Takagi-Sugeno Fuzzy Model Research Articles

Distributed event-triggered fuzzy control for nonlinear interconnected systems

This paper deals with the asynchronous distributed event-triggered control of continuous-time nonlinear interconnected systems. The nonlinear dynamics of the subsystems are represented by Takagi–Sugeno fuzzy models via the sector nonlinearity approach. Moreover, the nonlinear interconnections among the subsystems are assumed to be known and sector-bounded. In the event-triggered control setup, where the state information is asynchronously available to the local controllers only in specific time instants, it is necessary to deal with the asynchronous premise variables because they introduce extra difficulties to derive suitable co-design conditions. To deal with this issue, we propose a new triggering strategy such that the local event-triggering mechanisms (ETMs) counteract the effects of asynchronous premise variables. With this new distributed ETM, a co-design condition is proposed, and the existence of a strictly positive minimum inter-event time is proved to exclude Zeno behaviour. Moreover, a multi-objective optimization procedure is introduced to enlarge the estimate of the domain of attraction of the closed-loop equilibrium and minimize the number of transmissions provided by the ETMs. Finally, the approach is validated through the synchronization of interconnected oscillators.

Event‐triggered security control for fuzzy‐model‐based cyber‐physical systems under Denial‐of‐Service attacks and actuator faults

AbstractThis article addresses the issue of event‐triggered security control for nonlinear cyber‐physical systems, characterized by Denial‐of‐Service (DoS) attacks, time‐varying delays, and actuator faults. These complexities are captured using the Takagi–Sugeno fuzzy model. Significantly, this study focuses on DoS attacks targeting the controller‐to‐actuator channel, and subsequently introduces a model for actuator faults that considers the prolonged utilization or degradation of component parts. To optimize communication resource allocation, a model‐independent event‐triggered mechanism is proposed. Utilizing the Lyapunov–Krasovskii function approach, the objective of achieving stochastic stability is transformed into a linear matrix inequalities problem, thus deriving a set of sufficient conditions. The efficiency and validity of the proposed algorithms is demonstrated through simulation results.

Prediction of earth pressure balance for EPB-TBM using machine learning algorithms

Face stability control of excavation with earth pressure balance machine (EPB) approach is the best available method to reduce the ground deformation and settlement of surface structures in a tunneling project in urban areas. In the present paper, several models have proposed through a statistical method, including feed-forward stepwise regression (FSR) and machine learning techniques such as support vector machine (SVM), Takagi–Sugeno fuzzy model (TS), and multilayer perceptron neural network (ANN-MLP), to provide a predictive strategy for EPB machine during the tunnel excavation. For this purpose, a monitoring dataset of machine performance parameters including advance speed, screw conveyor speed, screw conveyor torque, thrust force, and cutterhead rotation speed from Tehran Metro Line 6 Southern Extension Sector (TML6-SE) has been compiled. Then, the relation between the performance parameters and target values were investigated to analyze the available inputs and offer a new equation using the FSR. Moreover, evaluation metrics and loss functions were utilized for the evaluation of the developed models’ efficiency. The results proved the significance of the presented methods in this paper that could be used to predict the earth pressure balance operation with high efficiency.

Fuzzy H∞ Control of Discrete-Time Nonlinear Markov Jump Systems via a Novel Hybrid Reinforcement Q -Learning Method.

In this article, a novel hybrid reinforcement Q -learning control method is proposed to solve the adaptive fuzzy H∞ control problem of discrete-time nonlinear Markov jump systems based on the Takagi-Sugeno fuzzy model. First, the core problem of adaptive fuzzy H∞ control is converted to solving fuzzy game coupled algebraic Riccati equation, which can hardly be solved by mathematical methods directly. To solve this problem, an offline parallel hybrid learning algorithm is first designed, where system dynamics should be known as a prior. Furthermore, an online parallel Q -learning hybrid learning algorithm is developed. The main characteristics of the proposed online hybrid learning algorithms are threefold: 1) system dynamics are avoided during the learning process; 2) compared with the policy iteration method, the restriction of the initial stable control policy is removed; and 3) compared with the value iteration method, a faster convergence rate can be obtained. Finally, we provide a tunnel diode circuit system model to validate the effectiveness of the present learning algorithm.

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.

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.

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.

Security-Guaranteed Fuzzy Networked State Estimation for 2-D Systems With Multiple Sensor Arrays Subject to Deception Attacks

In this paper, the security-guaranteed fuzzy networked state estimation issue is investigated for a class of two-dimensional (2-D) systems with norm-bounded disturbances. Considering the structural specificity of the 2-D systems, the membership function in the Takagi-Sugeno fuzzy model is established to reflect the spatial information. Multiple sensor arrays are utilized to improve the observation diversity and overcome the measurement obstacle induced by geographical restrictions. The network-based deception attacks, occurring in a probabilistic fashion, are characterized by a set of Bernoulli distributed random variables. By resorting to the 2-D fuzzy blending and augmentation operations, the error dynamics of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s$</tex-math></inline-formula> th 2-D fuzzy estimator is formulated and, subsequently, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">globally asymptotical stability</i> of the local error dynamics is studied in virtue of Lyapunov stability theory, fuzzy theory, and stochastic analysis technique. Then, sufficient conditions are derived to ensure the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><inline-formula><tex-math notation="LaTeX">$(\varrho _{1},\varrho _{2},\varrho _{3},\rho _{s})$</tex-math></inline-formula>-security</i> of the local error dynamics. Furthermore, the estimation fusion problem of the local fuzzy estimators is discussed and the corresponding <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><inline-formula><tex-math notation="LaTeX">$(\varrho _{1},\varrho _{2},\varrho _{3},\rho _{s})$</tex-math></inline-formula>-security</i> is also guaranteed. Finally, an illustrative example is provided to demonstrate the rationality and the effectiveness of the proposed state estimation algorithm.

Observer-Based Boundary Fuzzy Control Design of Nonlinear Parabolic PDE Systems Using Mobile Sensors

This paper studies the boundary fuzzy control problem for nonlinear parabolic partial differential equation (PDE) systems under spatially noncollocated mobile sensors. In a real setup, sensors and actuators can never be placed at the same location, and the noncollocated setting may be beneficial in some application scenarios. The control design is very difficult due to the noncollocated mobile observation, which can be solved by an observer-based technique. At first, a Takagi-Sugeno fuzzy PDE model is devoted to accurately representing the nonlinear parabolic PDE system. Next, we present a state estimation scheme including fuzzy Luenberger-type PDE state observer plus mobile sensor guidance. Then, an observer-based boundary fuzzy controller is posed to render the resulting closedloop system exponentially stable, and the exponential decay rate is increased by the designed mobile sensor guidance laws. At last, two examples verify the proposed method.

Event-triggered finite-time admissibilization of bio-economic singular semi-Markovian jump fuzzy systems

An event-triggered scheme-based admissibilization problem of bio-economic singular semi-Markovian jump systems over a finite-time interval is investigated in this study, where the commodity price is assumed to follow a semi-Markov process. To facilitate analysis, the addressed system is expressed using Takagi-Sugeno fuzzy modeling with two fuzzy rules, which is then generalized to a finite number of fuzzy rules. Following that, an affine membership-based event-triggered controller is proposed for the system under consideration to ensure the desired admissibility within a given finite-time interval. A new set of conditions that adequately guarantees the aforementioned problem is derived using the Lyapunov-Krasovskii stability theory, parameterized linear matrix inequality technique and dissipative theory. A numerical example based on the eel seedling harvesting model is considered to validate the developed theoretical findings, where the significance of the proposed control design method is clearly demonstrated.

Enhancing stability control of inverted pendulum using Takagi–Sugeno fuzzy model with disturbance rejection and input–output constraints

The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method.

A Hybrid Design of Fault Detection for Nonlinear Systems Based on Dynamic Optimization.

To ensure the safety of an automation system, fault detection (FD) has become an active research topic. With the development of artificial intelligence, model-free FD strategies have been widely investigated over the past 20 years. In this work, a hybrid FD design approach that combines data-driven and model-based is developed for nonlinear dynamic systems whose information is not known beforehand. With the aid of a Takagi-Sugeno (T-S) fuzzy model, the nonlinear system can be identified through a group of least-squares-based optimization. The associated modeling errors are taken into account when designing residual generators. In addition, statistical learning is adopted to obtain an upper bound of modeling errors, based on which an optimization problem is formulated to determine a reliable FD threshold. In the online FD decision, an event-triggered strategy is also involved in saving computational costs and network resources. The effectiveness and feasibility of the proposed hybrid FD method are illustrated through two simulation studies on nonlinear systems.

Actuator fault-tolerant control for discrete Takagi-Sugeno fuzzy systems using the matrices norms approach

The apparition of faults is a well-known phenomenon in automatic control systems. Faults cause undesired behaviour and disruption of a controlled plant, which can lead to damage. This article addresses the actuator fault problem for nonlinear systems described by a discrete time Takagi–Sugeno fuzzy systems. An active fault-tolerant control based on a fault estimator is designed using the matrices norms approach instead of the usual Lyapunov stability theory. In this work, we consider the case where the premise variables do not depend on the unmeasurable variables. This allows the separate design of the gains of the controller, the observer and the estimator. Two nonlinear systems represented by discrete Takagi–Sugeno fuzzy models are studied to investigate the validity of the proposed method.

Non-fragile guaranteed cost control of microbial fuel cells

A microbial fuel cell (MFC), which is a new type of energy source, utilises electrogenic bacteria in sewage or soil to convert chemical energy into electrical energy. MFCs typically require an external controller to provide a stable output voltage to the external load. This study develops a non-fragile guaranteed cost (NFGC) controller to suppress the interference of the controller of an MFC and ensure that the quadratic cost function of the system satisfies certain performance indexes. First, for the convenience of controller design, a Takagi–Sugeno fuzzy model is established to approximate a single-chamber single-population MFC model. Subsequently, the linear matrix inequality method is used to design the NFGC controller. This control scheme can reduce the influence of controller disturbances on the system and ensure asymptotic stability of the closed-loop system under the specified upper bound of the provided cost function. The simulation results demonstrate that the developed control method has a shorter adjustment time and smaller steady-state error than traditional control methods such as sliding mode control (SMC), backstepping control, and fuzzy SMC

A systematic approach to modeling synchronous generator using Markov parameters and Takagi–Sugeno fuzzy systems

The problem of precise modeling of Synchronous Generator (SG) devices is demanding and crucial for monitoring, stability, and control of electric grids and microgrids. SGs are known to exhibit nonlinear behavior, and because they may work in a wide range of operating points due to different electric network phenomena like load changes, current intermittent renewable energy resources, temperature variations, topological changes, etc., the modeling task of SG can be a challenging problem. This paper proposes a new method to find a global model for a synchronous generator from the input and output measurement data using state-of-the-art methods in artificial intelligence (AI) like fuzzy clustering, subspace identification, and Takagi–Sugeno (T–S) fuzzy modeling. The fuzzy C-means method is utilized to cluster the measurement data, and then using a subspace identification method based on Markov parameters concepts, the dynamic model of SG for each cluster is obtained in the form of a state space model. A Takagi–Sugeno fuzzy model is applied to determine the corresponding outputs based on the measured inputs and the available state space models. The effectiveness of the proposed approach is illustrated by applying it to the data obtained from simulations on a known fourth-order SG nonlinear model and the data obtained from real-world experimental tests.

Large-signal stability analysis for offshore wind power fractional frequency transmission system with modular multilevel matrix converter

Aiming to achieve zero carbon emission, the rapid development of offshore wind power transmission system faces stability challenge. The fractional frequency transmission system (FFTS) with modular multilevel matrix converter (M3C) holds considerable promise among the solutions for large-scale and long-distance offshore wind power transmission. Currently, numerous demonstration projects involving FFTS are being conducted worldwide, necessitating urgent attention to system stability analysis for practical engineering applications. Notably, conventional approaches focusing on small-signal stability are inadequate when confronted with large-signal disturbances. In this study, the Takagi–Sugeno fuzzy model of FFTS is proposed considering the complex control strategy of M3C and the system strong nonlinearity. Subsequently, the Lyapunov function and the large-signal stability domain of attraction (LS-DOA) are constructed expeditiously based on the proposed fuzzy model. When analyzing the system larger-signal stability, the novel stability strength and optimal optimization factor are further introduced to develop a quantitative and efficient methodology for parameter optimization guidance compared with the conventional method. Thus, the FFTS different-frequency interaction features are elucidated from normal and different characteristics parameters mathematically and comprehensively. The effectiveness of proposed methods is verified by the simulation-based study.

Reliable fuzzy control of uncertain nonlinear networked systems under actuator faults

This study investigates a reliable fuzzy static-output feedback control (SOFC) scheme for uncertain Takagi–Sugeno fuzzy model (TSFM)-based nonlinear systems under the networked induced delays, information package losses and actuator faults, simultaneously. For this purpose, firstly, a comprehensive model for the actuator fault is suggested to enhance the performance of the actuator in the networked control systems (NCSs). More precisely, the suggested model contains an additive stochastic perturbation term in the actuator to further realize the control scheme. Besides, the Markov chain (MC) is employed to model the networked induced arbitrary delays and the information package losses. Hence, the corresponding closed-loop system lies in the Markovian jump systems (MJS). Then, based on the Lyapunov theory, the stochastic robust stability of the obtained system is studied and necessary conditions are extracted in new offline linear matrix inequalities (LMIs). Since the accurate value of the transition probabilities (TP) of the MC is not definite and even the identification is difficult, in view of practical applications in our control strategy, partly unknown TPs are assumed. Finally, to validate the superiorities of the suggested control approach, a truck-trailer system is adopted and simulated. The simulation results confirm the superiorities of the suggested control approach.

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.

Nonfragile Output Feedback Tracking Control for Markov Jump Fuzzy Systems Based on Integral Reinforcement Learning Scheme.

In this article, a novel integral reinforcement learning (RL)-based nonfragile output feedback tracking control algorithm is proposed for uncertain Markov jump nonlinear systems presented by the Takagi-Sugeno fuzzy model. The problem of nonfragile control is converted into solving the zero-sum games, where the control input and uncertain disturbance input can be regarded as two rival players. Based on the RL architecture, an offline parallel output feedback tracking learning algorithm is first designed to solve fuzzy stochastic coupled algebraic Riccati equations for Markov jump fuzzy systems. Furthermore, to overcome the requirement of a precise system information and transition probability, an online parallel integral RL-based algorithm is designed. Besides, the tracking object is achieved and the stochastically asymptotic stability, and expected H∞ performance for considered systems is ensured via the Lyapunov stability theory and stochastic analysis method. Furthermore, the effectiveness of the proposed control algorithm is verified by a robot arm system.

Quantized-Output-Based Exponential Stabilization of Fuzzy DPSs With Time-Varying Delay and Nonlinearities

The exponential stabilization of nonlinear distributed parameter systems (DPSs) with time-varying delay is studied in this paper. With the employment of the Takagi-Sugeno (T-S) fuzzy model, the nonlinear DPSs are described as a fuzzy parabolic partial differential equation (PDE). Then, with the consideration of the measurement output and control input information quantized by a kind of dynamic quantizers, fuzzy static and dynamic output feedback controllers are proposed. The time-delayed feedback controllers are also provided in the forms of static and dynamic. On the basis of the derived T-S fuzzy PDE model, Lyapunov-based control design strategies are proposed with respect to the effect of quantization. Moreover, by constructing appropriate Lyapunov functionals, sufficient conditions for designing the output feedback control gains and the quantizers' adjusting parameters which guarantee the exponential stability of the fuzzy closed-loop system are provided in terms of standard linear matrix inequalities (LMIs). Finally, we explore the output feedback controllers into the FitzHugh-Nagumo (FHN) equation and Fisher equation as applications. The efficiency of the design strategies is indicated through the simulation results.