Mismatched Membership Functions Research Articles

Dynamic event-triggered formation control for Takagi–Sugeno fuzzy multi-agent systems with mismatched membership functions

The dynamic event-triggered control scheme is employed in this work to explore the formation control problem of Takagi–Sugeno fuzzy multi-agent systems. The formation control problem is examined by employing a multi-agent system in the form of a Takagi–Sugeno fuzzy model. To reduce the frequency of control updates during the desired formation, a dynamic event-triggered controller is designed by introducing an internal dynamic variable. Initially, the error systems between the agents and the desired formation are introduced. A suitable Lyapunov–Krasovskii functional is then specifically designed for these error systems. By applying an improved delay-dependent reciprocally convex inequality, sufficient conditions for the stability of the error systems are obtained, which guarantee the desired formation of the selected multi-agent systems. In particular, these conditions are obtained in the form of linear matrix inequalities. Finally, a numerical illustration is provided to validate the feasibility of the theoretical outcomes.

An improved event-triggered control method for fuzzy systems under membership functions online learning

This paper is concerned with the problem of adaptive event-triggered (AET) based optimal fuzzy controller design for nonlinear networked control systems (NCSs) characterized by Takagi–Sugeno (T–S) fuzzy models. An improved AET communication scheme with a memory adaptive rule is proposed to enhance the utilization of the state response vertex data. Different from the existing ET based results, the improved AET scheme can save more communication resources and acquire better system performance. The sufficient criteria of performance analysis and controller design are presented for the closed-loop control system subject to mismatched membership functions (MFs) and AET scheme. And then, a new MFs online learning algorithm on the basis of the gradient descent approach is employed to optimize the MFs of fuzzy controller and obtain optimal fuzzy controller for further improving system performance. Finally, two simulation examples are presented to verify the advantage and effectiveness of the provided controller design technique.

Admissible Control for Non-Linear Singular Systems Subject to Time-Varying Delay and Actuator Saturation: An Interval Type-2 Fuzzy Approach

Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when uncertainty also simultaneously affects the system under consideration. To address this issue, this paper investigated a feasible control strategy for nonlinear singular systems with time-varying delay that are subject to uncertainty and actuator saturation. The IT-2 fuzzy model was adopted to describe the dynamic of the non-linear delayed systems using lower and upper membership functions to deal with the uncertainty. Moreover, the polyhedron model was applied to characterize the saturation function. The goal of the control approach was to design a relevant IT2 fuzzy state feedback controller with mismatched membership functions so that the closed-loop system is admissible. On the basis of an appropriate Lyapunov–Krasovskii functional, sufficient delay-dependent conditions were established and an optimization problem was formulated in terms of linear matrix inequality constraints to optimize the attraction domain. Simulation examples are provided to verify the effectiveness of the proposed method.

Output feedback stabilization of type 2 fuzzy singular fractional-order systems with mismatched membership functions

Output feedback stabilization of type 2 fuzzy singular fractional-order systems with mismatched membership functions

Interval Type-2 Fuzzy Control for HMM-Based Multiagent Systems via Dynamic Event-Triggered Scheme

This article discusses the interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy asynchronous controller design problem for nonlinear multiagent systems via a dynamic event-triggered scheme in the discrete-time context. To formulate the asynchronous phenomena between the system modes and the anticipant controller modes, the hidden Markov model is proposed. The primary attention is focused on the explicit design of the dynamic event-triggered strategy that can be dynamically adjusted in line with system information, which mitigates the communication burden efficiently. On this occasion, the information renewal of the controller is aperiodic. Furthermore, the nonlinear characteristics are effectually disposed through utilizing a unique IT2 T-S fuzzy model, which is with mismatched membership functions (MFs). As a result, the resulting closed-loop fuzzy multiagent systems are accompanied by mismatched MFs and asynchronous modes, whereafter, via solving the convex optimization problem, the desired controller gains are acquired. Eventually, the validity and practicability of the developed control scheme are illustrated by two examples.

Guaranteed Cost Control for Interval Type-2 Fuzzy Semi-Markov Switching Systems Within a Finite-Time Interval

This article focuses on the finite-time guaranteed cost (FTGC) control problem for interval type-2 (IT2) fuzzy semi-Markov switching systems (S-MSSs) with additive disturbances. Based on the IT2 fuzzy S-MSSs and the state feedback control method, a novel IT2 mode-dependent fuzzy guaranteed cost (GC) controller is developed under the mismatched membership functions. Then, some new sufficient conditions are given to ensure that IT2 fuzzy S-MSSs are finite-time (FT) stochastically stable based on the designed IT2 mode-dependent fuzzy GC controller. Furthermore, the transition rate boundary condition is relaxed, and a new incomplete transition rate boundary model is constructed to reflect the transition rate information. For both the incomplete transition rate boundaries and the actuator fault phenomenon, the improved stability criteria are provided to stabilize the IT2 fuzzy S-MSSs within an FT interval and determine the gains of the IT2 mode-dependent fuzzy GC controller, resulting in a much greater design flexibility. Distinct from the existing results, the presented FTGC control scheme is more suitable for many practical systems because the IT2 fuzzy S-MSS model, which is more general compared with the traditional fuzzy system and S-MSSs, is considered. Finally, three illustrative examples are offered to explain the effectiveness and feasibility of the proposed FTGC control approach.

Observer-based asynchronous event-triggered control for interval type-2 fuzzy systems with cyber-attacks

This study investigates the observer-based asynchronous dynamic event-triggered control problem for networked interval type-2 fuzzy systems (IT-2 FSs) suffering from hybrid cyber-attacks, whereby the deception attacks (DAs) and the non-periodic denial-of-service (DoS) attacks are simultaneously considered. Contrasting with existing works, a new resilient dynamic event-triggering mechanism (DETM) is employed in the design process of the controller in the event of hybrid cyber-attacks. It is concluded that the resilient condition of DETM is adaptively varied based on current sampling, latest available packets, and a discrete dynamic function. Using a piecewise Lyapunov functional (PLF), new stochastically exponential stability conditions are developed to ascertain the link among asynchronous DETM, DAs, non-periodic DoS attacks and mismatched membership functions (MMFs). These results can further reduce the data transmissions and guarantee the exclusion of the Zeno behavior. The effectiveness of the concerned system under hybrid cyber-attacks is ultimately verified by a numerical simulation.

Polynomial fault detection filter design under adaptive event-triggered scheme via line-integral Lyapunov functions

This paper investigates the problem of polynomial fault detection filter design under an adaptive event-triggered scheme for continuous-time networked polynomial fuzzy model–based (PFMB) systems considering network transmission delays. The proposed adaptive polynomial event-triggered scheme is checked only at the sampling instant to eliminate the Zeno behavior as well as save the network bandwidth. With the consideration of the mismatched membership functions (MFs), the asynchronous problem between the physical plant and the polynomial fault detection filter (PFDF) is examined. A Lyapunov–Krasovskii (L-K) function is introduced to deal with the time delays caused by the network transmission and the zero-order holder (ZOH), and a proper line-integral Lyapunov function is also introduced to reduce the conservation of the design constraints, whose analytical procedure is rule-dependent. The design constraints are given in the form of sum of squares (SOS) to keep the PFMB fault detection system asymptotically stable with [Formula: see text] performance [Formula: see text]. Finally, an inverted pendulum example together with a numerical example is given to verify the effectiveness and superiority of the proposed scheme in terms of transfer rate and conservatism.

Event-Driven Fault Detection for Discrete-Time Interval Type-2 Fuzzy Systems

This article considers the event-driven fault detection (FD) problem for discrete-time interval type-2 (IT2) fuzzy networked control systems (NCSs) with nonlinear perturbations. To reduce signal transmission, an event-driven mechanism in the NCSs is introduced. A novel FD fuzzy filter is designed for generating a residual signal and detecting actuator faults by considering the event-driven strategy, nonlinear perturbations, communication delay, and mismatched membership functions. It is shown that the proposed event-driven FD technique is effective to optimize performance compared with the existing FD strategy. Finally, two examples are presented to verify the advantages of the novel design technique.

More relaxed stability analysis and positivity analysis for positive polynomial fuzzy systems via membership functions dependent method

In this paper, the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy-model-based (PPFMB) control system are studied. Also, in order to improve the flexibility of controller design, a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed. In the existing literatures, it is proved that the LCLF can reduce the conservatism of stability results. However, the LCLF generally results in non-convex conditions which is still a conservatism source. To handle the non-convex conditions, the sector nonlinear concept is applied to handle non-convex terms in stability conditions, and the obstacles caused by mismatched membership functions can be eliminated by PLMF dependent method. In addition, to relax the conservatism caused by the lack of membership functions information, the PLMF dependent positivity analysis are performed for the first time. Meanwhile, PLMF dependent method is extended to stability conditions to obtained more relaxed conditions. Finally, a simulation example is presented to verify the feasibility of this method.

Hankel Norm Model Reduction of Discrete-Time Interval Type-2 T–S Fuzzy Systems With State Delay

This article focuses on the model reduction problem of discrete-time time-delay interval type-2 Takagi-Sugeno (T–S) fuzzy systems. Compared with the type-1 T–S fuzzy system, the interval type-2 T–S fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties. In addition, in order to simplify the analysis process, complex high-order systems can be approximated as low-order systems, which is called model reduction. In previous studies, there are few researches on model reduction of the interval type-2 T–S fuzzy system with time delay. Hankel norm is adopted to limit the error after model reduction. Based on Jensen's inequality, a linear matrix inequality (LMI) condition for the Hankel norm performance of the error system is obtained. A membership-function-dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results. Next, by a convex linearization design, the model reduction problem is formulated as a convex LMI feasibility/optimization condition. Numerical examples are given to verify the validity of the analysis.

Adaptive event-triggered dynamic output feedback H ∞ control for networked T-S fuzzy systems

This paper investigates the design problem of fuzzy dynamic output feedback controller for nonlinear networked systems via mismatched membership functions and adaptive event-triggered (AET) mechanism. Firstly, an AET mechanism is introduced to save communication resources, which causes the controller and the original system's premise variables to be asynchronous. Then, considering the influence of AET and mismatched membership functions, a model of fuzzy control system is established. In addition, utilizing the Lyapunov-Krasovskii(L-K) functional, sufficient conditions for the global exponential stability of the closed-loop system with performance are derived. Besides, the controller parameters and event-triggered (ET) weight matrix are solved by a set of linear matrix inequalities (LMIs). Finally, an example is given to demonstrate the effectiveness of the proposed control method.

Aperiodic Sampled-Data-Based Control for Interval Type-2 Fuzzy Systems via Refined Adaptive Event-Triggered Communication Scheme

This article is devoted to event-triggered stabilization for a class of interval type-2 (IT2) fuzzy systems with aperiodic sampling. First, the IT2 Takagi-Sugeno fuzzy model and sampled-data controllers are established subject to mismatched membership functions. Second, considering a nonuniform sampling case, a refined adaptive event-triggered communication scheme is proposed in a hierarchy form to dynamically adjust the direction and rate of the event-triggered threshold parameter by state changing trend and relative state error, respectively. Thus, a complete dual-directional regulating mechanism with sensitivity to state variation is reasonably created to give extra flexibility, which is beneficial for a preferable tradeoff between control performance and network resource. Third, considering the practical behaviors on the sampling interval, a novel integral type of time-dependent Lyapunov function is constructed. Then, the stability criterion and the controller design approach are derived. Finally, the numerical examples are provided to demonstrate the effectiveness and advantages of the proposed methods.

Dissipative control of interval type-2 nonhomogeneous Markovian jump fuzzy systems with incomplete transition descriptions

This paper investigates the problem of designing a dissipative controller for interval type-2 nonhomogeneous Markovian jump fuzzy systems (MJFSs) with incomplete transition descriptions. To explore a generalized model for MJFSs under realistic situations, the coexistence of incompletely known transition rates and mismatched membership functions is considered in MJFS models, and the corresponding stabilization conditions are derived in terms of multi-parameterized linear matrix inequalities (M-PLMIs). In addition, to handle the problem of M-PLMIs, two novel relaxation techniques are additionally proposed such that the use of redundant constraints on multiple time-varying parameters can be significantly reduced. Finally, the validity of the proposed method is demonstrated via two illustrative examples.

Asynchronous Event-Triggered Control for Networked Interval Type-2 Fuzzy Systems Against DoS Attacks

This article investigates the asynchronous adaptive event-triggered control problem for networked interval type-2 (IT2) fuzzy systems subject to nonperiodic denial-of-service (DoS) attacks. Unlike some existing results, two resilient adaptive event-triggered mechanisms (AETMs) are applied independently to both sensor and controller output while resisting nonperiodic DoS attacks. In particular, the asynchronous resilient AETM thresholds are adaptively varied based on error information between current sampling and latest available packets. Then, a new switched IT2 fuzzy dynamical output feedback system is modeled by discussing the influence of the AETM and nonperiodic DoS attacks simultaneously. Furthermore, mismatched membership functions are considered between dynamic output feedback controller and IT2 fuzzy model, and a slack matrix is introduced to relax stability conditions. Besides, by utilizing the piecewise Lyapunov-Krasovskii function method, sufficient conditions are derived to guarantee that the newly constructed switching system is globally exponentially stable with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Finally, the effectiveness of the developed control approach is illustrated by two examples.

Security Sliding Mode Control of Interval Type-2 Fuzzy Systems Subject to Cyber Attacks: The Stochastic Communication Protocol Case

This article addresses the security control problem of a class of interval type-2 fuzzy systems via the sliding mode control strategy. A stochastic communication scheduling protocol is utilized to govern the transmission from the sensors to the controller, by which only one sensor node has the chance to transmit its value at every instant. Meanwhile, cyber attacks from malicious adversaries might be launched in vulnerable communication channels. To quantitatively analyze the effect of the stochastic communication protocol and cyber attacks, their mathematical model is first constructed based on a compensation scheme. Since the scheduling signal may be unavailable once cyber attacks are activated, a desirable sliding mode control law is synthesized with token-independent control gains, whose membership functions are mismatched with those of the fuzzy system. To deal with these mismatched membership functions, the relations between the membership functions of the system and the control law are reconstructed. Consequently, the favorable property of perfectly matched memberships could be employed. Sufficient conditions are derived so that the resultant closed-loop interval type-2 fuzzy system is stochastically stable and, at the same time, the state trajectories can be forced into a small domain around the prescribed sliding surface. The proposed control design approach is verified by two examples.

Event-triggered reliable dissipative filtering for nonlinear networked control systems

This paper investigates the event-triggered reliable dissipative filtering problem for nonlinear networked control systems (NCSs) described by interval type-2 T-S fuzzy models. First, a novel adaptive event-triggered scheme is proposed to save the limited network resources. Then, a new event-triggered reliable dissipative filter is designed subject to mismatched membership functions and asynchronous constraints. Furthermore, sufficient conditions for ensuring asymptotic stability and strict dissipativity of the filtering error system are derived by utilizing slack matrices and the information of the membership functions. Compared with the existing event-triggered schemes, it is shown that the proposed one can more effectively reduce the utilization of network resources while ensuring the better estimation performance. Finally, a simulation example is given to illustrate the advantages of the proposed method.

Event‐triggered stabilisation for T–S fuzzy systems with asynchronous premise constraints and its application to wind turbine system

In this study, an event-triggered fuzzy controller is designed to stabilise a class of non-linear systems expressed as a Takagi-Sugeno (T-S) fuzzy model with mismatched membership functions. At first, an event-triggered fuzzy controller has been designed in terms of induced time delay. Secondly, the event-triggered fuzzy system is presented as a time-delay model with the asynchronous premise variables. Then, by introducing a time-dependent Lyapunov-Krasovskii functional and based on the fuzzy based control approach, linear matrix inequality-based stability conditions are established to guarantee the asymptotic stability of the proposed T-S fuzzy model. The derived conditions utilise the information on the membership functions of both fuzzy system and fuzzy controller. Finally, the proposed theoretical results are applied to stabilise the variable speed wind turbine system while saving the limited network resources. Further, through the truck-trailer example, the merits and the design procedure of the proposed technique have been demonstrated.

Event-based reduced-order fuzzy filtering for networked control systems with time-varying delays

This paper investigates the event-based reduced-order fuzzy filtering problem for nonlinear networked control systems with network-induced time-varying delays. A novel fuzzy filter design approach is proposed to analyze the fuzzy systems under a reduced-order scheme. The problem of mismatched membership functions is presented in the fuzzy filtering to simplify implementation complexity and increase design flexibility of the designed reduced-order filter. In addition, the integrands of the Lyapunov–Krasovskii functional are dependent of membership functions and the existence conditions of the fuzzy filtering are given by utilizing a linearization approach. Compared with the existing reduced-order filter design approaches, the time-derivatives of membership functions are considered in the analysis process for reducing the conservativeness of obtaining the maximum delay bounds. Finally, a simulation result is given to show the effectiveness and advantages of the analysis scheme.

A novel event-based fuzzy control approach for continuous-time fuzzy systems

This paper investigates the event-based fuzzy control problem for continuous-time interval type-2 (IT2) fuzzy networked control systems (NCSs). A new Lyapunov–Krasovskii functional is introduced in the stability analysis, where the integrands of the Lyapunov–Krasovskii functional are dependent of membership functions. Applying the information of time-derivatives of membership functions, a novel switching event-based fuzzy controller is designed to ensure that the closed-loop IT2 fuzzy system with mismatched membership functions is asymptotically stable. Different from the existing event-based fuzzy control results, both of the information of membership functions and the time-derivatives of membership functions can be utilized in the stability analysis to reduce the conservativeness. Finally, a simulation example is given to show the effectiveness and advantages of the design and analysis.