The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Hakkeung Lam - One of the best experts on this subject based on the ideXlab platform.
-
stability analysis of polynomial fuzzy model based control systems with mismatched premise Membership Functions through taylor series Membership Functions
2016Co-Authors: Hakkeung LamAbstract:This chapter investigates the stability of polynomial fuzzy model-based control systems by bringing the approximated Membership Functions into the SOS-based stability conditions. Various approximation methods of Membership Functions are reviewed and their characteristics are discussed. Using the Taylor series expansion, the original Membership Functions are represented by approximated Membership Functions which are a weighted sum of local polynomials in a favorable form for stability analysis. SOS-based stability conditions are obtained which guarantee the system stability if the fuzzy model-based control system is stable at all chosen Taylor series expansion points. A simulation example is presented to illustrate the influence of the density of expansion points to the capability of stability conditions finding a feasible solution and demonstrate the effectiveness of the proposed stability conditions over some published results.
-
state and output feedback control of interval type 2 fuzzy systems with mismatched Membership Functions
IEEE Transactions on Fuzzy Systems, 2015Co-Authors: Xingjian Sun, Hakkeung LamAbstract:This paper is concerned with the problems of state and output feedback control for interval type-2 (IT2) fuzzy systems with mismatched Membership Functions. The IT2 fuzzy model and the IT2 state and output feedback controllers do not share the same Membership Functions. A novel performance index, which is expressed as an extended dissipativity performance, is introduced to be a generalization of $H_{\infty }$ , $L_{2}$ – $L_{\infty }$ , passive, and dissipativity performances indexes. First, the IT2 Takagi–Sugeno fuzzy model and the controllers are constructed by considering the mismatched Membership Functions. Second, on the basis of Lyapunov stability theory, the IT2 fuzzy state and output feedback controllers are designed, respectively, to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance. The existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems, which can be solved by standard software. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.
-
a new relaxed stability condition for takagi sugeno fuzzy control systems using quadratic fuzzy lyapunov Functions and staircase Membership Functions
International Journal of Fuzzy Systems, 2014Co-Authors: Kairui Cao, Hakkeung Lam, Xiaozhi Gao, A V Vasilakos, Witold PedryczAbstract:This paper presents a new relaxed stability condition for Takagi-Sugeno (T-S) fuzzy control systems. Using quadratic fuzzy Lyapunov Functions (QFLFs), the stability of closed-loop control system is guaranteed by the negative definiteness of several fuzzy summations. However, since the Membership Functions are continuous, the negative definiteness of these fuzzy summations implies an infinite number of linear matrix inequalities (LMIs), which cannot be solved directly by conventional convex optimization methods. To handle this problem, Staircase Membership Functions (SMFs) are employed to convert the infinite number of LMIs into a finite one. At the same time, the information of Membership Functions is brought into stability analysis, which substantially relaxes the proposed stability condition. The efficiency of the presented approach is demonstrated by using two simulation examples.
-
relaxed stability conditions based on taylor series Membership Functions for polynomial fuzzy model based control systems
IEEE International Conference on Fuzzy Systems, 2014Co-Authors: Chuang Liu, Hakkeung Lam, Xian Zhang, Sai Ho LingAbstract:In this paper, we investigate the stability of polynomial fuzzy-model-based (PFMB) control systems, aiming to relax stability conditions by considering the information of Membership Functions. To facilitate the stability analysis, we propose a general form of approximated Membership Functions, which is implemented by Taylor series expansion. Taylor series Membership Functions (TSMF) can be brought into stability conditions such that the relation between Membership grades and system states is expressed. To further reduce the con-servativeness, different types of information are taken into account: the boundary of Membership Functions, the property of Membership Functions, and the boundary of operating domain. Stability conditions are obtained from Lyapunov stability theory by sum of squares (SOS) approach. Simulation examples demonstrate the effect of each piece of information.
-
stability analysis of polynomial fuzzy model based control systems with mismatched premise Membership Functions
IEEE Transactions on Fuzzy Systems, 2014Co-Authors: Hakkeung Lam, Shunhung TsaiAbstract:This paper investigates the stability of polynomial-fuzzy-model-based (PFMB) control system, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. To enhance the design flexibility, the number of rules and the shape of premise Membership Functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model, however, which make the stability analysis more difficult and potentially lead to conservative stability analysis result. A sum-of-squares (SOS)-based stability analysis approach using the Lyapunov stability theory is proposed to investigate the stability of the PFMB control systems and synthesize the polynomial fuzzy controller. To facilitate the stability analysis and relax the stability analysis result, the property of the Membership Functions and the boundary information of the Membership grades and premise variables are taken into account in the stability analysis and incorporated into the SOS-based stability conditions. A simulation example is given to illustrate the effectiveness of the proposed approach.
Mohammad Narimani - One of the best experts on this subject based on the ideXlab platform.
-
sos based stability analysis of polynomial fuzzy model based control systems via polynomial Membership Functions
IEEE Transactions on Fuzzy Systems, 2010Co-Authors: Mohammad Narimani, Hakkeung LamAbstract: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.
-
stability analysis and stabilization of polynomial fuzzy model based control systems using piecewise linear Membership Functions
IEEE International Conference on Fuzzy Systems, 2010Co-Authors: Mohammad Narimani, F H F LeungAbstract:This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control system, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the published work, the PFMB control system is not required that the polynomial fuzzy controller shares the same premises Membership Functions as those of the polynomial fuzzy model. Piecewise linear Membership Functions are employed to approximate the Membership Functions of the polynomial fuzzy model and polynomial fuzzy controller to facilitate stability analysis and controller synthesis with consideration of approximation error. The piecewise linear Membership Functions offer a nice property that the grades of Membership are governed by a finite number of sampled points. It is worth mentioning that the piecewise linear Membership Functions, which are not necessarily implemented physically, are a tool to carry out the stability analysis. The nice property of the piecewise linear Membership Functions allows them to be brought to the SOS-based stability conditions derived based on the Lyapunov stability theory. Consequently, the proposed SOS-based stability conditions are applied to PFMB control systems with the specified piecewise linear Membership Functions rather than any shapes. A simulation example is given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.
-
quadratic stability analysis of fuzzy model based control systems using staircase Membership Functions
IEEE Transactions on Fuzzy Systems, 2010Co-Authors: Hakkeung Lam, Mohammad NarimaniAbstract: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.
Xudong Zhao - One of the best experts on this subject based on the ideXlab platform.
-
stability and stabilization analysis of positive polynomial fuzzy systems with time delay considering piecewise Membership Functions
IEEE Transactions on Fuzzy Systems, 2017Co-Authors: Xiaomiao Li, Xudong ZhaoAbstract:This paper is concerned with the stability analysis of positive polynomial-fuzzy-model-based control systems with time delay. Each of the polynomial fuzzy model and the polynomial fuzzy controller is allowed to have its own set of premise Membership Functions, which can improve the design and realization flexibility. Conditions showing the positivity of the system are first obtained. Then, to deal with the difficulty resulting from the mismatched premise Membership Functions to the stability/stabilization analysis, approximated Membership Functions representing the original ones are constructed, and the information of Membership Functions is brought into the stability conditions. This way, the stability conditions can be relaxed, since the extra knowledge on the system is considered. Stability conditions are obtained by using the sum-of squares approach based on the Lyapunov stability theory. A simulation example is provided to verify the effectiveness of this method.
-
Polynomial Fuzzy-Model-Based Control Systems: Stability Analysis via Approximated Membership Functions Considering Sector Nonlinearity of Control Input
IEEE Transactions on Fuzzy Systems, 2015Co-Authors: Ligang Wu, Xudong ZhaoAbstract:This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control systems, in which both the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise Membership Functions. In order to address the input nonlinearity, the control signal is considered to be bounded by a sector with nonlinear bounds. These nonlinear lower and upper bounds of the sector are constructed by combining local bounds using fuzzy blending such that local information of input nonlinearity can be taken into account. With the consideration of imperfectly matched Membership Functions and input nonlinearity, the applicability of the PFMB control scheme can be further enhanced. To facilitate the stability analysis, a general form of approximated Membership Functions representing the original ones is introduced. As a result, approximated Membership Functions can be brought into the stability analysis leading to relaxed stability conditions. The sum-of-squares approach is employed to obtain the stability conditions based on Lyapunov stability theory. Simulation examples are presented to demonstrate the feasibility of the proposed method.
F H F Leung - One of the best experts on this subject based on the ideXlab platform.
-
stability analysis and stabilization of polynomial fuzzy model based control systems using piecewise linear Membership Functions
IEEE International Conference on Fuzzy Systems, 2010Co-Authors: Mohammad Narimani, F H F LeungAbstract:This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control system, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the published work, the PFMB control system is not required that the polynomial fuzzy controller shares the same premises Membership Functions as those of the polynomial fuzzy model. Piecewise linear Membership Functions are employed to approximate the Membership Functions of the polynomial fuzzy model and polynomial fuzzy controller to facilitate stability analysis and controller synthesis with consideration of approximation error. The piecewise linear Membership Functions offer a nice property that the grades of Membership are governed by a finite number of sampled points. It is worth mentioning that the piecewise linear Membership Functions, which are not necessarily implemented physically, are a tool to carry out the stability analysis. The nice property of the piecewise linear Membership Functions allows them to be brought to the SOS-based stability conditions derived based on the Lyapunov stability theory. Consequently, the proposed SOS-based stability conditions are applied to PFMB control systems with the specified piecewise linear Membership Functions rather than any shapes. A simulation example is given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.
Shunhung Tsai - One of the best experts on this subject based on the ideXlab platform.
-
stability analysis of polynomial fuzzy model based control systems with mismatched premise Membership Functions
IEEE Transactions on Fuzzy Systems, 2014Co-Authors: Hakkeung Lam, Shunhung TsaiAbstract:This paper investigates the stability of polynomial-fuzzy-model-based (PFMB) control system, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. To enhance the design flexibility, the number of rules and the shape of premise Membership Functions of the polynomial fuzzy controller are considered to be chosen freely and are different from those of the polynomial fuzzy model, however, which make the stability analysis more difficult and potentially lead to conservative stability analysis result. A sum-of-squares (SOS)-based stability analysis approach using the Lyapunov stability theory is proposed to investigate the stability of the PFMB control systems and synthesize the polynomial fuzzy controller. To facilitate the stability analysis and relax the stability analysis result, the property of the Membership Functions and the boundary information of the Membership grades and premise variables are taken into account in the stability analysis and incorporated into the SOS-based stability conditions. A simulation example is given to illustrate the effectiveness of the proposed approach.
