Takagi-Sugeno Systems Research Articles

Interconnected Takagi-Sugeno system and fractional SIRS malware propagation model for stabilization of Wireless Sensor Networks

This paper is devoted to investigate the dynamical behaviors of malware attack on a familiar kind of complex heterogeneous networks, namely Wireless Sensor Network, and discuss an effective immunization treatment based on fractional interconnected Takagi-Sugeno (T-S) fuzzy systems. Our approach is based on the mathematical modeling to establish a controlled fractional network-based SIRS malware propagation model that better describes the attacking behavior of malicious objects on Wireless Sensor Network. After that, we point out some qualitative properties of the proposed network-based SIRS malware propagation model such as the existence of positively invariant set, backward bifurcation and asymptotic behavior. Especially, in order to study the model's stability, we evaluate an epidemiological threshold value R0, namely basic reproductive ratio, which ensures the existence of at least one endemic equilibrium P⁎ and the local asymptotic stability of malware-free equilibrium P0. As a consequence of theoretical result, the malware-free equilibrium P0 is unstable when R0>1 and hence, the rest of this paper is to address a stabilization problem for the proposed controlled network-based model and establish some sufficient conditions related to linear matrix inequalities and positive definite matrices. Finally, we illustrate the obtained theoretical results by a computational example.

Reliable [formula omitted] fuzzy control for fault-tolerant actuator failures of active suspension system

A new methodology for fault tolerant control (FTC) is proposed to compensate actuator failures using Takagi–Sugeno systems. This makes possible to design the controller that represents actuator failures using a scaling factor by solving a family of linear matrix inequalities (LMIs). The resulting control system guarantees asymptotic stability, compensates the effect of actuator faults and ensures certain an H∞ performance level. This methodology is applied to the active suspension systems that motivated this research, where in the context of active suspension (AS) systems, the guaranteed performance correspond to ride comfort in the presence of road disturbances. Thus, a controller is developed for a quarter-car model with active suspension. The simulated results illustrate the effectiveness of the proposed approach.

Relaxed Resilient Fuzzy Stabilization of Discrete-Time Takagi–Sugeno Systems Based on A New Switching Mechanism

Relaxed Resilient Fuzzy Stabilization of Discrete-Time Takagi–Sugeno Systems Based on A New Switching Mechanism

Enhanced Resilient Fuzzy Stabilization of Discrete-Time Takagi-Sugeno Systems Based on Augmented Time-Variant Matrix Approach.

In this technical correspondence, the resilient fuzzy stabilization is enhanced in the direction of elevating the feasible stabilization region as large as possible while the same alert threshold is chosen as the recent one. To do this, the switching-type fuzzy state-feedback controller is designed with a set of switch modes so that more groups of gain matrices can be introduced to enhance the degree of freedom. What is far more important is that a novel augmented time-variant matrix approach is proposed in order to collect the proprietary features of normalized fuzzy weighting functions with regard to each switch mode. Then, all the obtained augmented time-variant matrices are split into a set of positive/negative matrices, which can be elaborately assigned into different monomials of our designing conditions under the framework of homogeneous polynomials. Therefore, less conservative results of resilient fuzzy stabilization are obtained even if some higher alert thresholds are chosen for probably ensuring the establishment of the involved precondition. Finally, the superiority of our approach is validated by giving some detailed comparisons on the benchmark example.

Fuzzy Approach for Managing Renewable Energy Flows for DC-Microgrid with Composite PV-WT Generators and Energy Storage System

Recently, the implementation of software/hardware systems based on advanced artificial intelligence techniques for continuous monitoring of the electrical parameters of intelligent networks aimed at managing and controlling energy consumption has been of great interest. The contribution of this paper, starting from a recently studied DC-MG, fits into this context by proposing an intuitionistic fuzzy Takagi–Sugeno approach optimized for the energy management of isolated direct current microgrid systems consisting of a photovoltaic and a wind source. Furthermore, a lead-acid battery guarantees the stability of the DC bus while a hydrogen cell ensures the reliability of the system by avoiding blackout conditions and increasing interaction with the loads. The fuzzy rule bank, initially built using the expert’s knowledge, is optimized with the aforementioned procedure, maximizing external energy and minimizing consumption. The complete scheme, modeled using MatLab/Simulink, highlighted performance comparable to fuzzy Takagi–Sugeno systems optimized using a hybrid approach based on particle swarm optimization (to structure the antecedents of the rules) and minimum batch squares (to optimize the output).

Proportional multi-integral observer design for Takagi–Sugeno systems with unmeasurable premise variables: Conservatism reduction via polyquadratic Lyapunov function

In this paper, we present the design of a new unknown-input observer for Takagi–Sugeno fuzzy systems with unmeasurable premise variables. The work proposes an improvement of the simultaneous state and unknown-input observer. The main idea is to consider a non-quadratic Lyapunov function in order to reduce the conservatism of its quadratic counterpart. Moreover, the mean value theorem is used to express the error dynamics in a way that reduces the conservatism of the bounded terms assumptions. The stability conditions are formulated as Bilinear Matrix Inequalities. To address these, we propose an iterative algorithm based on linear matrix inequalities, which transforms the Bilinear form into a sets of linear matrix inequalities. Finally, two examples are given to highlight the performance of the proposed observer.

Observer design based on D-stability and Finsler’s lemma for interconnected Takagi–Sugeno systems with immeasurable premise variables

ABSTRACT This paper deals with the observer design for a class of Interconnected Takagi–Sugeno (TS) systems with Immeasurable Premise Variables (IPV). We first investigate the D-stability of Luenberger-like interconnected multiple observers. However, the resulting constraints can be somewhat conservative due to the use of a common Lyapunov matrix. Then, the so-called Finsler’s lemma is used to relax the D-stability conditions through the introduction of additional slack variables providing more flexibility and extra degrees of freedom. The designed conditions are expressed as Linear Matrix Inequalities (LMIs). The proposed approaches are applied in simulation to a Proton Exchange Membrane Fuel Cell (PEMFC) system and a four-tank system.

Multi-Instant Gain-Scheduling Fuzzy Observer of Discrete-Time Takagi-Sugeno Systems and Its Application: An Efficient Balanced Matrix Approach.

The problem of relaxed state estimation of discrete-time Takagi-Sugeno fuzzy systems is studied by constructing a novel multi-instant gain-scheduling fuzzy observer. First, a multi-instant gain-scheduling mechanism with a single adjustable parameter is given for the first time in order to produce more reasonable switch modes over previous results reported in recent literature. Second, for every switch mode, a batch of specified observer gain matrices is determined by developing an efficient balanced matrix approach so that the updated values of adjacent normalized fuzzy weighting functions can be flexibly exploited. Since the implied information of each specific switch mode is capable of being absorbed and utilized more thoroughly by the aid of the refined higher-order balanced matrices, the conservatism can be prominently reduced at the price of consuming extra computational burden within the allowable range. Finally, two benchmark examples are provided to test and verify the progressiveness of our proposed approach.

Estimation of Energy Consumption and Flight Time Margin for a UAV Mission Based on Fuzzy Systems

An essential aspect to achieving safety with a UAV is that it operates within the limits of its capabilities, the available flight time being a key aspect when planning and executing a mission. The flight time will depend on the relationship between the available energy and the energy required by the UAV to complete the mission. This paper addresses the problem of estimating the energy required to perform a mission, for which a fuzzy Takagi–Sugeno system was implemented, whose premises were developed using fuzzy C-means to estimate the power required in the different stages of the mission. The parameters used in the fuzzy C-means algorithm were optimized using particle swarm optimization. On the other hand, an equivalent circuit model of a battery was used, for which fuzzy modeling was employed to determine the relationship between the open-circuit voltage and the state of charge of the battery, which in conjunction with an extended Kalman filter allows determining the battery charge. In addition, we developed a methodology to determine the minimum allowable battery charge level. From this, it is possible to determine the available flight time at the end of a mission defined as the flight time margin. In order to evaluate the developed methodology, a physical experiment was performed using an hexarotor UAV obtaining a maximum prediction error equivalent to the energy required to operate for 7 s, which corresponds to 2% of the total mission time.

An intelligent estimation-based large-scale envelope control for variable cycle engine with packet dropout

The distributed control system is designed to match the advanced variable cycle engine (VCE) with significant advantages, such as the reduced weight and the low cost by introducing the network. In addition to these advantages, the packet dropout follows and may destroy the performances of the controlled systems. Therefore, except for the engine's strong nonlinearity and uncertainty, the effective control design should also possess the ability to handle the packet dropout. The contribution of this study is not only improving the control quality by creatively designing a large-scale intelligent dynamic estimator but also reinforcing the robustness and extending the application of engine control. A novel intelligent estimation-based large-scale envelope (IEBLE) control design for the VCE with packet dropout is proposed. The new framework consists of two parts: high-accuracy estimation and robust control. The intelligent dynamic estimator is developed by deep learning architecture to compensate for the missing information and supply the essential inputs for the control. With the estimated inputs, a model-based large-scale envelope control design is proposed. This separation between information compensation and control design distinguishes our approach from the centralized control of packet dropout. We formulate the engine's nonlinear dynamic in the full envelope as an optimal Takagi-Sugeno system. The engine dynamic and steady parameters are extracted as features. By the intelligent clustering of the features, the rule number and consequent models of each rule are optimized, which renders the resulting optimal system with the high accuracy of the engine's dynamic and steady performances as well as the minimum rules. Finally, the control gain is scheduled based on the fuzzy inference of the optimized system. Afterwards, this design is applied to a VCE as a demonstration. The comparisons between the proposed control and the H∞ and LQR controllers are conducted in different scenarios to evaluate the control quality and robustness. The experimental results show the superior performances, the effectiveness and robustness of the new control, regardless of the packet dropout, large-scale nonlinearity and uncertainty.

Relaxed Resilient Fuzzy Stabilization of Discrete-Time Takagi–Sugeno Systems via a Higher Order Time-Variant Balanced Matrix Method

Resilient fuzzy stabilization is capable of providing much less conservative results than conventional fuzzy stabilization while the alert threshold condition should be always satisfied at each sampling instant. In order to make the alert threshold condition more easily to be guaranteed, the short paper employs the switching-type gain-scheduling control law so that the real-time information, which is specific to the current sampling instant, can be integrated into resilient fuzzy stabilization. More importantly, a new kind of time-variant balanced matrix is introduced for the first time for adjusting positive/negative terms of different monomials in a more flexible way. As a result, the conservatism of resilient fuzzy stabilization can be further reduced even if the alert threshold condition becomes more difficult to be violated. Finally, the advantage of the developed method is tested and validated via related comparisons on a benchmark example.

Asynchronous H[formula omitted] filtering for semi-Markov jump T-S fuzzy systems within partial state delay and deception attack: Applied to aircraft-pilot state estimation

This article addresses an asynchronous filter design problem within partial state delay and deception attack for a class of discrete-time semi-Markov jump Takagi-Sugeno (T-S) systems which can describe estimation process for human pilot cognitive property. First, the emission probability, which relates to system mode and filtering mode, is introduced to consider the system process with asynchronously observation scheme. Second, state delay-independent condition and state delay-dependent condition designed within state delay boundary are proposed under the H∞ performance index γ. Third, the system output signal under deception attack is adopted as the information interference during the transmitted filter process. Through the Lyapunov-Krasovskii approach, stability of the proposed filtering scheme that is mode dependent can be guaranteed. Moreover, the filtering mode is also dynamically changed according to the prescribed asynchronous formula. A numerical example considered for aircraft-pilot state estimation is used to demonstrate the effectiveness and applicability of our proposed filtering method by obtaining the minimum γ. Experiments show that filter could play a better role in advancing signal estimation in aircraft-pilot state estimation scenario with properties like state delay and deception attack. Also, it contributes to modelling the fully human pilot cognitive decision-making in a human-computer interaction scenario.

Robust estimation of multiplicative faults on actuators based on Takagi-Sugeno systems with unmeasurable premise variables

In this paper, a simultaneous estimation of states and multiplicative faults on actuators is considered based on Takagi – Sugeno observer with unmeasurable premise variables. Observer design is derived of matrix linear inequalities deduced by method Lyapunov and a $H_infty$ performance criterion to minimize the effect of perturbation and uncertainty generated by the unmeasurable premise variables. The methodology is demonstrated by a nonlinear model of a helicopter to show performance of the observer in the presence of faults and disturbances.

Proporcional Integral Observer Design for Takagi-Sugeno system applied to a knee rehabilitator

The main objective of this paper is to describe the design of proportional integral observer (PIO) for Takagi-Sugeno system using the nonlinear sector approach. This observer improves the state estimation due to the integral part. Lyapunov functions are used to analize the stability of the error dynamic of the observer. Stability conditions are obtained in terms of linear matrix inequalities (LMIs). The effectives of the proposed approach is illustrated by knee rehabilitator robot.

Takagi-Sugeno Fuzzy Approach with Compressed Representation for Overhead Crane System

This paper proposes a Takagi-Sugeno (TS) fuzzy approach for 2-dimensional of freedom overhead crane. Since this system is underactuated with nonlinear mathematical dynamic model, the requirement of achieving accurate positioning while eliminating oscillation is a challenging issue. The nonlinear sector decomposition is taken into implementation which uses the nonlinear terms in the dynamic model as scheduling variables to transform the initial system to TS representation. However, the number of TS fuzzy rules is exponential in the number of nonlinear elements in the system, leading to the increase of computational expense. Therefore, the reduced complexity method is introduced to minimize the scheduling variables in TS system. In addition, the uncertain system’s components are also taken into consideration to enhance the robust property of the system when working in practical environment. The controller is constructed based on parallel distributed compensation (PDC) approach while the linear matrix inequalities (LMIs) technique is employed to analyse the system’s stability. The effectiveness of the proposed method is demonstrated through numeral simulations.

Proportional Observer design based on [formula omitted]-stability and Finsler's Lemma for Takagi-Sugeno systems

This paper concerns Proportional Observer design for Takagi-Sugeno (TS) systems with Immeasurable Premise Variables using D-stability constraints and L2-gain analysis. The D-stability is used to control the dynamics of the designed observer (eigenvalues clustering in a prescribed Linear Matrix Inequality region) while the L2 technique minimizes the effect of Immeasurable Premise Variables on the state estimation error. In addition, Finsler's Lemma provides more flexibility and extra degrees of freedom through slack variables to obtain relaxed stability conditions. Numerical examples are presented to illustrate the effectiveness of the proposed approaches.

Hybridization of ANFIS and fuzzy logic for groundwater quality assessment

In this paper, to analyse the groundwater quality, the hybridization of Takagi-Sugeno fuzzy model, and Adaptive Neuro-Fuzzy Inference System (ANFIS) has been used. Initially, the Takagi-Sugeno fuzzy inference system has been used to find the groundwater quality. The Takagi-Sugeno system results, along with primary data, have been applied in four ANFIS models to identify the best ANFIS model using training, testing, and validation processes. Four ANFIS models have been designed; ANFIS-1, ANFIS-2, ANFIS-3, and ANFIS-4. Five water quality parameters, Calcium (Ca), Fluoride (F−), Magnesium (Mg), Sulphate (SO42−), and Nitrate (NO3−), in 454 groundwater samples have been used to analyse groundwater quality. The results of Takagi-Sugeno fuzzy inference system indicates that all samples are useful for drinking purpose. As per the results obtained from all four models, the best model is ANFIS-2, as it has the minimum error. This paper's primary objective is to prepare a hybrid model that can be used to make a decision on drinking groundwater quality.

Enhanced fuzzy state estimation of discrete‐time nonlinear systems via a multi‐instant united switch‐type observer

AbstractThe performance of state estimation of discrete‐time Takagi–Sugeno systems is enhanced by proposing a featured multiinstant united switch‐type observer. The novelty of the proposed observer lies in both the definition and application of a set of switching modes. Since different time‐variant free matrices can be for the first time introduced in accordance with each switching mode, both the current time and the past time normalized fuzzy weighting functions are together considered for designing the corresponding observer gain matrices with much less conservatism than those recent methods reported in the literature. Furthermore, there are only two tuning parameters which are both located in a limited candidate set and thus this fact does benefit for giving the optimal solution of our developed multiinstant united switch‐type candidates. Finally, numerical comparisons are provided in order to verify the technical superiority of the results developed in this article.

Robust fault estimation and fault‐tolerant tracking control for uncertain Takagi–Sugeno fuzzy systems: Application to single link manipulator

SummaryThis article concerns the estimation and tracking control problems for Takagi–Sugeno systems with disturbances and norm bounded uncertainties in presence of sensor and actuator faults (SAF). First, we propose a robust fuzzy observer (RFO) design method to estimate both state and SAF for the considered class of the nonlinear systems. Then, this RFO‐based fault tolerant tracking control is developed not only to compensate the SAF effects but also to ensure the state convergence to desired trajectories in spite of their presence. To reduce the conservatism of design conditions, observer and controller gains are calculated in a single step by solving a set of linear matrix inequality constraints. H∞ criterion is used to attenuate disturbance effects and to reduce the tracking error. Finally, simulation results by considering two types of actuator fault and comparative study on a single link flexible joint manipulator are provided to underline the performances of the mentioned process.

Predictions on wheat crop yielding through fuzzy set theory and optimization techniques

Agricultural field’s production is commonly measured through the performance of the crops in terms of sow amount, climatology, and the type of crop, among other. Therefore, prediction on the performance of the crops canaid cultivators to make better informed decisions and help the agricultural field. This research work presents a prediction on wheat crop using the fuzzy set theory and the use of optimization techniques, in both; traditional methods and evolutionary meta-heuristics. The performance prediction in this research has its core on the following parameters: biomass, solar radiation, rainfall, and infield’s water extractions. Besides, the needed standards and the efficiency index (EFI) used come from already developed models; such standards include: the root-mean-square error (RMSE), the standard deviation, and the precision percentage. The applicationof a genetic algorithm on a Takagi-Sugeno system requires and highly precise prediction on wheat cropping;being, 0.005216 the error estimation, and 99,928 the performance percentage.