Takagi-Sugeno Research Articles

Interval-valued fuzzy estimation and its application to adaptive control of quadrotor

In this paper, a combination of fuzzy clustering estimation and sliding mode control is used to control a quadrotor system, whose mathematical model is complex and contains unknown elements, including structure and parameters. Additionally, the system may be susceptible to external environmental disturbances. Initially, the nonlinear unknown components of the system are estimated using a fuzzy model. We introduce a novel approach for constructing a Takagi–Sugeno (TS) interval-valued fuzzy model (IVFM) based on input–output data obtained from the identified system. Following the construction of the fuzzy model that estimates the unknown aspects of the quadrotor system, we implement a control strategy with online adjustments for the fuzzy-modeled dynamics. In this phase, the system’s model is estimated in an adaptive manner, allowing the dynamic equations to be utilized in sliding mode control. Finally, we apply the proposed technique to a quadrotor, presenting simulation results to demonstrate the effectiveness of this approach in controlling a system characterized by unknown nonlinear dynamics.

A Takagi–Sugeno fuzzy controller for minimizing cancer cells with application to androgen deprivation therapy

Androgen deprivation therapy (ADT) is frequently used to treat prostate cancer which is a widespread disease having a very low survival rate. A prolonged course of ADT can increase toxicity and drug resistance. This study proposes an adaptive therapy combining chemotherapy or immunotherapy with the discontinuation of hormone therapy to overcome these obstacles. The super-twisting sliding mode control (STSMC) algorithm is found to be one of the effective approach as an ADT model for obtaining suitable dosage adaptively. The primary objective is to rapidly reduce the number of cancer cells and the duration of drug exposure. The Takagi–Sugeno fuzzy controller-based active control algorithm is introduced, and it’s performance is compared with the STSMC algorithm. While maintaining global asymptotic stability, the Takagi–Sugeno fuzzy controller reduces the duration of therapy to six months. The controllers are implemented utilizing the linear matrix inequality (LMI) algorithm and the yet another LMI (YALMIP) toolset for MATLAB, and their efficacy is validated utilizing MATLAB and Simulink simulations. This study presents a novel approach to improve prostate cancer treatment outcomes by integrating nonlinear control algorithms and adaptive dosage strategies to reduce treatment duration and minimize drug exposure, thereby improving patient outcomes in prostate cancer management.

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-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.

Observer-based fuzzy integral sliding mode control for bilateral teleoperation systems with time-varying delays

This paper aims to examine the stability and tracking performance of a bilateral teleoperation system. The Takagi–Sugeno fuzzy method is utilized, through which the nonlinear master–slave dynamics is converted as a fuzzy-based system. The state observers are designed for the linearized fuzzy teleoperation systems, and the corresponding estimation errors are formulated. Importantly, a novel observer-based fuzzy integral sliding mode control is developed by deliberately introducing the delay term into the sliding surfaces. As such, advanced delay-product type of Lyapunov–Krasovskii functionals are constructed for the augmented state vectors, in order to acquire the additional delay information. In addition, the Wirtinger-based integral inequality along with an extended reciprocally convex matrix inequality is applied to the Lyapunov derivatives to establish the delay-dependent stability conditions. Numerical results are provided to demonstrate efficacy of the developed control mechanism.

An Improved Zonotopic Approach Applied to Fault Detection for Takagi–Sugeno Fuzzy Systems

In this work, an actuator fault detection problem for discrete-time Takagi-Sugeno fuzzy systems is tackled in a bounded error context where both state disturbances and measurement noise are assumed to be unknown but bounded with known bounds. First, a peak-to-peak performance synthesis method is applied to design a robust residual generator against the considered process disturbances and measurement noise. Meanwhile, an improved zonotopic approach is proposed to compute tight adaptive thresholds for residual evaluation. Then, a reliable set-membership fault detection strategy with the aid of generated residual signals and adaptive thresholds is introduced. Finally, the viability of the proposed method is demonstrated via a numerical simulation. Then, an experimentation on a 3D Crane system is performed to show its practicability.

Aperiodic Sampled-Data-Based Control for T-S Fuzzy Systems: An Improved Fuzzy-Dependent Adaptive Event-Triggered Mechanism

This paper is devoted to designing a novel aperiodic sampled-data-based event-triggered control strategy for Takagi-Sugeno (T-S) fuzzy systems. Firstly, via taking the structural features of fuzzy subsystems and the available information of fuzzy membership functions (FMFs) into consideration, an improved fuzzy-dependent adaptive event-triggered mechanism (FDAETM), which designs different adaptive event-triggered mechanisms for corresponding fuzzy subsystems, is proposed to provide extra design flexibility and further optimize communication efficiency. Then, the two-side looped-functional method (TSLFM) and dynamic partitioning approach are introduced in the construction of the novel Lyapunov-Krasovskii functional (LKF). These two methods contribute to deriving preferable stability criterion and stabilization approach via relaxing the positive definite constraint on LKF and fully utilizing the inner system state during the whole aperiodic sampling interval. Eventually, two simulation examples are introduced to verify the effectiveness of the proposed control strategy and its advantages in lightening communication frequency.

Input–Output Finite-Time Stability for Switched T–S Fuzzy Delayed Systems With a Time-Dependent Lyapunov–Krasovskii Functional Approach

This research concerns the finite-time performance analysis for switched Takagi-Sugeno (T-S) fuzzy (STSF) systems subject to time-varying delay. Since the existing relevant results for finite-time synthesis of general switched systems require the finite-time stability property of the individual subsystem, a more general situation that the STSF systems comprised fully of finite-time unstable delayed subsystems are considered in the investigation. For surmounting this situation, a novel time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) approach is developed by integrating a ranged dwell time switching mechanism. Then, the corresponding (input-output) finite-time stability criteria with less conservativeness are simultaneously derived for the (perturbed) STSF delayed systems to be (input-output) finite-time stable over the concerned finite-time interval. Finally, two illustrative examples are provided to demonstrate the accuracy and superiority of the developed (input-output) finite-time analysis framework.

Output regulation for time–delayed Takagi–Sugeno fuzzy model with networked control system

This article studies $H_{\infty}$ control problem based on the event--triggered scheme with time delays for the synchronization of an chaotic system represented by delayed Takagi--Sugeno models. Firstly, this method depending on two scenarios: a) Each local subsystem integrated that the delayed T-S fuzzy model for the same value of input matrices for the networked system and b) This is near steady-state zero-error diversification has to all be the same local subsystems. Generally, in the case of fuzzy regulation, these in lieu of generating the fuzzy regulator as a result of linear local controllers, circumstances were adjusted by addressing the issue of fuzzy regulation for the delayed Takagi--Sugeno models fuzzy model. Then, a delayed Takagi--Sugeno uses a fuzzy system to model the non--linear regulator. On the other hand, communication delays are a vital factor that cannot be ignored. To tackle the networked induced delay initially, author attempt to implement the event--triggered scheme for output regulation which reduce the cost of network transmission. By constructing a Lyapunov functional and making use of event--triggered method, some suitable circumstances that ensure asymptotic stability of $H_{\infty}$ performance index for the resulting model were derived. Additionally, as the variations of the aforementioned results, two scenarios were presented. Our developed approaches are demonstrated by a final example illustrating their superiority, usefulness and reliability.

Mamdani vs. Takagi-Sugeno Fuzzy Inference Systems in the Calibration of Continuous-Time Car-Following Models.

The transition to intelligent transportation systems (ITSs) is necessary to improve traffic flow in urban areas and reduce traffic congestion. Traffic modeling simplifies the understanding of the traffic paradigm and helps researchers to estimate traffic behavior and identify appropriate solutions for traffic control. One of the most used traffic models is the car-following model, which aims to control the movement of a vehicle based on the behavior of the vehicle ahead while ensuring collision avoidance. Differences between the simulated and observed model are present because the modeling process is affected by uncertainties. Furthermore, the measurement of traffic parameters also introduces uncertainties through measurement errors. To ensure that a simulation model fully replicates the observed model, it is necessary to have a calibration process that applies the appropriate compensation values to the simulation model parameters to reduce the differences compared to the observed model parameters. Fuzzy inference techniques proved their ability to solve uncertainties in continuous-time models. This article aims to provide a comparative analysis of the application of Mamdani and Takagi-Sugeno fuzzy inference systems (FISs) in the calibration of a continuous-time car-following model by proposing a methodology that allows for parallel data processing and the determination of the simulated model output resulting from the application of both fuzzy techniques. Evaluation of their impact on the follower vehicle considers the running distance and the dynamic safety distance based on the observed behavior of the leader vehicle. In this way, the identification of the appropriate compensation values to be applied to the input of the simulated model has a great impact on the development of autonomous driving solutions, where the real-time processing of sensor data has a crucial impact on establishing the car-following strategy while ensuring collision avoidance. This research performs a simulation experiment in Simulink (MATLAB R2023a, Natick, MA, USA: The MathWorks Inc.) and considers traffic data collected by inductive loops as parameters of the observed model. To emphasize the role of Mamdani and Takagi-Sugeno FISs, a noise injection is applied to the model parameters with the help of a band-limited white-noise Simulink block to simulate sensor measurement errors and errors introduced by the simulation process. A discussion based on performance evaluation follows the simulation experiment, and even though both techniques can be successfully applied in the calibration of the car-following models, the Takagi-Sugeno FIS provides more accurate compensation values, which leads to a closer behavior to the observed model.

T-S fuzzy model based event-triggered change control for product and supply chain systems

Product and supply chain systems are a class of complex nonlinear systems due to the uncertain demand fluctuation and unexpected events, and Takagi–Sugeno (T-S) fuzzy systems are suitable for modelling such product and supply chain systems with different production rates. According to the uncertainty customer demands, different subsystems which describe the corresponding production-inventory processes are orchestrated by the T-S fuzzy rule. Change control is designed to handle the supply chain blocking and event breaking caused by uncertain factors. Then, sufficient conditions are given such that the exponential stability with a prescribed bullwhip effect attenuation level can be guaranteed, and the control synthesis problem is transformed into the solvability of linear matrix inequalities for the product and supply chain systems. An example is introduced to verify the validness and efficiency of the proposed approach.

Design of Polynomial Observer-Based Control of Fractional-Order Power Systems

This research addresses the problem of globally stabilizing a distinct category of fractional-order power systems (F-OP) by employing an observer-based methodology. To address the inherent nonlinearity in these systems, we leverage a Takagi–Sugeno (TS) fuzzy model. The practical stability of the proposed system is systematically established through the application of a sum-of-squares (SOS) approach. To demonstrate the robustness and effectiveness of our approach, we conduct simulations of the power system using SOSTOOLS v3.00. Our study contributes to advancing the understanding of F-OP and provides a practical framework for their global stabilization.

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.

Passive Stabilization of Static Output Feedback of Disturbed Nonlinear Stochastic System

This paper investigates the Static Output (SO) control issue of the disturbed nonlinear stochastic system, which achieves passivity. Through the application of fuzzy sets and the stochastic differential equation, a Takagi–Sugeno (T-S) fuzzy model with the terms of multiplicative noise and external disturbance can be constructed to describe the considered systems. Furthermore, the Parallel Distributed Compensation (PDC) concept is used to design a fuzzy controller exhibiting an SO feedback scheme structure. To attenuate the effect of external disturbance, the PDC-based SO fuzzy controller is designed to exhibit passivity. During the derivation of some sufficient conditions, a line-integral Lyapunov function is utilized to avoid the conservative term produced using the derivative membership function. Using converting technologies, a stability criterion belonging to Linear Matrix Inequality (LMI) forms is proposed such that the derived conditions are convex hull problems and are solved through an optimization algorithm. Then, the proposed criterion is used to discuss the problem of SO controller design of ship fin stabilizing systems with added disturbance and noise.

Adaptive event‐triggered efficient output feedback model predictive control for networked interval type‐2 T–S fuzzy system with data loss

AbstractThis article is concerned with the adaptive event‐triggered (AET) efficient output feedback model predictive control (EOFMPC) for a set of nonlinear networked interval type‐2 Takagi–Sugeno (IT2 T–S) fuzzy control systems with data loss. For the reduction in data transmission burden and required control performance, the AET scheme and a novel dynamic triggering law are introduced jointly in this article. The efficient model predictive control approach as in Kouvaritakis et al. (IEEE Trans Automat Contr. 2000;45(8):1545–1549.), which transfers the main part of online optimization work to offline stage by incorporating an extra perturbation into the fixed feedback law, is extended to networked control systems to reduce their online computational burden. This article proposes the following: (1) an unified closed‐loop model representation of data loss process and IT2 T–S fuzzy nonlinearities is established under the framework of EOFMPC, which explicitly considers the AET condition; (2) a new design method for the state observer gain is presented based on an ellipsoidal invariant set, so that a smaller bound of estimation error can be obtained through an extra optimization problem; (3) some optimization problems are formulated to design the proposed controllers, and the corresponding EOFMPC algorithm is summarized; (4) by means of the extra matrix partition technique, the online optimization problem subject to one ellipsoidal constraint is transformed into a novel convex form to solve the uncertainty of the estimation error. A simulation example and a few comparative simulation experiments illustrate the effectiveness and availability of the aforementioned approach.

Quasi-Static Modelling of a Full-Channel Effective Magnetorheological Damper with Trapezoidal Magnetic Rings.

Magnetorheological damper (MRD) has been successfully applied to vehicle suspension systems as an intelligent core component. Most conventional MRDs have closed rectangle-shaped magnetic circuits, resulting in a short effective working length and negligible damping force. To address the above issues, a novel full-channel effective MRD with trapezoidal magnetic rings (FEMRD_TMR) is proposed. The trapezoidal magnetic ring can shunt the magnetic circuit, distributing it evenly along the damping channel and increasing the effective working length. Additionally, which has the same variation trend as the magnetic flux through it, makes the magnetic induction intensity distribution more uniform to reduce the magnetic saturation problem. Theoretically analyzing the damping characteristics of the FEMRD_TMR, a quasi-static model is developed to forecast the output damping force. The structural design of MRD is challenging since conventional quasi-static models rely on the yield stress of magnetorheological fluid (MRF) to reflect the rheological property, which cannot be directly observed and is challenging to calculate. The Takagi-Sugeno (T-S) fuzzy neural network and a unique magnetic circuit computation are offered as a novel quasi-static modeling approach to address the issue. The MRF's yield stress is linearized into magnetic induction intensity functions by the T-S fuzzy neural network and then converted into the MRD's structural size by the special magnetic circuit calculation. Therefore, the proposed quasi-static model can directly reflect the relationship between the damping force and structure size, simplifying MRD's structure design. The novel quasi-static model is shown to be more straightforward and understandable than the conventional Bingham quasi-static model and to have approximately accurate damping force prediction when compared to experimental data.

Sampled-data output tracking control based on T–S fuzzy model for cancer-tumor-immune systems

This study investigates the tracking control issue for a cancer-tumor immune nonlinear model, which explains the interaction between cancer cells and the immune system in the body. To achieve this, the nonlinear model is first converted into linear sub-models using the Takagi–Sugeno (T–S) fuzzy methodology. The tracking and control of cancer cell proliferation while preserving immune cells is proposed using a sample-data output tracking control technique. Time-dependent discontinuous Lyapunov Krasovskii functional is recommended based on the improved Wirtinger inequality, this may provide additional information about the sawtooth structure of the sampling interval. Less conservative stability criteria are extracted having the form of linear matrix inequalities (LMIs) in consequence of extended reciprocally convex matrix inequality and Wirtinger-based integral inequality. The proposed approach achieves the stabilization of an augmented time delay system that connects with a given fuzzy nonlinear model and tracking error system. Furthermore, the proposed approach reduces the impact of external disturbances under the H∞ norm bound.

LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system

This paper investigates the stochastic Takagi-Sugeno (T-S) fuzzy uncertainty-dependent state feedback sampled-data control, asymptotical stability and exponential stability analysis for a class of stochastic T-S fuzzy system with measurable uncertainties, mixed interval time varying delays and Gaussian white noise. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the system plant. Secondly, the stochastic T-S fuzzy uncertainty-dependent state feedback sampled-data controller is designed via uncertainty-dependent parameters and the hold times series of sampled-data. Thirdly, the Bernoulli probability distribution is employed to describe the random occurrence characteristic of multipath packet dropouts. Three classes of delay-dependent stability conditions in terms of linear matrix inequalities (LMIs) are derived for the closed-loop system. The multiple integral fuzzy-basis-dependent Lyapunov functional and augmented state variable are employed to derive the delay-dependent stability conditions, then the closed-loop system is asymptotically stable and exponentially stable. The congruence transformation method and prescribed H-infinity performance functional are employed to derive the less conservative delay-dependent stability conditions, and the prescribed H-infinity performance is guaranteed. The relaxation matrix and congruence transformation method are employed to design the linear transformation equalities and congruence transformation matrices, then the controller gain matrix is determined and computation complexity of solving LMIs is reduced. Finally, the proposed method is applied in the chaotic Lorenz system to show the effectiveness and advantage of proposed method.

Research on fuzzy impedance control of upper-limb rehabilitation robot based on membership functions online optimization learning strategy

PurposeTo improve the position tracking efficiency of the upper-limb rehabilitation robot for stroke hemiplegia patients, the optimization Learning rate of the membership function based on the fuzzy impedance controller of the rehabilitation robot is propose.Design/methodology/approachFirst, the impaired limb’s damping and stiffness parameters for evaluating its physical recovery condition are online estimated by using weighted least squares method based on recursive algorithm. Second, the fuzzy impedance control with the rule has been designed with the optimal impedance parameters. Finally, the membership function learning rate online optimization strategy based on Takagi-Sugeno (TS) fuzzy impedance model was proposed to improve the position tracking speed of fuzzy impedance control.FindingsThis method provides a solution for improving the membership function learning rate of the fuzzy impedance controller of the upper limb rehabilitation robot. Compared with traditional TS fuzzy impedance controller in position control, the improved TS fuzzy impedance controller has reduced the overshoot stability time by 0.025 s, and the position error caused by simulating the thrust interference of the impaired limb has been reduced by 8.4%. This fact is verified by simulation and test.Originality/valueThe TS fuzzy impedance controller based on membership function online optimization learning strategy can effectively optimize control parameters and improve the position tracking speed of upper limb rehabilitation robots. This controller improves the auxiliary rehabilitation efficiency of the upper limb rehabilitation robot and ensures the stability of auxiliary rehabilitation training.

Robust MPC-RG for an autonomous racing vehicle considering obstacles and the battery state of charge

The design of a controller able to deal with uncertainties and physical constraints plays an essential role in fast and complex systems. Then, a reference governor approach based on model predictive control (MPC-RG) for an autonomous racing vehicle is proposed. The MPC-RG guarantees constraint satisfaction and recursive feasibility online while including obstacle avoidance capability and energy-aware management by solving a multi-objective optimization problem. In particular, a trade-off between maximizing the longitudinal velocity and the state of charge of the vehicle’s battery, as well as minimizing the variation of control actions is adopted. Moreover, the proposed MPC-RG is combined with a state-feedback linear quadratic regulator (LQR) and a Kalman filter (KF) to compensate for modeling errors and exogenous disturbances, as well as to estimate the unmeasured lateral velocity. In fact, for control and estimation purposes, a data-driven Takagi–Sugeno (TS) model trained by an adaptive neuro-fuzzy inference network is used. The performance of the developed approach is assessed in simulations using a well-known case study based on a 1/10 scale RC electric car.