Design of an interval type-2 fuzzy neural network sliding mode robust controller for higher stability of magnetic spacecraft attitude control

This paper designs an interval type-2 fuzzy neural network sliding mode robust controller (IT2FNNSMRC) to improve the stability of the vibrational angle of the orbital plane in magnetic rigid spacecraft attitude control. The control system consists of an interval type-2 fuzzy neural network (IT2FNN) controller, a PD controller, and a robust controller in parallel connection. The IT2FNN controller, as a nonlinear regulator, compensates the nonlinearity of the controlled object; the PD controller, as a feedback controller, ensures the global asymptotic stability of the control system; the robust controller inhibits input load disturbance. The IT2FNN controller hereof has a self-organizing function which enables it to automatically determine the network structure and parameters online. At the stage of IT2FNN structure learning, the standard on rule growth is set according to the incentive intensities of IT2FNN rule premises. A new rule is generated when the incentive intensities of rules are all smaller than a certain threshold; next, a significance index is set for each rule. When the significance index of some rule decays to a certain threshold, the corresponding rule shall be deleted to achieve the goals of optimizing IT2FNN structure and reducing system complexity. At the stage of parameter learning, adaptive adjustment of IT2FNN parameters is made via the sliding mode control theory learning algorithm, and the stabilities of the algorithm and control system are proven using Lyapunov function. Finally, the proposed control scheme is used in the control of a magnetic rigid spacecraft, as compared to three other designed control methods. Simulation results show that IT2FNNSMRC has superior control precision and stability. And the IT2FNN which adopts the proposed learning algorithm can address uncertainty satisfactorily, with higher computational implementability.

Fetal Health State Detection Using Interval Type-2 Fuzzy Neural Networks

Diagnosis of fetal health is a difficult process that depends on various input factors. Depending on the values or the interval of values of these input symptoms, the detection of fetal health status is implemented. Sometimes it is difficult to determine the exact values of the intervals for diagnosing the diseases and there may always be disagreement between the expert doctors. As a result, the diagnosis of diseases is often carried out in uncertain conditions and can sometimes cause undesirable errors. Therefore, the vague nature of diseases and incomplete patient data can lead to uncertain decisions. One of the effective approaches to solve such kind of problem is the use of fuzzy logic in the construction of the diagnostic system. This paper proposes a type-2 fuzzy neural system (T2-FNN) for the detection of fetal health status. The structure and design algorithms of the T2-FNN system are presented. Cardiotocography, which provides information about the fetal heart rate and uterine contractions, is employed for monitoring fetal status. Using measured statistical data, the design of the system is implemented. Comparisons of various models are presented to prove the effectiveness of the proposed system. The system can be utilized in clinical information systems to obtain valuable information about fetal health status.

Altitude control of a quadcopter using interval type-2 fuzzy controller with dynamic footprint of uncertainty

Footprint of uncertainty (FOU) characteristics of interval type-2 membership functions (IT2-MFs) play an important role in the performance and robustness of interval type-2 fuzzy controllers (IT2-FCs). In literature, fixed FOU structures are used in almost all IT2-FC designs. In this study, an IT2-FC with dynamic FOU is proposed to provide high performance and robustness in the altitude control of a quadcopter. A proportional-derivative (PD) type FC with Takagi-Sugeno rule structure is used in the design procedure of the proposed controller. Additionally, input variables (error and derivative of error) are defined by using triangular IT2-MFs. To provide a dynamic FOU structure, the height of the lower MF (LMF) of each interval type-2 fuzzy set is defined as a function of the system error. In this way, FOU levels of IT2-MFs are adjusted dynamically since the height value of the LMF directly determines the FOU level of the IT2-MF. To evaluate the effectiveness of the proposed controller, comparison studies are performed under different conditions, including unmodeled measurement noises, an external disturbance, and a system parameter uncertainty. A classical PD, a type-1 fuzzy PD, and an interval type-2 fuzzy PD with fixed FOU controllers are used in the comparisons. The comparison results demonstrate that the proposed interval type-2 fuzzy PD controller with dynamic FOU exhibits better performance and more robustness than the other controllers.

A Robust Control via a Fuzzy System with PID for the ROV

Uncertainty and nonlinearity in the depth control of remotely operated vehicles (ROVs) have been widely studied, especially in complex underwater environments. To improve the motion performance of ROVs and enhance their robustness, the model of ROV depth control in complex water environments was developed. The developed control scheme of interval type-2 fuzzy proportional-integral-derivative control (IT2FPID) is based on proportional-integral-derivative control (PID) and interval type-2 fuzzy logic control (IT2FLC). The performance indicators were used to evaluate the immunity of the controller type to external disturbances. The overshoot of 0.3% and settling time of 7.5 s of IT2FPID seem to be more robust compared to those of type-1 fuzzy proportional-integral-derivative (T1FPID) and PID.

Study on non-iterative algorithms for center-of-sets type-reduction of Takagi–Sugeno–Kang type general type-2 fuzzy logic systems

The paper performs the center-of-sets (COS) type-reduction (TR) and de-fuzzification for Takagi–Sugeno–Kang (TSK) type general type-2 fuzzy logic systems (GT2 FLSs) on the basis of the $$\alpha$$ α -planes expression of general type-2 fuzzy sets. Actually, comparing the popular Karnik–Mendel (KM) algorithms with other non-iterative algorithms is an important question in T2 society. Here the modules of fuzzy inference, COS TR, and de-fuzzification for TSK type GT2 FLSs are discussed by means of non-iterative Nagar–Bardini (NB) algorithms, Nie–Tan (NT) algorithms, and Begian–Melek–Mendel (BMM) algorithms. Simulation instances are constructed to illustrate the performances of three types of non-iterative algorithms compared with the KM algorithms. It is proved that, the proposed non-iterative algorithms can enhance the computational efficiencies significantly, which afford the potential application value for designers of GT2 FLSs.

Smooth Compositions Made Stabilization of Fuzzy Systems: Easy and More Robust

Smooth fuzzy systems are the new structures of the fuzzy system which have recently taken attention for their capacity in system modeling. Hence, this article studies the stability of smooth fuzzy control systems and develops the sufficient conditions of the parameters for the stable closed-loop performance of the system. A major advantage of the presented conditions is that they do not call for a common Lyapunov function and therefore, no LMI is required to be solved to guarantee the stability of the fuzzy model. Besides, although they are the type-1 fuzzy model in nature, however, they show the high level of robustness to the noises and parametric uncertainties, which is comparable to the type-2 fuzzy models. Several comparative simulations demonstrate the capacity of the fuzzy models with the smooth compositions rather than the classical fuzzy models with the min-max or product-sum compositions.

Design of sampling-based noniterative algorithms for centroid type-reduction of general type-2 fuzzy logic systems

General type-2 (GT2) fuzzy logic systems (FLSs) become a popular research topic for the past few years. Usually the Karnik–Mendel algorithms are the most prevalent approach to complete the type-reduction. Nonetheless, the iterative quality of these types of computational intensive algorithms might impede applying them. For the improved types of algorithms, some noniterative algorithms can enhance the calculation efficiencies greatly, while it is still an open problem for comparing the relation between the discrete TR algorithms and corresponding continuous TR algorithms. First, the sum and integral operations in discrete and continuous noniterative algorithms are compared. Then, three kinds of noniterative algorithms originate from the type-reduction of interval type-2 FLSs are extended to complete the centroid type-reduction of general T2 FLSs. Four computer simulations prove that while changing the number of samples suitably, the calculational results of discrete types of algorithms may accurately gain on the related continuous types of algorithms, and the calculational times of discrete types of algorithms are obviously less than the continuous types of algorithms, this may offer the possible meaning for designing and applying T2 FLSs.

Solving the Formation and Containment Control Problem of Nonlinear Multi-Boiler Systems Based on Interval Type-2 Takagi–Sugeno Fuzzy Models

An interval type-2 (IT-2) fuzzy control design method is developed to solve the formation and containment problem of nonlinear multi-boiler systems. In most practical industrial systems such as airplanes, vessels, and power plants, the boiler system often exists as more than one piece of equipment. An efficient control theory based on the leader-following multi-agent system is applied to achieve the control purpose of multiple boiler systems simultaneously. Moreover, a faithful mathematical model of the nonlinear boiler system is extended to construct the multi-boiler system so that the dynamic behaviors can be accurately presented. For the control of practical multi-agent systems, the uncertainties problem, which will deteriorate the performance of the whole system greatly, must be considered. Because of this, the IT-2 Takagi–Sugeno (T–S) fuzzy model is developed to represent the nonlinear multi-boiler system with uncertainties more completely. Based on the fuzzy model, the IT-2 fuzzy formation and containment controllers are designed with the imperfect premise matching scheme. Thus, the IT-2 fuzzy control method design can be more flexible for the nonlinear multi-boiler system. Solving the formation problem, a control method without the communication between leaders differs from the previous research. Since leaders achieve the formation objective, the followers can be forced into the specific range formed by leaders. Via the IT-2 fuzzy control method in this paper, not only can the more flexible process of the controller design method be developed to solve the uncertainties problem magnificently, but a more cost-effective control purpose can also be achieved via applying the lower rules of fuzzy controllers. Finally, the simulation results of controlling a nonlinear multi-boiler system with four agents are presented to demonstrate the effectiveness of the proposed IT-2 fuzzy formation and containment control method.

Study on center-of-sets type-reduction of interval type-2 fuzzy logic systems with noniterative algorithms

In recent years, interval type-2 fuzzy logic systems (IT2 FLSs) have become a hot topic for the capability of coping with uncertainties. Compared with the centroid type-reduction (TR), investigating the center-of-sets (COS) TR of IT2 FLSs is more favorable for applying IT2 FLSs. Actually, it is still an open question for comparing Karnik-Mendel (KM) types of algorithms and other types of alternative algorithms for COS TR. This paper gives the block of fuzzy reasoning, COS TR, and defuzzification of IT2 FLSs based on Nagar-Bardini (NB), Nie-Tan (NT) and Begian-Melek-Mendel (BMM) noniterative algorithms. Six simulation experiments are used to show the performances of three types of noniterative algorithms. The proposed noniterative algorithms can obtain much higher computational efficiencies compared with the KM algorithms, which give the potential value for designing T2 FLSs.

Adaptive Neuro-Fuzzy Inference System Predictor with an Incremental Tree Structure Based on a Context-Based Fuzzy Clustering Approach

We propose an adaptive neuro-fuzzy inference system (ANFIS) with an incremental tree structure based on a context-based fuzzy C-means (CFCM) clustering process. ANFIS is a combination of a neural network with the ability to learn, adapt and compute, and a fuzzy machine with the ability to think and to reason. It has the advantages of both models. General ANFIS rule generation methods include a method employing a grid division using a membership function and a clustering method. In this study, a rule is created using CFCM clustering that considers the pattern of the output space. In addition, multiple ANFISs were designed in an incremental tree structure without using a single ANFIS. To evaluate the performance of ANFIS in an incremental tree structure based on the CFCM clustering method, a computer performance prediction experiment was conducted using a building heating-and-cooling dataset. The prediction experiment verified that the proposed CFCM-clustering-based ANFIS shows better prediction efficiency than the current grid-based and clustering-based ANFISs in the form of an incremental tree.

Designing a Robust Controller Using SMC and Fuzzy Artificial Organic Networks for Brushed DC Motors

Electric direct-current (DC) drives based on DC motor are extremely important in the manufacturing process, so it must be crucial to increase their performance when they are working on load disturbances or the DC motor’s parameters change. Usually, several load torque suddenly appears when electric drives are operating in a speed closed-loop, so robust controllers are required to keep the speed high-performance. One of the most well-known robust strategies is the sliding mode controller (SMC), which works under discontinue operation. This controller can handle disturbances and variations in the plant’s parameters, so the controller has robust performance. Nevertheless, it has some disadvantages (chattering). Therefore, this paper proposed a fuzzy logic controller (FLC) that includes an artificial organic network for adjusting the command signal of the SMC. The proposed controller gives a smooth signal that decrements the chattering in the SMC. The stability condition that is based on Lyapunov of the DC motor is driven is evaluated; besides, the stability margins are calculated. The proposed controller is designed using co-simulation and a real testbed since co-simulation is an extremely useful tool in academia and industry allows to move from co-simulation to real implementation in short period of time. Moreover, there are several universities and industries that adopt co-simulation as the main step to design prototypes. Thus, engineering students and designers are able to achieve excellent results when they design rapid and functional prototypes. For instance, co-simulation based on Multisim leads to design directly printed circuit boards so engineering students or designers could swiftly get an experimental DC drive. The experimental results using this platform show excellent DC-drive performance when the load torque disturbances are suddenly applied to the system. As a result, the proposed controller based on fuzzy artificial organic and SMC allows for adjusting the command signal that improves the dynamic response in DC drives. The experimental response using the sliding-mode controller with fuzzy artificial organic networks is compared against an auto-tuning, Proportional-Integral-Derivative (PID), which is a conventional controller. The PID controller is the most implemented controller in several industries, so this proposal can contribute to improving manufacturing applications, such as micro-computer numerical control (CNC) machines. Moreover, the proposed robust controller achieves a superior-speed response under the whole tested scenarios. Finally, the presented design methodology based on co-simulation could be used by universities and industry for validating and implementing advanced control systems in DC drives.

Design and Hardware Implementation Based on Hybrid Structure for MPPT of PV System Using an Interval Type-2 TSK Fuzzy Logic Controller

The major drawback of photovoltaic (PV) systems is their dependence on environmental conditions, such as solar radiation and temperature. Because of this dependency, maximum power point tracking (MPPT) control methods are used in PV systems in order to extract maximum power from the PV panels. This study proposes a controller with a hybrid structure based on angle of incremental conductance (AIC) method and Interval Type-2 Takagi Sugeno Kang fuzzy logic controller (IT2-TSK-FLC) for MPPT. MPPT performance of proposed hybrid controller is evaluated via detailed simulation studies and dSPACE-based experimental study. The results validate that the proposed hybrid controller offers fast-tracking speed, high stability, and robust performance against uncertainties arising from disturbance to inputs of the PV system.

Robust Learning Control for Shipborne Manipulator With Fuzzy Neural Network

The shipborne manipulator plays an important role in autonomous collaboration between marine vehicles. In real applications, a conventional proportional-derivative (PD) controller is not suitable for the shipborne manipulator to conduct safe and accurate operations under ocean conditions, due to its bad tracing performance. This paper presents a real-time and adaptive control approach for the shipborne manipulator to achieve position control. This novel control approach consists of a conventional PD controller and fuzzy neural network (FNN), which work in parallel to realize PD+FNN control. Qualitative and quantitative tests of simulations and real experiments show that the proposed PD+FNN controller achieves better performance in comparison with the conventional PD controller, in the presence of uncertainty and disturbance. The presented PD+FNN eliminates the requirements for precise tuning of the conventional PD controller under different ocean conditions, as well as an accurate dynamics model of the shipborne manipulator. In addition, it effectively implements a sliding mode control (SMC) theory-based learning algorithm, for fast and robust control, which does not require matrix inversions or partial derivatives. Furthermore, simulation and experimental results show that the angle compensation deviation of the shipborne manipulator can be improved in the range of ±1°.

Transductive Joint-Knowledge-Transfer TSK FS for Recognition of Epileptic EEG Signals

Intelligent recognition of electroencephalogram (EEG) signals is an important means to detect seizure. Traditional methods for recognizing epileptic EEG signals are usually based on two assumptions: 1) adequate training examples are available for model training and 2) the training set and the test set are sampled from data sets with the same distribution. Since seizures occur sporadically, training examples of seizures could be limited. Besides, the training and test sets are usually not sampled from the same distribution for generic non-patient-specific recognition of EEG signals. Hence, the two assumptions in traditional recognition methods could hardly be satisfied in practice, which results in degradation of model performance. Transfer learning is a feasible approach to tackle this issue attributed to its ability to effectively learn the knowledge from the related scenes (source domains) for model training in the current scene (target domain). Among the existing transfer learning methods for epileptic EEG recognition, transductive transfer learning fuzzy systems (TTL-FSs) exhibit distinctive advantages-the interpretability that is important for medical diagnosis and the transfer learning ability that is absent from traditional fuzzy systems. Nevertheless, the transfer learning ability of TTL-FSs is restricted to a certain extent since only the discrepancy in marginal distribution between the training data and test data is considered. In this paper, the enhanced transductive transfer learning Takagi-Sugeno-Kang fuzzy system construction method is proposed to overcome the challenge by introducing two novel transfer learning mechanisms: 1) joint knowledge is adopted to reduce the discrepancy between the two domains and 2) an iterative transfer learning procedure is introduced to enhance transfer learning ability. Extensive experiments have been carried out to evaluate the effectiveness of the proposed method in recognizing epileptic EEG signals on the Bonn and CHB-MIT EEG data sets. The results show that the method is superior to or at least competitive with some of the existing state-of-art methods under the scenario of transfer learning.

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

Multi-Output Interval Type-2 Fuzzy Logic System for Protein Secondary Structure Prediction

A new multi-output interval type-2 fuzzy logic system (MOIT2FLS) is introduced for protein secondary structure prediction in this paper. Three outputs of the MOIT2FLS correspond to three structure classes including helix, strand (sheet) and coil. Quantitative properties of amino acids are employed to characterize twenty amino acids rather than the widely used computationally expensive binary encoding scheme. Three clustering tasks are performed using the adaptive vector quantization method to construct an equal number of initial rules for each type of secondary structure. Genetic algorithm is applied to optimally adjust parameters of the MOIT2FLS. The genetic fitness function is designed based on the Q3 measure. Experimental results demonstrate the dominance of the proposed approach against the traditional methods that are Chou-Fasman method, Garnier-Osguthorpe-Robson method, and artificial neural network models.

A fast algorithm to compute precise type-2 centroids for real-time control applications

An interval type-2 fuzzy set (IT2 FS) is characterized by its upper and lower membership functions containing all possible embedded fuzzy sets, which together is referred to as the footprint of uncertainty (FOU). The FOU results in a span of uncertainty measured in the defuzzified space and is determined by the positional difference of the centroids of all the embedded fuzzy sets taken together. This paper provides a closed-form formula to evaluate the span of uncertainty of an IT2 FS. The closed-form formula offers a precise measurement of the degree of uncertainty in an IT2 FS with a runtime complexity less than that of the classical iterative Karnik-Mendel algorithm and other formulations employing the iterative Newton-Raphson algorithm. This paper also demonstrates a real-time control application using the proposed closed-form formula of centroids with reduced root mean square error and computational overhead than those of the existing methods. Computer simulations for this real-time control application indicate that parallel realization of the IT2 defuzzification outperforms its competitors with respect to maximum overshoot even at high sampling rates. Furthermore, in the presence of measurement noise in system (plant) states, the proposed IT2 FS based scheme outperforms its type-1 counterpart with respect to peak overshoot and root mean square error in plant response.

Simplified interval type-2 fuzzy neural networks

This paper describes a self-evolving interval type-2 fuzzy neural network (FNN) for various applications. As type-1 fuzzy systems cannot effectively handle uncertainties in information within the knowledge base, we propose a simple interval type-2 FNN, which uses interval type-2 fuzzy sets in the premise and the Takagi-Sugeno-Kang (TSK) type in the consequent of the fuzzy rule. The TSK-type consequent of fuzzy rule is a linear combination of exogenous input variables. Given an initially empty the rule-base, all rules are generated with on-line type-2 fuzzy clustering. Instead of the time-consuming K-M iterative procedure, the design factors ql and qr are learned to adaptively adjust the upper and lower positions on the left and right limit outputs, using the parameter update rule based on a gradient descent algorithm. Simulation results demonstrate that our approach yields fewer test errors and less computational complexity than other type-2 FNNs.

An Efficient Interval Type-2 Fuzzy CMAC for Chaos Time-Series Prediction and Synchronization

This paper aims to propose a more efficient control algorithm for chaos time-series prediction and synchronization. A novel type-2 fuzzy cerebellar model articulation controller (T2FCMAC) is proposed. In some special cases, this T2FCMAC can be reduced to an interval type-2 fuzzy neural network, a fuzzy neural network, and a fuzzy cerebellar model articulation controller (CMAC). So, this T2FCMAC is a more generalized network with better learning ability, thus, it is used for the chaos time-series prediction and synchronization. Moreover, this T2FCMAC realizes the un-normalized interval type-2 fuzzy logic system based on the structure of the CMAC. It can provide better capabilities for handling uncertainty and more design degree of freedom than traditional type-1 fuzzy CMAC. Unlike most of the interval type-2 fuzzy system, the type-reduction of T2FCMAC is bypassed due to the property of un-normalized interval type-2 fuzzy logic system. This causes T2FCMAC to have lower computational complexity and is more practical. For chaos time-series prediction and synchronization applications, the training architectures with corresponding convergence analyses and optimal learning rates based on Lyapunov stability approach are introduced. Finally, two illustrated examples are presented to demonstrate the performance of the proposed T2FCMAC.