Interval Type-2 Takagi Sugeno Research Articles

Observer-based MPC for fuzzy cyber–physical system with hybrid attacks via a dynamic event-triggered mechanism

In this article, a secure model predictive control (MPC) algorithm is addressed for a nonlinear cyber–physical system (CPS) subject to hybrid attacks and parameter uncertainties via a dynamic event-triggered mechanism (DETM). The nonlinear CPS with parameter uncertainties is represented by the interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model. Considering that the full states of system are unmeasurable and aiming at decreasing the transmission burden, a DETM is proposed in the observer-based MPC scheme. Moreover, the hybrid attacks, including denial-of-service (DoS) attacks and deception attacks, are investigated in a unified framework due to the vulnerability of communication network. Furthermore, a secure MPC algorithm is presented, which consists of an off-line designed state observer and an on-line optimized MPC algorithm. Besides, by considering the internal dynamic variable in DETM, a new formula for updating estimation errors bounds is proposed to guarantee the feasibility of proposed algorithm. Finally, a practical example and comparative studies confirm the effectiveness of the proposed scheme.

Event-based predictive control for interval type-2 Takagi–Sugeno fuzzy systems under Kalman filter

In this article, the event-based predictive control problem for a class of interval type-2 Takagi–Sugeno fuzzy system is investigated. To reduce the influence of Gaussian noise, an improved Kalman filter is proposed, in which the system state is filtered or not depends on an event-triggered mechanism. Then, by designing the network predictive control scheme via interval type-2 fuzzy model, some sufficient conditions are derived, which guarantee the Schur stabilization of the concerned system subject to network delays. Finally, the correctness and effectiveness are verified by two simulation examples.

Integrated Fault-Tolerant Control Design With Sampled-Output Measurements for Interval Type-2 Takagi-Sugeno Fuzzy Systems.

This article is concerned with the integrated design of fault estimation (FE) and fault-tolerant control (FTC) for uncertain nonlinear systems suffering from actuator faults and external disturbance. The uncertain nonlinear systems are characterized as the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model, and IT2 membership functions are employed to effectively handle uncertainties. A fuzzy observer, utilizing only sampled-output measurements, is applied to simultaneously estimate actuator faults and system states. Based on the estimation, the fault-tolerant controller is designed to ensure the system stability under a predefined H∞ performance. The sampling behavior complicates the system dynamics and makes the integrated FTC design more challenging. To confront this issue, the discontinuous Lyapunov functional technique is exploited to enhance stability results by considering the sampling characteristic, upon which FE and FTC units are co-designed in the linear matrix inequality (LMI) framework. To further relax stability criteria, the analysis process incorporates the bound information of membership functions through the membership-function-dependent (MFD) method. Additionally, the relationship of mismatched premise variables resulting from the sampling scheme is also taken into account. Moreover, considering the imperfect premise matching (IPM) framework, the proposed fault-tolerant controller provides greater flexibility in selecting the shapes of membership functions and number of fuzzy rules that can vary from the counterpart of the fuzzy system. Finally, the efficacy of the proposed FTC technique is validated through a detailed numerical example.

Relaxed Stabilization of Event-Triggered Interval Type-2 T–S Fuzzy Positive Systems With Stochastic Actuator Failure

This paper studies the membership-function-dependent (MFD) stability and positivity analysis of positive Interval Type-2 (IT2) Takagi-Sugeno (T-S) fuzzy fault-tolerant control systems under the event-triggered control framework. Considering the fact that parameter uncertainties may exist in nonlinear plants, the IT2 T-S fuzzy model as an effective mathematical tool is employed to approximately express a complex positive system with nonlinearities and uncertainties. In order to save communication resources and improve the security of system operation, an event-triggered fault-tolerant control strategy is then designed based on the Imperfectly Premise Matching (IPM) concept. In addition, for capturing positivity characteristic and matching with the linear co-positive Lyapunov function, a novel event-triggered condition in the 1-norm rather than in the 2-norm is developed to control the positive IT2 T-S fuzzy systems. Thereinto, the non-convex problem as the first obstacle is required to be cleared since feasible solutions usually cannot be obtained based on the non-convex conditions. For dealing with this problem, a valid approach is presented to conduct convexification with the help of a user-chosen constant vector. Besides, because of event-triggered action, the inherent mismatched issue of the premise variables of the fuzzy model and the ones of the fuzzy controller is encountered. Fortunately, the advanced MFD analysis, which is capable of bringing the information contained in the membership functions (MFs) into the stability and positivity conditions, provides an effective strategy to remove this barrier. Consequently, relaxed results which can accomplish the stability and positivity for wider positive systems are developed and displayed in sum-of-squares (SOS) form. Detailed simulation results are given to clarify the effectiveness of the designed event-triggered fault-tolerant control method.

Observer-Based Security Fuzzy Control for Nonlinear Networked Systems Under Weighted Try-Once-Discard Protocol

This paper is concerned with the observer-based security fuzzy control problem for a class of nonlinear networked systems with imperfectly matched membership functions (MFs) under weighted try-once-discard (WTOD) protocol. The nonlinear networked system is constructed based on interval type-2 (IT2) Takagi-Sugeno (T-S) model, which can properly handle parameter uncertainties via lower and upper MFs. To mitigate the communication load, WTOD protocol is exploited to schedule the transmission order of the signals, in which those signals may be subjected to randomly occurring deception attacks. The observer is constructed under unmeasurable premise variables, and then the controller with imperfect matching MFs is designed according to the estimated states. Moreover, the observer-based controller is derived with Lyapunov stability theory such that the stochastic stability of the augmented closed-loop system with predefined disturbance attenuation performance can be guaranteed. Subsequently, sufficient conditions are provided for the desired observer and controller gain matrices based on linear matrix inequalities (LMIs) technique. Numerical simulation example demonstrates the validity of the proposed observer-based security fuzzy control design scheme.

Asynchronous Sliding Mode Control for Nonlinear Markov Jumping Systems With PDT-Switched Transition Probabilities

This paper studies the asynchronous sliding mode control for nonlinear Markov jump systems (NMJSs), whose transition probabilities is piecewise-constant and subjected to the persistent dwell-time (PDT) switching rule. By resorting to the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy set theory, the nonlinearity and uncertainty features of the investigated systems are modeled. Taking the uncertain membership functions (MFs) of IT2 T-S fuzzy systems into consideration, the non-parallel distributed compensation strategy is employed for designing the MFs of the controller such that them do not need to be obtained in time. Furthermore, in view of the difficulty of accurately acquiring the mode of NMJSs with complex transition probabilities, the hidden Markov model is employed to provide a detected mode for constructing the sliding mode law. Afterwards, a novel fuzzy sliding surface is proposed, and an asynchronous IT2-fuzzy-model-based sliding mode control law is designed for forcing the closed-loop systems to move on the predefined sliding surface. Thereafter, a novel two-mode-dependent Lyapunov-like function is conceived for the studied systems, where modes of NMJSs and transition probabilities are permitted to change simultaneously. Through applying an improved technique to handle the parametric matrix inequalities, some less-conservative sufficient conditions in the form of linear matrix inequality are obtained for ensuring the stochastic exponentially asymptotical stability of the sliding mode with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance. Finally, a mass-spring mechanical system is presented to substantiate the validity of the proposed main results.

Event-triggered non-fragile state estimator design for interval type-2 Takagi–Sugeno fuzzy systems with bounded disturbances

In this paper, the state estimator design problem of interval type-2 Takagi–Sugeno fuzzy systems suffering from bounded disturbances is studied. To enhance the resilience of the estimator, a non-fragile design scheme is proposed to tackle the estimator gain variations. Meanwhile, an event-triggered communication mechanism is introduced for relieving the transmission burden over networks. To settle down the non-fragile estimator design issue subject to bounded disturbances and event-induced error, we propose a new definition of quadratic boundedness via the multiple Lyapunov functions. Based on this definition, a novel co-design method of estimator and event generator for fuzzy system models in the presence of both measurable and immeasurable premise variables is presented. In virtue of quadratic boundedness framework, less conservative conditions of the existence and quadratic stability of the fuzzy estimators are obtained, and the upper bound of estimation error is given explicitly. The desired estimator gains are determined by convex optimization technique using slack matrices. Two illustrative examples are exploited to validate the availability and superiority of the addressed design approach.

Distributed-Delay-Dependent Stabilization for Networked Interval Type-2 Fuzzy Systems With Stochastic Delay and Actuator Saturation

In this article, a distributed-delay-dependent method is proposed to deal with the stabilization for interval type-2 Takagi–Sugeno fuzzy systems subject to stochastic network delay and actuator saturation. To deal with the stochastic feature of network-induced delays, their probability density function is utilized to establish the distributed delay model, which is more practical than the traditional time-varying network delay model. Meanwhile, in order to enlarge the estimation of the domain of attraction, a polytopic strategy composed of a state vector and a distributed-delay-dependent vector is proposed to treat the saturation nonlinearity. By constructing a distributed-delay-dependent Lyapunov–Krasovskii functional, new and less conservative conditions are achieved to guarantee the stability of the established closed-loop system. Additionally, two simulation examples are carried out to illustrate the advantages of the proposed strategy.

Observer-based model predictive control for uncertain NCS subject to hybrid attacks via interval type-2 T–S fuzzy model

In this study, an observer-based model predictive control (MPC) algorithm is addressed for an uncertain discrete-time nonlinear networked control system (NCS) subject to hybrid malicious attacks by using interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy theory. Hybrid malicious attacks, including two typical attacks, i.e., denial-of-service (DoS) attacks and false data injection (FDI) attacks, are considered in the communication networks. Under DoS attacks, the control signals will be interfered, which cause the degradation of signal-to-interference-plus-noise ratio, then lead to packets loss. Under FDI attacks, the false signals are injected and output signals are modified so that the system performance is deteriorated. For the NCS subject to hybrid attacks, a secure observer that can resist FDI attacks is devised and a fuzzy MPC algorithm that can solve the controller gains is proposed. Besides, by updating the bound of augmented estimation error, the recursive feasibility can be guaranteed. Finally, illustrative examples are given to show the effectiveness of proposed scheme.

Output feedback control of interval type-2 T-S fuzzy fractional order systems subject to actuator saturation

This paper investigates the stabilization problem of interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs). Firstly, IT2 fuzzy model is constructed to approximate the subject to actuator saturation of systems. Then, the sufficient conditions of output feedback control of IT2 fuzzy FOSs in terms of linear matrix inequalities (LMIs) are presented by using the method involving matrix singular value decomposition (SVD). Furthwemore, we solve optimization problems to estimate stable regions according to the proposed stability conditions. Finally, we proposed a numerical example to demonstrate the availability of theoretical analysis results.

An interval type-2 fuzzy linear quadratic regulator method for an overhead crane

The overhead crane systems contain parameter uncertainties and external disturbances, which will affect the control performance of the systems. To overcome this problem, an interval type-2 Takagi–Sugeno (T-S) fuzzy linear quadratic regulator (LQR) approach is proposed for overhead crane system in this paper. First, an interval type-2 T-S fuzzy model is constructed based on the nonlinear dynamic model of the overhead crane system. The type-2 model can capture the system uncertainties. Second, the fuzzy LQR is designed on the basis of the fuzzy model and the asymptotic stability of the closed-loop system is analyzed using Lyapunov method. Finally, simulations and experiments are studied. The results show that the proposed method can give the overhead crane system faster trolley positioning speed, smaller load swing, and better anti-disturbance ability than the existing LQR control method.

Sampled-Data-Based Dissipative Stabilization of IT-2 TSFSs Via Fuzzy Adaptive Event-Triggered Protocol.

In this research, the fuzzy adaptive event-triggered control (FAETC) issue is addressed for uncertain nonlinear networked control systems with network-induced delays (NIDs) and external disturbance. In order to effectively capture parameter uncertainties, the interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy model is utilized to represent such a system. Considering the fact that the controller is fuzzy and the threshold can promptly update its state according to the current and latest sampled signals (SSs), it becomes quite challenging to solve the dissipative stabilization problem (DSP) with the existing schemes. Then, a novel FAETC protocol is put forward to reduce the utilization of communication resources while maintaining the desired control performance. By employing the fuzzy-logic technique and the looped Lyapunov functional (LLF) approach, sufficient conditions related to the relationship between the stabilization and desired dissipative performance for the resulting system are formulated. A numerical example is used to validate the feasibility of our attained results.

Unknown Input Functional Observer Design for Discrete-Time Interval Type-2 Takagi–Sugeno Fuzzy Systems

This article proposes a novel unknown input functional observer design approach toward discrete-time interval type-2 Takagi–Sugeno fuzzy system models subject to measurable and unmeasurable premise variables. By constructing a new state vector that contains both the unknown inputs and the system states, functional observers are proposed for the cases with measurable and unmeasurable premise variables to estimate this new state vector for unknown input and/or state estimation. The observer design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices, and the existence conditions of the observers are explicitly obtained based on matrix rank analysis. Meanwhile, instead of solving the intricate Sylvester equation directly, the solution of the simplified matrix equation is employed to derive the observer gains. Moreover, the effectiveness and the superiority of the presented method are demonstrated via two illustrative examples.

Stability for IT2 T-S fuzzy systems under alternate event-triggered control

In this paper, an alternate event-triggered control is proposed to achieve stability of interval type-2 Takagi–Sugeno fuzzy systems. Comparing with the existing literature, this new control strategy displays an almost complete aperiodic feature which eliminates the conservativeness caused by time-triggered property of the traditional aperiodically intermittent control. Moreover, with two events being triggered alternately in this control strategy through examining two predetermined conditions, the efficiency of control can be further improved and the resources consumption can be greatly reduced. By employing the Lyapunov function and graph theory, several stability criteria are rigorously demonstrated. In addition, Zeno behavior is excluded in our system through obtaining a positive lower bound of the time interval between two triggering points. Subsequently, the validity of the presented strategy is evidenced by single-link robot arms systems. Finally, a numerical example is given to lend insight into the feasibility of our theoretical results.

Robust control of a planar snake robot based on interval type-2 Takagi–Sugeno fuzzy control using genetic algorithm

This paper presents trajectory tracking control of a snake robot in the presence of system uncertainty such as disturbances and parameter uncertainties. First, we derive a realistic dynamic model of the snake robot in the framework of the bond graph technique. Next, we present an interval type-2 Takagi–Sugeno fuzzy proportional–derivative (IT2FPD) control scheme, whose parameters are tuned using a genetic algorithm (GA) optimization approach. An improved optimization formulation with randomness is employed for robust near-optimal parameters. Under the assumption that forward velocity of the robot is always positive, we apply the proposed IT2FPD controller to the snake robot model so that the robot can have locomotion along the desired trajectory against uncertainties. To validate the performance of the proposed robot model and control scheme, we conduct in-depth numerical experiments using 20-sim software. Experimental results demonstrate that the snake robot embedded with the IT2FPD controller achieves a straight-line locomotion with the serpenoid gait function despite infiltration of external disturbances and parameter changes.

Interval type-2 T-S fuzzy MPC for CPS under hybrid attacks over a multi-channel framework

In this paper, the problem of observer-based model predictive control (MPC) for a multi-channel cyber-physical system (CPS) with uncertainties and hybrid attacks is investigated via interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model. Both denial-of-service (DoS) and false data injection (FDI) attacks are studied due to the vulnerability of wireless transmission channels. The objective of the addressed problem is to improve the security performance of the multi-channel CPS under malicious attacks, which has not been adequately investigated in the existing MPC algorithms. Moreover, uncertainties which appear not only in the membership functions but in both state and input matrices are considered. In this paper, different from the method that FDI attacks are handled by the bounded functions, an off-line observer is designed to actively defend against the FDI attacks. Meanwhile, an on-line MPC optimization algorithm, which minimizes the upper bound of objective function respecting input constraints, is presented to obtain the secure controller gains. Finally, an illustrative example is provided to verify the effectiveness and superiority of presented approach.

A Novel Interval Type-2 Fuzzy System Identification Method Based on the Modified Fuzzy C-Regression Model.

In this article, a novel interval type-2 Takagi-Sugeno fuzzy c -regression modeling method with a modified distance definition is proposed. The modified distance definition is developed to describe the distance between each data point and the local type-2 fuzzy model. To improve the robustness of the proposed identification method, a modified objective function is presented. In addition, different from most previous studies that require numerous free parameters to be determined, an interval type-2 fuzzy c -regression model is developed to reduce the number of such free parameters. Furthermore, an improved ratio between the upper and lower weights is proposed based on the upper and lower membership function with each input data, and the ordinary least-squares method is adopted to establish the type-2 fuzzy model. The Box-Jenkins model and two numerical models are given to illustrate the effectiveness and robustness of the proposed results.

Interval fuzzy robust non-fragile finite frequency control for active suspension of in-wheel motor driven electric vehicles with time delay

This paper proposes a fuzzy non-fragile finite frequency H∞ control algorithm for the active suspension system (ASS) of the electric vehicles driven by in-wheel motors with an advanced dynamic vibration absorber (DVA). Firstly, an interval type-2 Takagi-Sugeno (T-S) fuzzy model is established to formulate the nonlinear time-delay ASS with the uncertainties of sprung mass, unsprung mass, suspension stiffness, and tire stiffness. Secondly, a differential evolution (DE) algorithm is adopted to optimize the parameters of vehicle suspension and DVA. Thirdly, a non-fragile finite frequency H∞ control controller is developed under the consideration of controller perturbation and input delay to improve the comprehensive performance of the chassis under the finite frequency external disturbances. Finally, simulation tests are carried out to verify the effectiveness of the proposed controller.

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.

Dynamic-output-feedback based interval type-2 fuzzy control for nonlinear active suspension systems with actuator saturation and delay

This paper proposes a fuzzy dynamic output feedback (DOF) controller for uncertain nonlinear active suspension systems (ASSs) with actuator saturation and time-varying delay. Firstly, given the time-delay and nonlinear characteristics of the suspension systems, an interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy model is introduced to characterize the uncertain nonlinear ASSs with actuator saturation. Secondly, with the Lyapunov-Krasovskii function and the reciprocally convex technique, a series of sufficient delay-dependent conditions are derived to make sure that the control system with optimized H∞ performance and mechanical constraints is asymptotically stable. Thirdly, a DOF controller is designed to estimate the unmeasurable parameters of the system. Finally, the performance evaluation of the proposed controller is conducted through numerical and experimental tests.