolution aims to recover a fine-resolution image from one or more low-resolution image(s). In this paper, we propose a novel image super-resolution approach based on the recent development of coupled deep auto-encoder. In the training step, the vector of the local low resolution (LR) and high resolution image (HR) patches and the corresponding edge information are extracted to be the input of the autoencoder. Then we learn the intrinsic representations of LR and HR image patches by auto-encoders respectively. Then we learn their relationship by a two-layer neural network. In the test step, given a LR image patch, we can obtain the corresponding HR patch through the trained deep network efficiently and effectively. Expensive experimentation results show that the proposed algorithm generates higher-quality super-resolution image compared to other state-of-the-art methods.

Image super-resolution (SR) can help people obtain a high-resolution (HR) image through a series of low-resolution (LR) images. Deep convolutional neural network (CNN) is one of deep learning methods, and has been applied in the field of machine vision successfully. Recently, people developed a CNN model, which learns an end-to-end mapping between LR/HR images directly. However, this method only considers the local gray information of images in the training step, and we find that the experimental results produce local edge blurring. In this paper, we consider a combination of local gray information and local gradient information to reduce the local edge blurring. We calculate the 1st (first) and 2nd (second) order for each pixel to represent image edge information by gradient algorithm. Then, we combine our training samples and the gradient information together to train the SRCNN model. Finally, the experimental result shows that our method is effective by comparing with the state-of-the-art SR methods.

Antilock braking system (ABS) has been designed to attain maximum negative acceleration and prevent the wheels from locking. Many efforts had been paid to design controller for ABS to improve the brake performance, especially when road condition changes. In this paper, an adaptive fuzzy fractional-order sliding mode controller (AFFOSMC) design method is proposed for ABS. The proposed AFFOSMC combines the fractional-order sliding mode controller (FOSMC) and fuzzy logic controller (FLC). In FOSMC, the sliding surface is PDα, which is based on fractional calculus (FC) and is more robust than conventional sliding mode controllers. The FLC is designed to compensate the effects of parameters varying of ABS. The tuning law of the controller is derived based on Lyapunov theory, and the stability of the system can be guaranteed. Simulation results demonstrate the effectiveness of AFFOSMC for ABS under different road conditions.

Fractional-order PID (FOPID) controller is a generalization of standard PID controller using fractional calculus. Compared to PID controller, the tuning of FOPID is more complex and remains a challenge problem. This paper focuses on the design of FOPID controller using chaotic ant swarm (CAS) optimization method. The tuning of FOPID controller is formulated as a nonlinear optimization problem, in which the objective function is composed of overshoot, steady-state error, raising time and settling time. CAS algorithm, a newly developed evolutionary algorithm inspired by the chaotic behavior of individual ant and the self-organization of ant swarm, is used as the optimizer to search the best parameters of FOPID controller. The designed CAS-FOPID controller is applied to an automatic regulator voltage (AVR) system. Numerous numerical simulations and comparisons with other FOPID/PID controllers show that the CAS-FOPID controller can not only ensure good control performance with respect to reference input but also improve the system robustness with respect to model uncertainties.

In this paper, a new method is proposed for prediction of ship roll motion based on extreme learning machine (ELM). To improve the prediction accuracy and avoid over or under fitting, two techniques are adopted to select the appropriate structure of ELM. First, the inputs of the ELM are selected from the roll motion time series using Lipschitz quotient method. Second, the number of hidden layer nodes is determined via ℓ1 regularized technique. Finally, the ℓ1 regularized ELM is solved by least angle regression (LAR) algorithm. The effectiveness of the proposed method is demonstrated by ship roll motion prediction experiments based on the real measured ship roll motion time series.

Spatial correlation information between pixels is considered to be very important in thresholding methods. However, it is often ignored and thus unsatisfied segmentation results maybe obtained. To overcome this shortcoming, we propose a new image segmentation approach by taking not only pixels&rsquo, spatial information but also pixels&rsquo, s gray level into account. First, a non-local mean filter is imposed on the image. Then the filtered image and the original image together are adopted to build a two dimensional histogram, it is called non-local mean two dimensional histogram. Finally, a minimum relative entropy criteria is used to select the ideal thresholding vector. Since the non-local mean filter process is performed in a neighborhood of current pixel, it carries out the spatial information of current pixel. Segmentation results on several images illustrate the effectiveness of the proposed thresholding method, whose segmentation accuracy are greatly improved compared to most existing thresholding methods.

The identification problem of delay time as well as parameters of time-delay chaotic system is investigated in this paper. The identification problem is converted to that of parameter optimization by constructing suitable fitness function. A novel optimization method, called CAS (chaotic ant swarm), which simulates the chaotic behavior of single ant and the self-organization behavior of ant colony, is used to solve this optimization problem. Illustrative example demonstrates the effectiveness of the proposed method.

As a highly complex multi-input and multi-output system, blast furnace plays an important role in industrial development. Although much research has been done in the past few decades, there still exist many problems, such as the modeling and control problems. In view of these reasons, this paper is concerned with developing a Wiener model to predict the silicon content of blast furnace. Unlike traditional Wiener model, this paper avoids the optimization of high number of model parameters. The Wiener model here is composed of a basis filter filter expansion named Laguerre filter and a linear programming support vector regression (LP-SVR). They are used to represent the linear dynamic component and the nonlinear static element. Take the advantages that Laguerre filter can approximate linear systems with a lower model and order and LP-SVR can achieve a sparse solution, the proposed Wiener model not only improves the prediction accuracy but also reduces the computation complexity. Simulation results show that this Wiener model is suitable for the prediction of blast furnace silicon content.

This paper deals with the parameter identification of Wiener model with discontinuous nonlinear. The arameter identification problemis converted to an optimal problem ith a suitable objective function. A hybrid optimal method, which integrates the Nelder-Mead simplex search and particle swarm optimization (NM-PSO), is used to optimize the objective function. The hybrid optimal method NM-PSO can get obtain the global optimal solution with fast convergent rate. Two illustrative examples are included to emonstrate the effectiveness and feasible of the proposed identification method

Counting of leukocytes in peripheral blood is commonly used in basic clinical diagnosis. The reliable approach to count leukocytes depends on morphological assessment of cellular materials under a light microscopy. Microscopic evaluation by medical technologists is a time-consuming and stuffy job. It is of interest to apply computer-aided analysis with image processing and pattern recognition, instead of human to count leukocytes. In this paper, a novel segmentation method is developed to count leukocytes by incorporating textural information. The proposed method integrates a non-decimated (or called shift invariant) complex wavelet transform into watershed segmentation, and uses information obtained by adaptive threshold segmentation to refine the result of watershed segmentation. Experiments demonstrate that the proposed method can obtain satisfactory results in comparison with the judgments of medical technologists.

Fuzzy Kohonen clustering network(FKCN) shows great superiority in processing the clustering in image segmentation. In this paper, an intensified Fuzzy Kohonen clustering Network (IFKCN) is proposed for texture segmentation. The method adjusts fuzzy factors to accelerate the speed of convergence. It intensifies the biggest membership and suppresses the other. By using this network in Brodatz texture segmentation, its iteration is fewer and the speed of convergence is quicker than FKCN and AFKCN(Adaptive Fuzzy Kononen clustering Network), and segmentation results are as well as FKCN.