IT2 Fuzzy Systems Research Articles

Premise‐Variable‐Domain‐Partition‐Dependent Output Feedback Switched Controllers Design for Switched IT2 Fuzzy Systems With Switching Signal Transmission Delays and Local Nonlinear Model

ABSTRACTThis article studies the guaranteed cost extended dissipative stabilization problem of switched IT2 fuzzy systems (SIT2FSs) with switching signal transmission delays and local nonlinear model. The guaranteed cost performance, guaranteed cost strict dissipative performance, guaranteed cost − performance and guaranteed cost passivity performance are considered for SIT2FSs in a unified form. First, a novel asynchronous control scheme is proposed for SIT2FSs with local nonlinear model. The controller gains in mismatched interval are designed separately. By using a premise‐variable‐domain‐partition‐dependent switched fuzzy Lyapunov functions (PDSFLFs) approach, the membership‐function‐shape‐independent (MFSI) existence conditions of a class of IT2 fuzzy switched controllers, which can ensure the guaranteed cost extended dissipative performance of SIT2FSs, are established. Then, by utilizing the shape information of membership functions and dividing the premise variable domain into multiple partitions, the membership‐function‐shape‐dependent (MFSD) existence conditions of a class of premise‐variable‐domain‐partition‐dependent (PVDPD) IT2 fuzzy switched controllers are presented. The results indicate that less conservative results can be achieved by using the PVDPD IT2 fuzzy switched controllers, and better system performance can be gotten compared with the Type‐1 fuzzy switched controllers. Finally, the effectiveness of the results is demonstrated through a robot arm model.

Design and application of interval type-2 fuzzy neural network systems optimized with hybrid algorithms

Interval type-2 fuzzy neural network systems (IT2 FNNSs) own the advantages of IT2 fuzzy logic systems (FLSs) and NN. The paper designs a kind of IT2 FNNSs for permanent magnetic drive (PMD) forecasting. For each rules of IT2 FNNSs, whose antecedents, consequents and input measurements are chosen as Gaussian IT2 membership functions (MFs). The proposed hybrid backpropagation (BP) algorithms and recursive least square (RLS) algorithms are adopted to tune all the parameters simultaneously. Simulation instances on the basis of data of permanent magnetic drive (PMD) torque and revolutions per minute (rpm) are adopted for testing the performances of proposed hybrid optimized IT2 FNNSs for forecasting. Convergence analysis illustrates that the IT2 FNNSs have excellent generalization capability compared with both singleton and non-singleton T1 FNNSs.

Rate-Based Output Regulation for Switched IT2 Fuzzy Systems With Application to Ship Formation

Rate-Based Output Regulation for Switched IT2 Fuzzy Systems With Application to Ship Formation

Annular finite-time stability for IT2 fuzzy networked switched system via non-fragile AETS under multiple attacks: Application to tank reactor chemical process model

This study examines the issue of annular finite-time H∞ performance for interval type-2 fuzzy (IT2) fuzzy networked switched systems vulnerable to multiple attacks via non-fragile adaptive event-triggered control. An adaptive event-triggered scheme (AETS) is presented to minimize the impact of multiple attacks and it effectively reduces redundant data transmission while guaranteeing reliable system performance which differs from the traditional event-triggered scheme. We describe the impact of deception and reply attacks by introducing two random variables that satisfy the Bernoulli distribution. Furthermore, IT2 fuzzy networked switched systems were developed to demonstrate the effects of multiple attacks, and the IT2 fuzzy model describes the nonlinear characteristics. Also, a delay-dependent Lyapunov functional with a free-weighting matrix technique are used. There are limited study findings on the class of IT2 fuzzy networked switching systems using adaptive event-triggered scheme. This paper discusses the advantages of establishing an efficient adaptive event-triggered mechanism for IT2 fuzzy networked switching systems based on previous discussions and necessity. Furthermore, some sufficient conditions that are required to ensure that the system is annular finite-time stable with the stated H∞ performance index is presented along with two examples to demonstrate the suggested control design methodology.

Sampled-Data Control for IT-2 Fuzzy Systems With Packet Losses: Fragmentation-Based Integral Inequality Technique

Sampled-Data Control for IT-2 Fuzzy Systems With Packet Losses: Fragmentation-Based Integral Inequality Technique

Guaranteed cost extended dissipative stabilization of switched IT2 fuzzy systems via intermittent control and its applications

This paper deals with the guaranteed cost extended dissipative stabilization problem of switched IT-2 fuzzy systems (SFSs) via intermittent control. Firstly, we propose a new class of system performance coefficients, taking both the extended dissipative performance and quadratic cost function performance into account. Then, by using a switched-path-dependent fuzzy Lyapunov functions (SFLFs) approach, the membership-function-shape-dependent (MFSD) existence conditions of a set of intermittent controllers are established. Furthermore, we apply the designed intermittent control scheme to three practical control problems: 1) A controller/actuator-failure-triggered intermittent controller is designed, and the guaranteed cost extended dissipative performance of SFSs is ensured in the presence of controller/actuator failures; 2) A switching-triggered intermittent controller is designed, and the guaranteed cost extended dissipative performance of SFSs is ensured in the presence of transmission delay of switching signal, and the asynchronous phenomena is eliminated; 3) A hybrid-triggered intermittent controller is designed, and the guaranteed cost extended dissipative performance of SFSs is ensured while the control resources are saved. Finally, the effectiveness of the results are demonstrated through a robot arm model.

Observer-Based Optimal Fuzzy Control for Networked IT-2 Fuzzy Systems Against Hybrid Cyber-Attacks

Observer-Based Optimal Fuzzy Control for Networked IT-2 Fuzzy Systems Against Hybrid Cyber-Attacks

Event-Triggered Input–Output Finite-Time Stabilization for IT2 Fuzzy Systems Under Deception Attacks

This article addresses the issue of input–output finite-time stabilization for interval type-2 fuzzy systems in the presence of deception attack effects. Our main goal is to make efficient use of network resources by developing an event-triggered controller for interval type-2 fuzzy systems. For the stabilization process, an event-triggered controller that does not share the same membership functions as the system is designed by using affine transformation parameters. Following that, by using an asymmetric Lyapunov–Krasovskii functional and some advanced integral inequalities to establish the sufficient conditions for the existence of the proposed controller. Furthermore, an asymptotic stabilization result is presented and discussed in a comparative analysis as a special case. Due to the asymmetric Lyapunov–Krasovskii functional structure, the transmission delay interval is large compared with some recent studies. Finally, two simulation examples are carried out and the efficiency of designed controller is verified.

Sensor fault estimation and fault tolerant control for IT2 fuzzy system via sliding mode approach

AbstractThe point of this article is the sensor fault estimation and fault‐tolerant controller design for IT2 fuzzy systems via sliding mode approach. In order to estimate accurately the system states and sensor faults, a novel proportional and derivative sliding mode observer is introduced, which provide more design freedom and eliminate the effects of sensor faults. By splitting the operating domain and estimating the membership functions, a set of relaxation stability conditions subject to the information of membership functions and system states are obtained. Then, a sliding mode controller in form of IT2 fuzzy model is designed to stabilize the closed‐loop systems. An example of bolt‐tightening tool model is considered to demonstrate the validity of the proposed results.

Reachable set bounding of output-feedback control for discrete-time large-scale IT-2 fuzzy descriptor systems using distributed event-based broadcasts

This paper studies the distributed event-based broadcasting of output-feedback control for discrete-time large-scale fuzzy descriptor systems subject to reachable set bounding. First, each nonlinear subsystem is represented by the interval type-2 fuzzy model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into the linear one. Then, we introduce an output-feedback fuzzy controller with distributed event-based broadcasting, where all subsystems communicate with each other via a distributed network, and each subsystem broadcasts its decision-making of transmission based on a prescribed event. Two event-based mechanisms (EBMs) are respectively proposed to examine when the system output and fuzzy premise variable should be transmitted to the controller. Moreover, by further employing a descriptor redundancy representation, combined with reachable set analysis method, it will be shown that the proposed fuzzy controller guarantees that the estimation error is bounded within the ellipsoidal boundary while communication data are transmitted to the controller as little as possible, and sufficient condition for designing the desired controller is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study is given to show the effectiveness of the proposed method.

Performance analysis and extended dissipative controller design for Itô stochastic-delayed IT2 fuzzy models

This paper deals with the problems of stochastic asymptotic stability analysis and extended dissipativity as well as controller design for Itô stochastic-delayed IT2 fuzzy systems by using line integral type Lyapunov–Krasovskii functional (LKF). A good estimate of the upper bound for the line integral type LKF is achieved, based on which, the conditions of stochastic asymptotic stability and extended dissipativity are derived. A comparison has been drawn between the conditions derived by line integral type LKF and the ones by the quadratic LKF in a numerical example, to indicate that the conditions by line integral approach are more general than the ones via quadratic method. Meanwhile, these conditions are of nonlinear form with respect to some matrix variables which makes the determination of the extended dissipative controller difficult. Inspired by cone complementarity linearisation algorithm and a novel matrix decoupling method, the state feedback controller is developed by transforming the nonlinear matrix inequalities into a quadratic optimisation problem with linear matrix inequality constraints. Finally, two examples are given to show the validity of our proposed approach.

Dynamic adaptation of the PID’s gains via Interval type-1 non-singleton type-2 fuzzy logic systems whose parameters are adapted using the backpropagation learning algorithm

This work presents a new design to dynamically adapt the proportional, the integral and the derivative (PID) controller’s gains using three interval type-1 non-singleton type-2 fuzzy logic systems (IT2 NSFLS-1), one fuzzy system for each gain of the PID, being the first main contribution of this proposal. This assembly is named as hybrid IT2 NSFLS-1 PID. Each IT2 NSFLS-1 system requires two non-singleton input values each period of discrete time $$ \left( \varvec{k} \right) $$, (1) the error $$ \varvec{e}\left( \varvec{k} \right) $$ and its standard deviation $$ \varvec{\sigma e}\left( \varvec{k} \right) $$, and (2) the change of error $$ \Delta \varvec{e}\left( \varvec{k} \right) $$ and its standard deviation $$ \varvec{\sigma}\Delta \varvec{e}\left( \varvec{k} \right) $$, to calculate the corresponding adjustment $$ \Delta \varvec{KP}\left( \varvec{k} \right) $$, $$ \Delta \varvec{KI}\left( \varvec{k} \right) $$, and $$ \Delta \varvec{KD}\left( \varvec{k} \right) $$ for the PID controller’s gains $$ \varvec{K}_{\varvec{p}} \left( \varvec{k} \right) $$, $$ \varvec{K}_{\varvec{i}} \left( \varvec{k} \right) $$, and $$ \varvec{K}_{\varvec{d}} \left( \varvec{k} \right) $$. The second main contribution of this proposal is that the parameters of each IT2 NSFLS-1 system are tuned each period of discrete time $$ \left( \varvec{k} \right) $$ by the non-singleton backpropagation (BP) algorithm using the plant output error and its standard deviation, which are processed as non-singleton values together with its non-singleton partial derivatives with respect to each IT2 fuzzy system parameter. Then these updated gains are used by the PID controller to calculate the best control signal for the plant under control. The uncertainty and the mean value of the measurement are used to calculate the non-singleton error which is processed as (a) input and (b) as gradient vector by each of the three IT2 NSFLS-1 systems. Simulation results show that the proposed hybrid assembly presents the better performance than the next five benchmarking control systems (a) the classic Zeigler–Nichols PID controller, and (b) four hybrid assemblies using PID controller and fuzzy systems with fixed fuzzy rule bases (T1 SFLS, T1 NSFLS, IT2 SFLS, IT2 NSFLS-1). The proposed assembly produces the better performance in a shortest period of time and it maintains a stable behavior on the output of the second-order plant model subject to variations and noise.

A Constrained Representation Theorem for Well-Shaped Interval Type-2 Fuzzy Sets, and the Corresponding Constrained Uncertainty Measures

The representation theorem for interval type-2 fuzzy sets (IT2 FSs), proposed by Mendel and John, states that an IT2 FS is a combination of all its embedded type-1 (T1) FSs, which can be nonconvex and/or subnormal. These nonconvex and/or subnormal embedded T1 FSs are included in developing many theoretical results for IT2 FSs, including uncertainty measures, the linguistic weighted averages (LWAs), the ordered LWAs (OLWAs), the linguistic weighted power means (LWPMs), etc. However, convex and normal T1 FSs are used in most fuzzy logic applications, particularly computing with words. In this paper, we propose a constrained representation theorem (CRT) for well-shaped IT2 FSs using only its convex and normal embedded T1 FSs, and show that IT2 FSs generated from three word encoding approaches and four computing with words engines (LWAs, OLWAs, LWPMs, and perceptual reasoning) are all well-shaped IT2 FSs. We also compute five constrained uncertainty measures (centroid, cardinality, fuzziness, variance, and skewness) for well-shaped IT2 FSs using the CRT. The CRT and the associated constrained uncertainty measures can be useful in computing with words, IT2 fuzzy logic system design using the principles of uncertainty, and measuring the similarity between two well-shaped IT2 FSs.

State and fault estimation based on interval type-2 fuzzy inference system optimised by genetic algorithms

In this paper, an optimisation method is proposed for state and fault estimation in a non-linear system that is described by interval type-2 fuzzy model. The method concerns the development of an optimised interval type-2 fuzzy Kalman observer (IT2 FKO). At each fuzzy rule, a local fuzzy observer is associated. As the main advantage is to obtain an unbiased estimation, the membership functions (MFs) parameters of IT2 fuzzy logic system were adjusted using genetic algorithms (GAs). These MFs are interval type-2 fuzzy sets which represent an extension version of typical type-1 fuzzy sets and provide additional degrees of freedom to directly handle uncertainties and external disturbances. To illustrate the performance of the developed observer, comparison with an IT2 FKO before tuning their MFs parameters and an optimised type-1 fuzzy Kalman observer is performed on a three-tank system for estimating their states under faults. Simulation results demonstrate the superiority of the proposed approach in spite of the presence of faults.

On answering the question “Where do I start in order to solve a new problem involving interval type-2 fuzzy sets?”

This paper, which is tutorial in nature, demonstrates how the Embedded Sets Representation Theorem (RT) for a general type-2 fuzzy set (T2 FS), when specialized to an interval (I)T2 FS, can be used as the starting point to solve many diverse problems that involve IT2 FSs. The problems considered are: set theoretic operations, centroid, uncertainty measures, similarity, inference engine computations for Mamdani IT2 fuzzy logic systems, linguistic weighted average, person membership function approach to type-2 fuzzistics, and Interval Approach to type-2 fuzzistics. Each solution obtained from the RT is a structural solution but is not a practical computational solution, however, the latter are always found from the former. It is this author’s recommendation that one should use the RT as a starting point whenever solving a new problem involving IT2 FSs because it has had such great success in solving so many such problems in the past, and it answers the question “Where do I start in order to solve a new problem involving IT2 FSs?”

Uncertainty measures for interval type-2 fuzzy sets

Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. These definitions should be useful in IT2 fuzzy logic systems design using the principles of uncertainty, and in measuring the similarity between two IT2 FSs.