Takagi-Sugeno Type Research Articles

Optimal Design of Fuzzy Systems Using Differential Evolution and Harmony Search Algorithms with Dynamic Parameter Adaptation

This paper presents a study of two popular metaheuristics, namely differential evolution (DE) and harmony search (HS), including a proposal for the dynamic modification of parameters of each algorithm. The methods are applied to two cases, finding the optimal design of a fuzzy logic system (FLS) applied to the optimal design of a fuzzy controller and to the optimization of mathematical functions. A fuzzy logic controller (FLC) of the Takagi–Sugeno type is used to find the optimal design in the membership functions (MFs) for the stabilization problem of an autonomous mobile robot following a trajectory. A comparative study of the results for two modified metaheuristic algorithms is presented through analysis of results and statistical tests. Results show that, statistically speaking, optimal fuzzy harmony search (OFHS) is better in comparison to optimal fuzzy differential evaluation (OFDE) for the two presented study cases.

An optimal [formula omitted]-differentially private learning of distributed deep fuzzy models

This study introduces a privacy-preserving framework for distributed deep fuzzy learning. Assuming training data as private, the problem of learning of local deep fuzzy models is considered in a distributed setting under differential privacy framework. A local deep fuzzy model, formed by a composition of a finite number of Takagi-Sugeno type fuzzy filters, is learned using variational Bayesian inference. This paper suggests an optimal (∊,δ)-differentially private noise adding mechanism that results in multi-fold reduction in noise magnitude over the classical Gaussian mechanism and thus leads to an increased utility for a given level of privacy. Further, the robustness feature, offered by the rule-based fuzzy systems, is leveraged to alleviate the effect of added data noise on the utility. An architecture for distributed form of differentially private learning is suggested where a privacy wall separates the private local training data from the globally shared data, and fuzzy sets and fuzzy rules are used to aggregate robustly the local deep fuzzy models for building the global model. The privacy wall uses noise adding mechanisms to attain differential privacy for each participant’s private training data and thus the adversaries have no direct access to the training data.

Intelligent Controller Design by the Artificial Intelligence Methods.

With the rapid growth of sensor networks and the enormous, fast-growing volumes of data collected from these sensors, there is a question relating to the way it will be used, and not only collected and analyzed. The data from these sensors are traditionally used for controlling and influencing the states and processes. Standard controllers are available and successfully implemented. However, with the data-driven era we are facing nowadays, there is an opportunity to use controllers, which can include much information, elusive for common controllers. Our goal is to propose a design of an intelligent controller–a conventional controller, but with a non-conventional method of designing its parameters using approaches of artificial intelligence combining fuzzy and genetics methods. Intelligent adaptation of parameters of the control system is performed using data from the sensors measured in the controlled process. All parts designed are based on non-conventional methods and are verified by simulations. The identification of the system’s parameters is based on parameter optimization by means of its difference equation using genetic algorithms. The continuous monitoring of the quality control process and the design of the controller parameters are conducted using a fuzzy expert system of the Mamdani type, or the Takagi–Sugeno type. The concept of the intelligent control system is open and easily expandable.

Resilient Distributed Fuzzy Load Frequency Regulation for Power Systems Under Cross-Layer Random Denial-of-Service Attacks.

In this article, a novel distributed fuzzy load frequency control (LFC) approach is investigated for multiarea power systems under cross-layer attacks. The nonlinear factors existing in turbine dynamics and governor dynamics as well as the uncertain parameters therein are modeled and analyzed under the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The cross-layer attacks threatening the stability of power systems are considered and modeled as an independent Bernoulli process, including denial-of-service (DoS) attacks in the cyber layer and phasor measurement unit (PMU) attacks in the physical layer. By using the Lyapunov theory, an area-dependent Lyapunov function is proposed and the sufficient conditions guaranteeing the system's asymptotically stability with the area control error (ACE) signals satisfying H∞ performance are deduced. In simulations, we adopt a four-area power system to verify the resiliency enhancement of the presented distributed fuzzy control strategy against random cross-layer DoS attacks. Results show that the designed resilient controller can effectively regulate the load frequency under different cross-layer DoS attack probabilities.

Event-Triggered Prescribed-Time Fuzzy Control for Space Teleoperation Systems Subject to Multiple Constraints and Uncertainties

Limited by the operation time window and working space, space teleoperation tasks need to be completed within an expected time while ensuring that the end effector meets the physical constraints. Meanwhile, the interaction with unknown environments would cause uncertainty in the closed-loop system, which brings great challenges to the control design. To solve the above problems, the control performance issue for a class of space teleoperation systems subject to multiple constraints and interaction uncertainties is investigated in this article. The force interaction with the human operator/space environment is represented by interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy systems, where the uncertain equivalent mass and damping parameters can be effectively described and captured by IT2 membership functions. In order to reduce the communication burden and satisfy the constraints of settling time, transient-state performance and operating space, a time-varying threshold event-triggered control scheme together with exponential-type Lyapunov function is developed for the first time. We show that, with the proposed controller, the synchronization tracking errors are guaranteed to converge to a user-defined residual set within preassigned settling time, and never exceed the prescribed range despite unknown control direction and actuator faults, which solves the long-standing constraint issue with more flexibility due to the fact that the related constraints can be arbitrarily specific within the physically available range. Moreover, the convergence set is only dependent on fewer user-defined parameters rather than approximation errors, which provides an effective analysis technique to deal with the difficulty that the convergence accuracy is difficult to calculate quantitatively in the presence of unknown disturbance. Detailed simulation results are provided to show the effectiveness and merit of the proposed control strategy.

A Novel Hammerstein Model for Nonlinear Networked Systems Based on an Interval Type-2 Fuzzy Takagi–Sugeno–Kang System

In this article, a novel Hammerstein structure is proposed for nonlinear networked systems based on an interval type-2 Takagi–Sugeno–Kang (IT2TSK) fuzzy system. The proposed approach is designed based on the general Hammerstein form, where an autoregressive moving average and an IT2TSK structures are designed as the linear energetic and nonlinear static components, respectively. The consequents of the nonlinear subsystem are characterized by a TSK-type system while the antecedents are characterized by interval type-2 fuzzy sets. The structure of the nonlinear subsystem is learned online based on the type-2 fuzzy clustering. Two new updating algorithms are introduced based on the Lyapunov theorem for learning the proposed model parameters and adaptive learning rates to assure the model stability and the parameter fast convergence. To illustrate the proposed model robustness, a test is performed under networked environment with time-varying delay and packet losses. The simulation results prove a higher performance for the proposed model than that of compared models.

Fault Detection Filtering Design for Discrete-Time Interval Type-2 T–S Fuzzy Systems in Finite Frequency Domain

This article focuses on the problem of fault detection filtering design for discrete-time interval type-2 Takagi-Sugeno (T-S) fuzzy systems in finite frequency domain. Considering the fact that external disturbances and faults are usually reside in finite frequency ranges, the finite frequency H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> performances are introduced to reflect the disturbance robustness and fault sensitiveness in finite frequency domain, respectively. Based on discrete-time Fourier transform and its properties, finite frequency performance analysis results are first obtained. Then, by exploiting the information on upper and lower membership functions, the membership-function-dependent filtering design conditions in the form of linear matrix inequalities are established for discrete-time interval type-2 T-S fuzzy systems in finite frequency domain. With the obtained filter, a fault detection scheme is then proposed and it is shown that the resulting fault detection system is asymptotically stable with prescribed finite frequency H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</sub> performances. Finally, the effectiveness of the proposed method is validated by simulation studies.

Efficient Model-Predictive Control for Networked Interval Type-2 T–S Fuzzy System With Stochastic Communication Protocol

In this article, the efficient model-predictive control (EMPC) problem of a class of nonlinear systems in the framework of interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy is investigated. In order to improve the reliability of the data transmission while reducing the network communication burden, a so-called stochastic communication protocol (SCP) governed by a Markov chain is adopted to orchestrate the data transmission order from the controller to the actuator. The purpose of the addressed problem is to design a set of desired EMPC controllers so as to guarantee the mean-square system stability and obtain a good balance among the computation burden, initial feasible region, and the control performance. A novel control model is established for the SCP and IT2 T-S fuzzy nonlinearities in a unified representation by using a fuzzy periodic switching related to the transmission token and the membership function. Then, the system state, the SCP-based control perturbation, and the previous input under the SCP are fully taken into consideration for constructing the objective function. By virtue of the “min-max” strategy, a few optimizations are formulated, and the corresponding EMPC algorithm is provided, where the feedback gain is designed offline, while the control perturbation is obtained online. Furthermore, by means of the matrix partition technique, sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying IT2 T-S fuzzy system. Finally, two illustrative examples are utilized to demonstrate the validity of the proposed EMPC strategy.

Fault-Tolerant Control for Stochastic Switched IT2 Fuzzy Uncertain Time-Delayed Nonlinear Systems.

This article devotes to solve the fault-tolerant control problem based on interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy stochastic switched uncertain time-delayed systems with signal quantization. Stochastic switched systems can model a dynamic structure susceptible to abrupt faults, making it more practically significant in power systems or economic systems. The core design is an observer-based fault-tolerant control scheme that can estimate incomplete measurable variables and eliminate the influence of fault dynamically well and enhancing the robust stability of the systems subject to quantization effects. A novel method in seeking the upper bound solution of time-varying delay efficiently decreases conservativeness, especially for the proposed time-delayed system. The simulated analysis is specified to verify the availability and validity of the obtained design method.

Adaptive Event-Triggered Fault Detection for Interval Type-2 T–S Fuzzy Systems With Sensor Saturation

This article deals with the adaptive event-triggered (AET) fault detection filter (FDF) problem for nonlinear-networked control systems with component and sensor faults, network-induced delays, uncertainties, external disturbances, and asynchronous premise variables. This system is represented by the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model, which can effectively capture parameter uncertainties. A new AET mechanism with many advantages, such as no singular problem, no degradation into a traditional time-triggered mechanism, fewer triggers, and no Zeno behavior, is constructed. The error caused by the AET mechanism is first regarded as a disturbance and thus can be attenuated by the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm bound. Based on Lyapunov's stability theory, novel sufficient conditions for H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and stability are then derived. In addition, the filter parameters and the weight matrix of the trigger condition are obtained in terms of linear matrix inequality (LMI) techniques. Finally, a numerical example is used to demonstrate the feasibility and merit of the proposed fault detection scheme.

SYNTHESIS OF A NEURO-FUZZY MODEL OF RADICAL POLYMERIZATION PROCESS KINET-ICS

There was considered the kinetic scheme of the processes of methyl methacrylate and styrene polymers synthesis by the radical polymerization method. It is shown that the main difference in the above kinetic schemes is observed in the last stage of the reaction and lies in the mechanisms of breaking the polymer chain – by recombination for polystyrene and by disproportionation for polymethyl methacrylate. There were given the well-known mathematical models describing the kinetic scheme for the polymerization of methyl methacrylate and styrene and showing the dependence of the degree of monomer to polymer conversion on the time. It is shown that each of the presented models contains a large number of empirical constants, the values of which differ by orders of magnitude among different researchers, which greatly complicates the use of these models and often leads to confusion and incorrect results of simulation modeling. In addition, some of the known models do not take into account the phenomenon of auto-acceleration of the process - the gel effect inherent in the radical polymerization of styrene and, to a greater extent, methyl methacrylate. Thus, the necessity of developing a simpler in its structure adequate mathematical model of the processes under consideration based on the methods of neuro-fuzzy modeling was substantiated. The results of studying the rate of polymerization of methyl methacrylate and styrene in a laboratory reactor under different initial conditions were used as initial data in the development of a fuzzy model. With the help of an adaptive neuro-fuzzy system, there were obtained primary models of the Takagi-Sugeno type, after processing which, we obtained the final fuzzy model. The accuracy of the obtained model was verified by conducting a comparative analysis of the results of process simulation with different initial data and results obtained in a laboratory reactor. The good data convergence were shown and recommendations were given for using the model.

State-dependent asynchronous intermittent control for IT2 T–S fuzzy interconnected systems under deception attacks

In this paper, a class of interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy interconnected system subjected to deception attacks is investigated by developing a state-dependent asynchronous intermittent control scheme. Whether control actions should be imposed or not is decided by an asynchronous activated mechanism in each subsystem, which contains two exponential attenuation surfaces and three state-dependent subregions. Besides, a switching controller is designed, which includes three sub-controllers with respect to above three subregions. Specially, this new type controller not only can avoid potential chattering behaviors resulted from the switchings among sub-controllers, but also can describe the attack signals as an intermittent nonlinear term to decrease the potential success rate of cyber intrusions. Moreover, under the concept of exponentially input-to-state stable (EISS), the concerned system is verified to be EISS by transforming the attack signals into a residual term. Finally, the validity of the proposed control strategy is verified by two illustrative examples.

Finite-time non-fragile filtering for nonlinear networked control systems via a mixed time/event-triggered transmission mechanism

This paper is aimed at investigating the problem of mixed time/event-triggered finite-time non-fragile filtering for nonlinear networked control systems with delay. First, a fuzzy nonlinear networked control system model is established by interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy model, the designed non-fragile filter resolves the filter parameter uncertainties and uses different membership functions from the IT2 T-S fuzzy model. Second, a novel mixed time/event-triggered transmission mechanism is proposed, which decreases the waste of network resources. Next, Bernoulli random variables are used to describe the cases of random switching mixed time/event-triggered transmission mechanism. Then, the error filtering system is designed by considering a Lyapunov function and a sufficient condition of finite-time boundedness. In addition, the existence conditions for the finite-time non-fragile filter are given by the linear matrix inequalities (LMIs). Finally, two simulation results are presented to prove the effectiveness of the obtained method.

Admissibilisation of singular interval type‐2 Takagi–Sugeno fuzzy systems with time delay

This study investigates the admissibility analysis and stabilisation problems for singular interval type-2 Takagi–Sugeno fuzzy systems with time delay. A generalised integral inequality method is used to obtain the delay-dependent condition. The criteria for admissibility analysis and controller synthesis are given in terms of linear matrix inequalities. In order to reduce the conservatism of the system, some free weighting matrices and advanced integral inequalities are introduced. Finally, two illustrative examples are exhibited to demonstrate the effectiveness of the proposed method.

Design and Hardware Implementation Based on Hybrid Structure for MPPT of PV System Using an Interval Type-2 TSK Fuzzy Logic Controller

The major drawback of photovoltaic (PV) systems is their dependence on environmental conditions, such as solar radiation and temperature. Because of this dependency, maximum power point tracking (MPPT) control methods are used in PV systems in order to extract maximum power from the PV panels. This study proposes a controller with a hybrid structure based on angle of incremental conductance (AIC) method and Interval Type-2 Takagi Sugeno Kang fuzzy logic controller (IT2-TSK-FLC) for MPPT. MPPT performance of proposed hybrid controller is evaluated via detailed simulation studies and dSPACE-based experimental study. The results validate that the proposed hybrid controller offers fast-tracking speed, high stability, and robust performance against uncertainties arising from disturbance to inputs of the PV system.

Event-Based Impulsive Control of IT2 T–S Fuzzy Interconnected System Under Deception Attacks

In this article, impulsive control issue of the interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy interconnected system is investigated via dynamic event-triggered mechanism (DETM), wherein deception attacks are considered. First of all, a more constrictive DETM is proposed, in which an exponential attenuation function is introduced to approximate the system states such that the error part is reconstructed. Then, under this exponential-type DETM, a new event-based impulsive control strategy is designed, which not only include the impulsive control on event instants, but also a state feedback control part with time-varying gains during the interval time of two consecutive events. The core idea is that the added feedback part can be regarded as a “bridge,” which connects the two consecutive impulse injections. Besides, input-to-state stability of the concerned system is investigated by transforming the attack signals into a residual term, so that some stability criteria are derived in spite of the unpredictable deception attacks. The nonexistence of Zeno behaviors is also guaranteed indirectly by utilizing the comparison relationship between DETM and its static counterpart. Finally, the validity of the proposed control strategy is verified by two illustrative examples.

Application of fuzzy logic for power change rate constraint in core power control at Reaktor TRIGA PUSPATI

The 1MWth Reaktor TRIGA PUSPATI (RTP) in Malaysia Nuclear Agency has been in operation more than 37 years. The existing core power control uses a conventional controller known as Feedback Control Algorithm (FCA). It is technically challenging to keep the core power output stable and operate within the acceptable error bands for the safety demand of the RTP. At present, the power tracking performance of the system could be considered unsatisfactory where constant gains of power change rate constraint and control rod speed constraint are used. Hence, a study of a new power change rate constraint design to achieve safe control rod speed range is conducted to improve the current performance. In this paper, a new power change rate constraint (PCRC) method using fuzzy logic is proposed to control the core power. The Takagi-Sugeno (T-S) type Fuzzy model is chosen due to its capability to work well with linear controller and making the computational control algorithm efficient. The model for core power control consists of mathematical models of the reactor core, FCA, and control rods selection algorithm. The mathematical models of the reactor core are based on point kinetics model, thermal-hydraulic models and reactivity models. The performance of power tracking and actuation signal for control rod drive input are compared between the conventional PCRC (cPCRC) and Fuzzy PCRC using MATLAB. In conclusion, the proposed Fuzzy PCRC has satisfactory performance in core power tracking for controlling the nuclear reactor with high reliability and safety.

Stability analysis of dynamic nonlinear interval type-2 TSK fuzzy control systems based on describing function

This paper focuses on the limit cycles prediction problem to discuss the stability analysis of dynamic nonlinear interval type-2 Takagi–Sugeno–Kang fuzzy control systems (NIT2 TSK FCSs) with adjustable parameters. First, in order to alleviate computational burden, a simple architecture of NIT2 TSK FCS using two embedded nonlinear type-1 TSK fuzzy control systems (NT1 TSK FCSs) is proposed. Then, describing function (DF) of NIT2 TSK FCS is obtained based on the DFs of embedded NT1 TSK FCSs. Subsequently, integrating the stability equation and parameter plane approaches provides a solution to identify the limit cycle and the asymptotically stable regions. Moreover, particle swarm optimization technique is applied to minimize the limit cycle region. Furthermore, for robust design, a gain-phase margin tester is utilized to specify the minimum gain margin ( $$\hbox {GM}_{\mathrm{min}}$$ ) and phase margin ( $$\hbox {PM}_{\mathrm{min}}$$ ) when limit cycles can arise. Finally, two simulation examples are considered to validate the advantages of the presented method.

Distributed fuzzy filtering for load frequency control of non‐linear interconnected power systems under cyber‐physical attacks

In this study, a new distributed filtering approach is proposed for the load frequency control of uncertain non-linear power systems with cyber-physical attacks. Specifically, the non-linear power system is firstly modelled under interval type-2 Takagi–Sugeno fuzzy framework and the uncertainty therein is captured by designing corresponding membership functions. Both denial of service cyber attack and physical sensor attack are considered and modelled as independent Bernoulli process. Based on the Lyapunov stability theory, less conservative sufficient conditions have been derived to guarantee the robustly mean-square asymptotic stability with an average performance standard for the dynamic filtering error system. Moreover, artful matrix transformation techniques have been adopted to decouple the intertwined matrix variables in designing the distributed filter gains. In simulations, a three-area non-linear power system with internal uncertainties is used to validate the robustness of the proposed distributed filtering strategy to system parametric uncertainties and cyber-physical attacks.

Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy Framework.

This article is concerned with the problem of the Hankel-norm model reduction for stochastic discrete-time nonlinear systems in interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The IT2 T-S fuzzy model is an efficient model for describing uncertain nonlinear systems, and the model reduction is to simplify the high-order complex systems by reducing the order of the original system. The aim of this article is to reduce the order of the original stochastic discrete-time IT2 fuzzy system into lower order system without ignoring the influence of IT2 membership functions. First, the Hankel-norm performance of the stochastic discrete-time IT2 fuzzy model is analyzed. Then, based on the projection theorem and cone complementary linearization approach, a convex Hankel-norm-based model reduction approach subject to conditions in the form of linear matrix inequalities (LMIs) is obtained. A membership-functions-dependent (MFD) technique is applied to capture the information of IT2 membership functions and further reduce the conservativeness. A numerical example is presented to illustrate the effectiveness of the proposed results.