Fuzzy-model-based Research Articles

Stability analysis of nonlinear-function fuzzy-model-based control systems

This paper presents the stability analysis of nonlinear-function fuzzy-model-based (FMB) control systems. A fuzzy model with nonlinear function terms is proposed to represent nonlinear plants. A fuzzy controller with the nonlinear function terms is then proposed to close the feedback loop. The nonlinear function terms enhance the capability of fuzzy modelling and feedback compensation. Following the linear-matrix-inequality (LMI) based stability analysis approach for the traditional FMB control systems, it will lead to stability conditions involving the nonlinear terms for the proposed nonlinear-function FMB control systems. As a result, the stability conditions will have an infinite number of LMIs, which make it impractical to find a feasible solution numerically using convex programming techniques. A stability analysis approach is proposed to obtain effective LMI-based stability conditions for the proposed nonlinear-function FMB control systems. Simulation examples are given to illustrate the merits of the proposed fuzzy control approach.

Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy model

Nonlinear actuator fault estimation observer: An inverse system approach via a T-S fuzzy modelBased on a Takagi-Sugeno (T-S) fuzzy model and an inverse system method, this paper deals with the problem of actuator fault estimation for a class of nonlinear dynamic systems. Two different estimation strategies are developed. Firstly, T-S fuzzy models are used to describe nonlinear dynamic systems with an actuator fault. Then, a robust sliding mode observer is designed based on a T-S fuzzy model, and an inverse system method is used to estimate the actuator fault. Next, the second fault estimation strategy is developed. Compared with some existing techniques, such as adaptive and sliding mode methods, the one presented in this paper is easier to be implemented in practice. Finally, two numerical examples are given to demonstrate the efficiency of the proposed techniques.

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model‐based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS) approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS‐based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

Takagi-Sugeno Fuzzy Model-Based Flight Control and Failure Stabilization

This paper presents a Takagi–Sugeno fuzzy model-based approach to modeling, controlling, and stabilizing an aircraft in both normal and damaged conditions. The major contributions of this paper are as follows. First, it introduces the Takagi–Sugeno modeling and the parallel distributed compensation control approach. Then, it demonstrates how the approach can be applied to aircraft in a systematic manner. Finally, the approach is applied to the modified NASA F-15 number 837 nonlinear model, and preliminary simulation results are presented. The benefits of using a Takagi–Sugeno model-based parallel distributed compensation control approach include a systematic controller design procedure, mathematical proof of stability for classes of failures, and intuitive insight into damage effects on an aircraft. This work is the first to present this control approach as applied to aircraft.

LMI-Based Stability Analysis for Fuzzy-Model-Based Control Systems Using Artificial T–S Fuzzy Model

This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Sugeno (T-S) fuzzy model are represented by the staircase ones. With the nice property of the staircase membership functions, it turns the set of infinite number of linear-matrix-inequality (LMI) based stability conditions into a finite one. Furthermore, the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions. The stability of the original FMB control systems is guaranteed by the satisfaction of the LMI-based stability conditions. The proposed stability analysis is applied to the FMB control systems of which the T-S fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to enhance the design flexibility of the fuzzy controller. A simulation example is given to illustrate the merits of the proposed approach.

T–S Fuzzy Model-Based Robust Stabilization for Networked Control Systems With Probabilistic Sensor and Actuator Failure

The system studied in this paper has four main features: 1) It is a networked controlled system (NCS), and therefore, the signal transfer is subject to random delay and/or loss; 2) it is a nonlinear system approximated by a Takegi--Sugeno (T-S) fuzzy model; 3) its multisensors and multiactuators are subject to various possible faults/failures; and 4) there are uncertainties in the plant model parameters. A comprehensive model is first developed in this paper to cover these features for a class of NCS nonlinear systems. This model has removed some limitations of similar models in the published literature. Then, the Lyapunov functional and the linear matrix inequality (LMI) are applied to develop two new stability conditions (Theorems 1 and 2). These conditions and an algorithm are used to design a controller to achieve robust mean square stability of the system. Finally, two examples are used to demonstrate the application of the modeling and the controller design method developed.

Fuzzy Model-based Servo Control for Discrete-Time Nonlinear Systems with Constraints

AbstractThis paper presents servo control for discrete-time nonlinear systems with constraints on inputs and states using the fuzzy model-based control approach. Firstly, the nonlinear error system is constructed based on error vector between state and the target point by utilizing the input difference between current input and cancellation input. Secondly, the error system is exactly converted into a Takagi-Sugeno fuzzy model utilizing sector nonlinearity approach. Finally, the fuzzy servo controller is designed by simultaneously solving servo controller design condition and the constraint conditions on inputs and states. The design conditions are given in the form of LMI. Servo control with constraints on inputs and states is achieved by the designed servo controller. Design examples illustrate the utility of this approach.

Design of stable fuzzy controller for non-linear systems subject to imperfect premise matching based on grid-point approach

This study investigates the systems stability of fuzzy-model-based (FMB) control systems. Based on the T-S fuzzy model representing the non-linear system, a fuzzy controller using grid-point (GP) technique is proposed to close the feedback loop. A GP is defined as the sub-operating domain of the non-linear system. For each GP, a corresponding GP fuzzy controller is employed to control the system. As the non-linearity in each GP is lower compared to that of the full operating domain, it is in favour of yielding relaxed stability analysis result using the GP control technique of which the nature of the membership functions and operating domain are taken into account. Furthermore, unlike most of the fuzzy control approaches, the proposed one can be applied to FMB control systems subject to imperfect premise matching that the fuzzy model and fuzzy controller do not share the same premise membership functions. As a result, some simple membership functions can be employed for the fuzzy controllers to lower the implementation cost. Based on the Lyapunov stability theory, stability conditions in terms of linear matrix inequalities are derived to guarantee the system stability and facilitate the controller synthesis. Simulation examples are given to demonstrate the merits of the proposed FMB control scheme using the proposed GP technique.

SOS-Based Stability Analysis of Polynomial Fuzzy-Model-Based Control Systems Via Polynomial Membership Functions

This paper presents stability analysis of polynomial fuzzy-model-based (FMB) control systems using the sum-of-squares (SOS) approach. Recently, stability analysis of the polynomial fuzzy-control systems, which is a generalized form of the well-known Takagi-Sugeno (T-S) FMB control systems, has been reported in the form of SOS-based stability conditions. Lack of information on the relations between membership functions and premise variables, in the existing stability analysis approaches, causes conservatism of their results. In this paper, to derive relaxed stability conditions for polynomial FMB control systems, membership functions which are approximated with polynomials and carrying relations between membership functions and premise variables are brought into the stability analysis. Considering a polynomial FMB control system and based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived, where each term contains product of membership functions of the polynomial fuzzy model and polynomial fuzzy controller. Each product term is approximated by a polynomial. In order to obtain better approximation, the operating domain of membership functions is partitioned to subregions. Then, SOS-based stability conditions for all subregions are derived. Unlike some published stability-analysis approaches, the proposed one can be employed for stability analysis of polynomial fuzzy-control systems under imperfect premise matching of which the fuzzy model and fuzzy controller do not share the same membership functions. The solution of the SOS-based stability conditions can be found numerically using SOSTOOLS, which is a free third-party MATLAB Toolbox. Numerical examples are given to illustrate the effectiveness of the proposed stability conditions.

Quadratic-Stability Analysis of Fuzzy-Model-Based Control Systems Using Staircase Membership Functions

This paper presents the stability analysis of fuzzy-model-based (FMB) control systems. Staircase membership functions are introduced to facilitate the stability analysis. Through the staircase membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov-stability theory, stability conditions in terms of linear-matrix inequalities (LMIs) are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability-analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated FMB control system. Furthermore, the proposed stability-analysis approach can be applied to the FMB control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers. By employing membership functions with simple structure, it is possible to lower the structural complexity and the implementation cost. Simulation examples are given to illustrate the merits of the proposed approach.

Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems

This paper presents the stability analysis of interval type-2 fuzzy-model-based (FMB) control systems. To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model, which can be regarded as a collection of a number of type-1 T-S fuzzy models, is proposed to represent the nonlinear plant subject to parameter uncertainties. With the lower and upper membership functions, the parameter uncertainties can be effectively captured. Based on the interval type-2 T-S fuzzy model, an interval type-2 fuzzy controller is proposed to close the feedback loop. To facilitate the stability analysis, the information of the footprint of uncertainty is used to develop some membership function conditions, which allow the introduction of slack matrices to handle the parameter uncertainties in the stability analysis. Stability conditions in terms of linear matrix inequalities are derived using a Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed interval type-2 FMB control approach.

Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems

This paper presents the stability analysis of interval type-2 fuzzy-model-based (FMB) control systems. To investigate the system stability, an interval type-2 Takagi-Sugeno (T-S) fuzzy model, which can be regarded as a collection of a number of type-1 T-S fuzzy models, is proposed to represent the nonlinear plant subject to parameter uncertainties. With the lower and upper membership functions, the parameter uncertainties can be effectively captured. Based on the interval type-2 T-S fuzzy model, an interval type-2 fuzzy controller is proposed to close the feedback loop. To facilitate the stability analysis, the information of the footprint of uncertainty is used to develop some membership function conditions, which allow the introduction of slack matrices to handle the parameter uncertainties in the stability analysis. Stability conditions in terms of linear matrix inequalities are derived using a Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed interval type-2 FMB control approach.

Fuzzy Model-based Charpy Impact Toughness Assessment for Ship Steels

The present research aims at linking steel composition and microstructure to a prediction of Charpy impact properties of ship structural steel, including Charpy impact energy, transition temperature (ITT) and fracture appearance (brittleness). In this paper, adaptive fuzzy modelling techniques were applied to develop generic models for the prediction of Charpy impact properties of Grade A and AH36 ship steels. Using the proposed fuzzy modelling approach, the rule-based fuzzy prediction models, which involved chemical composition, grain size, tensile strength and Charpy impact energy, were generated and optimised automatically from numerical data. The investigation of the relationship between Charpy impact energy and fracture surface characteristics is also presented in the paper. Numerical analysis shows that using the obtained fuzzy models we are able to predict Charpy toughness for given steel compositions and microstructures, and also reveal useful qualitative information linking composition-microstructure to Charpy impact properties.

1A1-D08 ファジィモデル制御によるアクロボットの倒立

1A1-D08 ファジィモデル制御によるアクロボットの倒立