Takagi-Sugeno Fuzzy Systems Research Articles

Observer-based control for networked Takagi-Sugeno fuzzy systems with stochastic packet losses

This paper addressed the observer-based control problem for Takagi-Sugeno (T-S) fuzzy systems with stochastic packet losses. More specifically, an sampled-data (SD) control technique is introduced to reduce the burden of the limited bandwidth of the network, a general consecutive packet loss model is used to represent the stochastic packet loss behavior between sensor-to-controller and controller-to-actuator, and an observer scheme based on received SD output information is used to obtain the estimated system states. Based on the above scenarios, an exact discrete-time model approach is developed for stabilizing networked T-S fuzzy systems. First, the considered system with the observer-based control scheme is transformed into its discrete-time model such that subsequent analysis will be carried out in the discrete-time domain. On this basis, stability criteria are derived by fully considering the probability distribution of consecutive packet losses. Furthermore, an observer-based controller is designed by introducing some auxiliary matrices. Finally, the correctness and practicability of the designed controller is demonstrated by a mass-spring-damper system.

$\mathcal{l}_{1}$ Filtering for Positive Takagi–Sugeno Fuzzy Systems via Successive Linear Programming

This paper studies the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {l}_{1}$</tex-math></inline-formula> filtering problem for positive Takagi-Sugeno (T-S) fuzzy systems. A pair of filters are sought to assure stability and positivity of filtering error systems with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {l}_{1}$</tex-math></inline-formula> performance indices. For this purpose, a pair of linear co-positive Lyapunov functions that capture the positivity characteristics of filtering error systems are adopted to derive sufficient conditions for the existence of filters, which boils down to the bilinear programming problem. To solve this dilemma, we propose a convex approximation strategy, and thus a sequence of convex surrogates are developed to reasonably replace the non-convex constraints, based on which a successive linear programming algorithm is constructed. Therefore, the filters can be achieved by solving a battery of linear programmings. Finally, the efficiency of the designed filtering scheme was justified by simulation validations.

Event-Triggered-Based Antidisturbance Switching Control for Switched T–S Fuzzy Systems

This investigation proposes an event-triggered-based anti-disturbance switching control technique for the switched Takagi-Sugeno (T-S) fuzzy systems (FSs) subject to multiple disturbances as well as unavailable system state. The disturbances are comprised of two parts, i.e., the unavailable modeled disturbances and the available unmodeled disturbances. First, a composite observer is constructed to capture the unavailable system state and unavailable modeled disturbances. Then, on the basis of the observer, a switching controller with an eventtriggered program inserted is established. Meanwhile, a switching criterion is formulated. Further, under the developed controller and switching criterion, the sufficient conditions are presented for the switched T-S FSs to achieve the multiple disturbance suppression and the communication transmission resource saving. In the end, the reasonability of the raised event-triggered-based anti-disturbance switching control scheme is verified with the employed simulation example.

Unknown input observers for time-varying delay Takagi–Sugeno fuzzy systems with unmeasured nonlinear consequents

This paper investigates the problem of unknown input observer (UIO) design for Takagi–Sugeno (TS) fuzzy systems with time-varying delay. For observer design, all the unmeasured nonlinearities are isolated in the nonlinear consequent parts of TS fuzzy systems. This allows dealing with the well-known issue related to unmeasured premise variables for TS fuzzy observer design in a more effective fashion via the mean value theorem. Using the unknown input (UI) decoupling technique, no a priori information on the UI is needed for the proposed TS fuzzy observer design, which can guarantee the asymptotic estimations of both the system state and the unknown input. Employing a fuzzy Lyapunov–Krasovskii functional with a suitable augmented vector, the effect of time-varying delay on the estimation error dynamics is taken into account in the observer design. Numerical examples are presented to demonstrate the effectiveness of the proposed fuzzy UIO design method for nonlinear time-varying delay systems.

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.

A novel [formula omitted] control for T-S fuzzy systems with transform matching membership functions

This article studies H∞ optimization issue of Takagi-Sugeno (T-S) fuzzy systems with an improved transform matching membership functions (MFs) approach. Different from existing transform matching MFs control method, a polynomial disassembling strategy is first proposed for T-S fuzzy systems. Then, combining with parameterized linear matrix inequality (LMI) technique which can remove the inequality constraints between the MFs in systems and fuzzy controllers, sufficient conditions are presented to maintain asymptotic stability and desired H∞ performance for studied plants. Afterwards, a novel MFs online optimization algorithm is proposed for the first time to automatically adjust the values of scaling and bias parameters so as to realize better H∞ performance. In contrast to the traditional control using improved matching MFs, the practical behavior of disturbance attenuation index is reduced efficiently. Additionally, the proposed MFs online optimization algorithm is capable of sustaining the desired H∞ performance when the disturbance channels exist modeling errors, i.e., the practical disturbance attenuation index γ is still less than the preset value. For guaranteeing the convergence of cost function, sufficient condition is obtained based upon Lyapunov stability theory. Finally, two demonstrative simulations are presented to confirm the advantages and benefits of the novel MFs online optimization control strategy.

A Discrete Integral Sliding Manifold for a Nonlinear System with Time Delay: An Event-Triggered Scheme

This paper presents a new approach to integral sliding mode control for discrete nonlinear systems with time delay. The approach is based on an event-triggered scheme and is applied to Takagi–Sugeno fuzzy models. In the first step, a new integral sliding function is constructed, which avoids the limited assumptions of most existing fuzzy sliding mode control schemes. The design parameter matrices defining the sliding surface are obtained by solving linear matrix inequalities. In the second step, an event trigger-based integral sliding mode control protocol is developed to ensure the state trajectories of the Takagi–Sugeno fuzzy systems with time delays. Finally, the proposed strategies are evaluated through a simulation example to demonstrate their effectiveness.

Observer-Based Non-PDC Control Design for PMSG-Based Wind Energy Conversion Systems

In this study, the nonparallel distribution compensation (PDC) control is proposed for permanent magnet synchronous generator (PMSG)-based wind energy conversion systems (WECS). To do this, the nonlinear PMSG-based WECS is expressed by Takagi-Sugeno (T-S) fuzzy systems. Based on the imperfect premise matching, the T-S fuzzy observer is delineated for estimating the unmeasurable states of the proposed WECS. Unlike the traditional PDC control, a general non-PDC control strategy is designed via the T-S fuzzy observer. The designed control scheme indicates that it is not required to share the same membership functions as the observer and system. By constructing the Lyapunov functional with available information on the fuzzy membership function and introducing the slack variables, sufficient conditions are obtained to assure the asymptotic stability of error dynamic for the PMSG-based T-S fuzzy system and its observer. Finally, the feasibility and applicability of the derived theoretical results are validated through the numerical example.

Delay-Derivative/Distribution Dependent Stability and Stabilization Criteria for T–S Fuzzy Systems With Random Time-Varying Delay

This paper is concerned with the problems of stability and stabilization for Takagi-Sugeno(T-S) fuzzy systems with random time-varying delay. Since the stochastic nature of delay is considered, the original systems are transformed into equivalent new system models. Then, by borrowing the constant delay decomposition method, an appropriate Lyapunov-Krasovskii(L-K) functional is constructed. Based on the L-K functional, the variation range, the probabilities in intervals and the derivative of delay can be effectively utilized. And the reciprocally convex inequality is used to estimate the upper bound of the integral terms from the derivative of L-K functional. The new delay-derivative/distribution dependent stability and stabilization criteria are derived. Different from the previous works, the information of delay derivative is effectively utilized to analyze and design the systems with random time-varying delay for the first time. Moreover, if delay is a known time-varying function, less conservative stability and stabilization conditions can be obtained by the proposed delay decomposition method. Finally, the merits of the obtained stability and stabilization criteria are illustrated via several examples.

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.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems via An Enhanced Gain-Scheduling Mechanism.

This article is concerned with developing a featured multi-instant Luenberger-like observer of discrete-time Takagi-Sugeno fuzzy systems with unmeasurable state variables, that is, not only to reduce the conservatism but also (at the same time) to alleviate the computational complexity over the recent approach reported in the literature. Contrary to previous approaches, an enhanced gain-scheduling mechanism is proposed for constructing much abundant working modes by online evaluating the updated variation information of normalized fuzzy weighting functions across two adjacent sampling instants and, thus, a different group of observer gain matrices with less conservatism is designed in order to employ the exclusive features for each working mode. Moreover, all the redundant terms containing both surplus and unknown system information are discriminated and removed in this study and, thus, the required computational complexity is reduced to a certain extent than the counterpart one. Finally, numerical examples are provided to illustrate the superiority of the developed approach.

Formula omitted] Sampled-Data Control for Uncertain Fuzzy Systems under Markovian Jump and FBm

This study concerns the sampled-data H∞ control problems of Markovian jump uncertain fuzzy systems constrained by the fractional Brownian motion (fBm). By constructing a piecewise Lyapunov-Krasovskii functional (LKF) and derivating it, sufficient conditions are gained for the stability of the Takagi-Sugeno (T-S) fuzzy systems. Especially, the free-weighting matrix and Newton-Leibniz formula are exploited to relax the conservatism. At last, state curves of three classic practical examples show the rationality of our design.

Adaptive neural networks-based integral sliding mode control for T-S fuzzy model of delayed nonlinear systems

This paper presents a method for designing adaptive neural networks (NNs) based on integral sliding mode control (ISMC) for delayed Takagi-Sugeno fuzzy systems with external disturbances. To do this, a fuzzy sliding surface is constructed with the information of the delayed states, and an adaptive radial basis function (RBF) NNs-based fuzzy ISMC is designed. Here, the RBF NN function is utilized to approximate the nonlinear perturbation term. The resulting stability criteria are derived based on suitable Lyapunov functionals with the help of generalized free-weight matrix-based inequality. The resulting conditions ensure the asymptotic stability with H∞ attenuation level. Moreover, the designed sliding motion achieved the reachability condition under the adaptive RBF NNs based on the sliding mode controller. To end with, a design and comparative examples are given to show the success of the nominated control scheme and less conservatism of the derived sufficient conditions.

Fault isolation and fault‐tolerant control for nonlinear stochastic distribution control systems with multiplicative faults

AbstractIn this paper, a fault isolation, diagnosis and fault tolerant control algorithm is proposed for nonlinear multiple multiplicative faults stochastic distribution control systems employing Takagi–Sugeno fuzzy system. To obtain the detailed fault information, a fault detection algorithm is introduced to discover the fault occurrence time. Then a fault isolation observer is built to produce the residual, and the error system is separated to subsystems affected only by disturbance and multiplicative faults. Moreover, a fault estimation scheme is presented to obtain the fault magnitude information. When faults occur, the system output probability density function will deviate from the desired distribution. So the model predictive control fault tolerant control scheme is needed to minimize the impact of faults as much as possible to make sure that the post fault output probability density function track the desired probability density function. The validity of the designed algorithm is demonstrated through a simulation example, where the fault tolerant control algorithm ensures that the system output probability density function still track the given output probability density function despite the complex case of multiple multiplicative faults occurring simultaneously.

Adaptive fuzzy observer based non-quadratic control for nonlinear system subject to actuator faults and saturation

This paper provides a new non-quadratic stabilization conditions based on adaptive fuzzy observer for a class of Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and both actuator faults and saturation. Firstly, an observer based fault tolerant control (FTC) is proposed, not only to estimate both system states and actuator faults but also to compensate for the actuator faults and to stabilize the faulty system with input constraints. The saturation effect is transformed into dead-zone nonlinearity and the generalized sector bound condition is used to estimate the attraction domain. To less the conservatism of the quadratic Lyapunov technique, a proper integral structure based on the non-quadratic function is investigated. The H∞ criteria is considered and the robust stabilization conditions of the faulty closed-loop system are expressed as a linear matrix inequalities (LMIs) optimization problem. Finally, the robustness and the advantages of the proposed approach are demonstrated through a mixed CSTR and a numerical example.

Adaptive neural network sliding mode control for reliable stabilization of uncertain Takagi–Sugeno fuzzy systems regulated by switching rules

The problem of adaptive sliding mode control for a class of continuous-time Takagi–Sugeno fuzzy systems regulated by the event of switching rules relying on neural network estimation method is put forward in this paper, where the plant suffers from state delay, internal structure uncertainty, and unknown nonlinearity. By proposing a switching surface in integral type, it obtains a sliding motion with desired property. In addition, to compensate the plant unknown nonlinearity and to meet the reaching condition, a radial basis function neural-network-based adaptive law is designed to ensure the existence of sliding motion in finite time. Furthermore, for the purpose of exponential stabilization of the sliding motion, a linear matrix inequality condition accompanied with switching signal characterized by an average dwell time is put forward. Finally, two numerical examples, one with all subsystems unstable and the other with stable subsystems and unstable systems, are shown to confirm the validity.

Fuzzy Observer-Based Consensus Tracking Control for Fractional-Order Multi-Agent Systems Under Cyber-Attacks and Its Application to Electronic Circuits

Consensus control of multi-agent systems (MASs) has applications in various domains. As MASs work in networked environments, their security control becomes critically desirable in response to cyber-attacks. In this paper, the observer-based consensus tracking control problem is investigated for a class of Takagi-Sugeno fuzzy fractional-order multi-agent systems (FOMASs) under cyber-attacks. The malicious cyber attacks can impact the security of topologies of the communication networks of both controllers and observers. To estimate unmeasurable system states, a fuzzy observer is built. It is found that the topology of contact for observer states may be different from that of the feedback signals. A novel mathematical model for T-S fuzzy FOMASs with cyber-attacks is proposed. By using algebraic graph theory, Lyapunov functional, and fractional calculus theory, a distributed feed-back controller is developed for each agent, which guarantee the secure performance of tracking consensus error and observer error. Finally, two numerical examples demonstrate the effectiveness of the suggested control scheme, and the controller design for electronic network circuits shows the applicability of the proposed theoretical results. Simulations results for different differential-orders and coupling strength scenarios are given.

Event-Based Fuzzy Tracking Control for Nonlinear Networked Systems Subject to Dynamic Quantization

This paper investigates the problem of event-based output feedback tracking control for discrete-time nonlinear networked systems with dynamic quantization. The Takagi-Sugeno (T-S) fuzzy systems theory is utilized to approximate the investigated nonlinear systems. Three general dynamic quantizers and an improved asynchronous event-triggering communication scheme are carried out to comprehensively decrease the amount of data in the communication of network and realize the rational utilization of limited communication resources. The objective is to design an event-based static output feedback tracking controller such that, in the presence of dynamic quantization, the closed-loop system can be asymptotically stabilized, and the tracking error achieves the predefined tracking performance. Moreover, the parameters for the desired dynamic quantizers and tracking controller can be obtained simultaneously by solving a set of linear matrix inequalities. Finally, the simulation responses are provided to demonstrate the validity of the proposed tracking control strategy.

Enhanced Local Stabilization of Constrained N-TS Fuzzy Systems With Lighter Computational Burden

The constrained Takagi–Sugeno fuzzy systems with local nonlinear models (N-TS fuzzy systems) are much more practical than the conventional T–S fuzzy models, but their applications are seriously affected by either the great conservatism or the heavy computational burden. In this short article, an enhanced local stabilization of constrained N-TS fuzzy systems is investigated with the purpose of not only reducing conservatism but also relieving computational burden. To do this, a new class of threshold functions are established in order to achieve real-time online assessment of the variation of the normalized fuzzy weighting functions (NFWFs) at different sampling instants, i.e., the one-step-past one and the current one. Thus, a key alternative is proposed for eliminating all the involved terms containing the one-step-past NFWFs while their main information is retained. Since our obtained design criteria are merely dependent on the current NFWFs, the conservatism can be reduced at the expense of lighter computational burden. The benefits of our proposed results are validated by implementing several objective comparisons with those recent results.

Enhanced Fuzzy Fault Estimation of Discrete-Time Nonlinear Systems via a New Real-Time Gain-Scheduling Mechanism.

The problem of enhancing the robust performance of nonlinear fault estimation (FE) is addressed by proposing a novel real-time gain-scheduling mechanism for discrete-time Takagi-Sugeno fuzzy systems. The real-time status of the operating point for the considered nonlinear plant is characterized by using these available normalized fuzzy weighting functions at both the current and the past instants of time. To achieve this, the developed fuzzy real-time gain-scheduling mechanism produces different switching modes by introducing key tunable parameters. Thus, a pair of exclusive FE gain matrices is designed for each switching mode on the strength of time-varying balanced matrices developed in this study, respectively. Since the implementation of more FE gain matrices can be scheduled according to the real-time status of the operating point at each sampling instant, the robust performance of nonlinear FE will be enhanced over the previous methods to a great extent. Finally, considerable numerical comparisons are implemented in order to illustrate that the proposed method is much superior to those existing ones reported in the literature.