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Hakkeung Lam - One of the best experts on this subject based on the ideXlab platform.
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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.
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Output-Feedback Tracking Control for Polynomial Fuzzy-Model-Based Control Systems
IEEE Transactions on Industrial Electronics, 2013Co-Authors: Hakkeung LamAbstract:This paper presents the output-feedback tracking control of the polynomial Fuzzy-Model-based control system which consists of a polynomial Fuzzy Model representing the nonlinear plant and an output-feedback polynomial Fuzzy controller connected in a closed loop. The output-feedback polynomial Fuzzy controller is employed to drive the system states of the nonlinear plant to follow those of a stable reference Model subject to an H∞ performance. Based on the Lyapunov stability theory, sum-of-squares-based stability conditions are obtained to determine the system stability and facilitate the control synthesis. A feasible solution can be found numerically using the third-party Matlab toolbox SOSTOOLS. Simulation results are provided to demonstrate the merits of the proposed control approach.
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stability analysis of polynomial Fuzzy Model based control systems using switching polynomial lyapunov function
IEEE Transactions on Fuzzy Systems, 2013Co-Authors: Hakkeung Lam, Mohammad Narimani, Honghai LiuAbstract:This paper investigates the stability problem of polynomial-Fuzzy-Model-based control system, which is formed by a polynomial Fuzzy Model and a polynomial Fuzzy controller connected in a closed loop. A switching polynomial Lyapunov function consisting of a number of local polynomial Lyapunov functions is proposed to investigate the system stability. It demonstrates a nice property in favor of the stability analysis that each local polynomial Lyapunov function transits continuously to each other. As different local polynomial Lyapunov functions are employed to investigate the system stability according to the operating domain, relaxed stability conditions compared with the stability analysis result with a common Lyapunov function can be developed. In order to allow a greater design flexibility for the polynomial Fuzzy controller, the proposed polynomial-Fuzzy-Model-based control scheme does not require that both the polynomial Fuzzy Model and polynomial Fuzzy controller share the same premise membership functions. Stability conditions in terms of sum of squares are obtained to guarantee system stability and facilitate control synthesis. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed polynomial Fuzzy control scheme.
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membership function dependent stability analysis of Fuzzy Model based control systems using Fuzzy lyapunov functions
Information Sciences, 2013Co-Authors: Hakkeung Lam, Jimmy LauberAbstract:This paper investigates the stability of Fuzzy-Model-based (FMB) control system, formed by a T-S Fuzzy Model and a Fuzzy controller connected in a close loop, based on a Fuzzy-Lyapunov function. A general FMB control system that the T-S Fuzzy Model and Fuzzy controller not sharing the same premise membership functions and/or the same number of Fuzzy rules is considered. A membership-function-dependent stability analysis approach is proposed to consider the membership functions of both the T-S Fuzzy Model and Fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities. As the stability conditions are membership-function dependent, they are dedicated to the FMB control system with the specified membership functions under consideration. It is thus the membership-function-dependent stability conditions are more relaxed compared to the existing membership-function-independent stability conditions. A Fuzzy-Lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work. In this paper, this criterion is not required and thus the stability conditions can be further relaxed. Some simulation examples are given to demonstrate the merits of the proposed approach.
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output regulation of polynomial Fuzzy Model based control systems
IEEE Transactions on Fuzzy Systems, 2013Co-Authors: Hakkeung LamAbstract:This paper investigates the output regulation problem of polynomial-Fuzzy-Model-based (PFMB) control systems with the consideration of system stability and control synthesis using the sum-of-squares (SOS)-based approach. A PFMB control system is formed by a polynomial Fuzzy Model and a polynomial Fuzzy controller with integral action connected in a closed loop. Three cases of PFMB control systems regarding the premise membership functions and number of Fuzzy rules, which have their own properties and advantages, are considered. The stability of the PFMB control systems is investigated based on the Lyapunov stability theory. With consideration of the information of membership functions, SOS-based stability conditions corresponding to each case are obtained to guarantee system stability and to realize output regulation. Simulation examples are given to compare the three cases and illustrate the effectiveness of the proposed approach.
Lakmal Seneviratne - One of the best experts on this subject based on the ideXlab platform.
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stability analysis of polynomial Fuzzy Model based control systems under perfect imperfect premise matching
Iet Control Theory and Applications, 2011Co-Authors: Hakkeung Lam, Lakmal SeneviratneAbstract:This study presents an improved sum-of-squares (SOS)-based stability analysis result for the polynomial Fuzzy-Model-based control system, formed by a polynomial Fuzzy Model and a polynomial Fuzzy controller connected in a closed loop. Two cases, namely perfect and imperfect premise matching, are considered. Under the perfect premise matching, the polynomial Fuzzy Model and polynomial Fuzzy controller share the same premise membership functions. While different sets of membership functions are employed, it falls into the case of imperfect premise matching. Based on the Lyapunov stability theory, improved SOS-based stability conditions are derived to determine the system stability and facilitate the controller synthesis. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.
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stability analysis of interval type 2 Fuzzy Model based control systems
Systems Man and Cybernetics, 2008Co-Authors: Lakmal SeneviratneAbstract: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.
Mohammad Narimani - One of the best experts on this subject based on the ideXlab platform.
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stability analysis of polynomial Fuzzy Model based control systems using switching polynomial lyapunov function
IEEE Transactions on Fuzzy Systems, 2013Co-Authors: Hakkeung Lam, Mohammad Narimani, Honghai LiuAbstract:This paper investigates the stability problem of polynomial-Fuzzy-Model-based control system, which is formed by a polynomial Fuzzy Model and a polynomial Fuzzy controller connected in a closed loop. A switching polynomial Lyapunov function consisting of a number of local polynomial Lyapunov functions is proposed to investigate the system stability. It demonstrates a nice property in favor of the stability analysis that each local polynomial Lyapunov function transits continuously to each other. As different local polynomial Lyapunov functions are employed to investigate the system stability according to the operating domain, relaxed stability conditions compared with the stability analysis result with a common Lyapunov function can be developed. In order to allow a greater design flexibility for the polynomial Fuzzy controller, the proposed polynomial-Fuzzy-Model-based control scheme does not require that both the polynomial Fuzzy Model and polynomial Fuzzy controller share the same premise membership functions. Stability conditions in terms of sum of squares are obtained to guarantee system stability and facilitate control synthesis. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed polynomial Fuzzy control scheme.
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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.
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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.
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stability analysis and performance design for Fuzzy Model based control system under imperfect premise matching
IEEE Transactions on Fuzzy Systems, 2009Co-Authors: Mohammad NarimaniAbstract:This paper investigates the stability analysis and performance design of nonlinear systems. To facilitate the stability analysis, the Takagi-Sugeno (T-S) Fuzzy Model is employed to represent the nonlinear plant. Under the imperfect premise matching in which T-S Fuzzy Model and Fuzzy controller do not share the same membership functions, a Fuzzy controller with enhanced design flexibility and robustness property is proposed to control the nonlinear plant. However, the nice characteristic given by the perfect premise matching, leading to conservative stability conditions, vanishes. In this paper, under the imperfect premise matching, information of membership functions of the Fuzzy Model and controller are considered in stability analysis. With the introduction of slack matrices, relaxed linear matrix inequality (LMI)-based stability conditions are derived using Lyapunov-based approach. Furthermore, LMI-based performance conditions are provided to guarantee system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.
Gašper Mušič - One of the best experts on this subject based on the ideXlab platform.
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hybrid Fuzzy Model based predictive control of temperature in a batch reactor
Computers & Chemical Engineering, 2007Co-Authors: Gorazd Karer, Igor Škrjanc, Gašper Mušič, Borut ZupancicAbstract:Processes in industry, such as batch reactors, often demonstrate a hybrid and non-linear nature. Model predictive control (MPC) is one of the approaches that can be successfully employed in such cases. However, due to the complexity of these processes, obtaining a suitable Model is often a difficult task. In this paper a hybrid Fuzzy Modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno Fuzzy formulation for the hybrid Fuzzy Modelling purposes is presented. An efficient method for identifying the hybrid Fuzzy Model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the proposed hybrid Fuzzy Model are verified on a batch-reactor simulation example: a comparison between MPC employing a hybrid linear Model and a hybrid Fuzzy Model was made. We established that the latter approach clearly outperforms the approach where a linear Model is used. © 2007 Elsevier Ltd. All rights reserved.
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Generalized predictive control of a thermal plant using Fuzzy Model
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000Co-Authors: Drago Matko, K. Kavsek-biasizzo, Igor Škrjanc, Gašper MušičAbstract:A new approach to predictive control of highly nonlinear processes based on Takagi-Sugeno Fuzzy Model is proposed. It is investigated how the Takagi-Sugeno Fuzzy Models can be linked to a special type of Model based predictive control algorithm, the generalized predictive control (GPC). In original GPC design purely linear transfer function Model is used for long-range prediction. The advantage of GPC and other linear Model based predictive control methods is the guaranteed convergence within each time sample, but they are not able to deal with strong process nonlinearities. In our approach, approximate linear Models are extracted at each time sample by instantaneous linearization of nonlinear Fuzzy Model and adaptive GPC is used. Applicability of this approach to control a real world process (nonlinear laboratory-scale thermal plant) with operating point dependent gain and time constants is demonstrated.
Nicolai Christov - One of the best experts on this subject based on the ideXlab platform.
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Sensor fault estimation of PEM fuel cells using Takagi Sugeno Fuzzy Model.
International Journal of Hydrogen Energy, 2020Co-Authors: A. Aitouche, Haoping Wang, Nicolai ChristovAbstract:This paper presents a sensor fault estimation scheme for polymer electrolyte membrane (PEM) fuel cells using Takagi Sugeno (TS) Fuzzy Model. First, PEM fuel cell systems with sensor faults are Modelled by TS Fuzzy Model. Next, by adding a first order filter, an augmented TS Fuzzy system with actuator fault is obtained. Then, for the augmented system, an unknown input observer (UIO) and a fault estimator are developed. The UIO gains are computed by solving linear matrix equalities (LMEs) and linear matrix inequalities (LMIs). The UIO convergence and stability are analyzed and the performances of the proposed fault estimation scheme is demonstrated by numerical simulations for a PEM fuel cell system with return manifold pressure and hydrogen mass sensors.
