The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Kazuo Tanaka - One of the best experts on this subject based on the ideXlab platform.
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stabilization and robust stabilization of polynomial fuzzy systems a piecewise polynomial Lyapunov Function approach
International Journal of Fuzzy Systems, 2018Co-Authors: Alissa Ully Ashar, Motoyasu Tanaka, Kazuo TanakaAbstract:This paper presents a piecewise polynomial Lyapunov Function (PPLF) approach to stabilization and robust stabilization of polynomial fuzzy systems that are a generalized form of the well-known Takagi–Sugeno fuzzy systems. Both stabilization and robust stabilization conditions are formulated as sum of squares (SOS) optimization problems which can be solved by an SOS solver. A switching polynomial fuzzy controller based on switching information on the PPLF is designed to stabilize both polynomial fuzzy systems and polynomial fuzzy systems with uncertainties. In particular, by fully considering the properties of the piecewise and polynomial Lyapunov Function, some relaxation are carried out in the derivation of SOS robust stabilization conditions for polynomial fuzzy systems with uncertainties. Four design examples are demonstrated to show the effectiveness of the proposed design approach in comparison with the existing approaches, i.e., linear matrix inequalities approaches and SOS stabilization and robust stabilization approaches.
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relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise Lyapunov Function based switching fuzzy controller
IEEE Transactions on Fuzzy Systems, 2012Co-Authors: Yingjen Chen, Kazuo Tanaka, Hiroshi Ohtake, Wenjune Wang, Hua O WangAbstract:This paper proposes the minimum-type piecewise-Lyapunov-Function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov Function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov Function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie et al. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov Functions as the Lyapunov Function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov Function as the Lyapunov Function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.
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relaxed stabilisation criterion for discrete t s fuzzy systems by minimum type piecewise non quadratic Lyapunov Function
Iet Control Theory and Applications, 2012Co-Authors: Y J Chen, Kazuo Tanaka, Hiroshi Ohtake, Wenjune Wang, Hua O WangAbstract:Piecewise Lyapunov Functions and non-quadratic Lyapunov Functions have been employed to analyse Takagi–Sugeno (T–S) fuzzy systems for getting relaxed results in the literature. Nevertheless, until now piecewise non-quadratic Lyapunov Functions have not been used to design T–S fuzzy control systems. Motivated by the aforementioned concerns, this study utilises the minimum-type piecewise non-quadratic Lyapunov Function to design the discrete T–S fuzzy control system. Based on the piecewise non-quadratic Lyapunov Function, the switching non-parallel distributed compensation control law is proposed to obtain the relaxed stabilisation criterion. Owing to that some conditions of the proposed criterion are bilinear matrix inequalitiy conditions, the particle swarm optimisation algorithm is applied for finding out the solution of the criterion. An example is provided to illustrate the effectiveness of the proposed criterion.
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switching fuzzy controller design based on switching Lyapunov Function for a class of nonlinear systems
Systems Man and Cybernetics, 2006Co-Authors: Hiroshi Ohtake, Kazuo Tanaka, Hong WangAbstract:This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov Function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov Function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov Function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.
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a multiple Lyapunov Function approach to stabilization of fuzzy control systems
IEEE Transactions on Fuzzy Systems, 2003Co-Authors: Kazuo Tanaka, T Hori, Hua O WangAbstract:This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov Function which is a multiple Lyapunov Function. The fuzzy Lyapunov Function is defined by fuzzily blending quadratic Lyapunov Functions. Based on the fuzzy Lyapunov Function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov Function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership Functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov Function approach and the new PDC stabilization method.
Hua O Wang - One of the best experts on this subject based on the ideXlab platform.
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relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise Lyapunov Function based switching fuzzy controller
IEEE Transactions on Fuzzy Systems, 2012Co-Authors: Yingjen Chen, Kazuo Tanaka, Hiroshi Ohtake, Wenjune Wang, Hua O WangAbstract:This paper proposes the minimum-type piecewise-Lyapunov-Function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov Function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov Function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie et al. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov Functions as the Lyapunov Function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov Function as the Lyapunov Function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.
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relaxed stabilisation criterion for discrete t s fuzzy systems by minimum type piecewise non quadratic Lyapunov Function
Iet Control Theory and Applications, 2012Co-Authors: Y J Chen, Kazuo Tanaka, Hiroshi Ohtake, Wenjune Wang, Hua O WangAbstract:Piecewise Lyapunov Functions and non-quadratic Lyapunov Functions have been employed to analyse Takagi–Sugeno (T–S) fuzzy systems for getting relaxed results in the literature. Nevertheless, until now piecewise non-quadratic Lyapunov Functions have not been used to design T–S fuzzy control systems. Motivated by the aforementioned concerns, this study utilises the minimum-type piecewise non-quadratic Lyapunov Function to design the discrete T–S fuzzy control system. Based on the piecewise non-quadratic Lyapunov Function, the switching non-parallel distributed compensation control law is proposed to obtain the relaxed stabilisation criterion. Owing to that some conditions of the proposed criterion are bilinear matrix inequalitiy conditions, the particle swarm optimisation algorithm is applied for finding out the solution of the criterion. An example is provided to illustrate the effectiveness of the proposed criterion.
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a multiple Lyapunov Function approach to stabilization of fuzzy control systems
IEEE Transactions on Fuzzy Systems, 2003Co-Authors: Kazuo Tanaka, T Hori, Hua O WangAbstract:This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov Function which is a multiple Lyapunov Function. The fuzzy Lyapunov Function is defined by fuzzily blending quadratic Lyapunov Functions. Based on the fuzzy Lyapunov Function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov Function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership Functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov Function approach and the new PDC stabilization method.
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 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 of t s fuzzy control systems using parameter dependent Lyapunov Function
Iet Control Theory and Applications, 2009Co-Authors: Hakkeung LamAbstract:The system stability of T–S fuzzy-model-based control systems with a parameter-dependent Lyapunov Function (PDLF) is investigated. As PDLF approach includes information of the membership Function (time derivatives of membership Functions), it has been reported that relaxed stability conditions can be achieved compared to the parameter-independent Lyapunov Function (PILF). To investigate the system stability, the non-linear plant is represented by a T–S fuzzy model. Various non-parallel distribution compensation (PDC) fuzzy controllers, which can better utilise the characteristic of the PDLF, are proposed to close the feedback loop. To relax the stability conditions, an improved PDLF is employed. Some inequalities are proposed to relate the membership Functions and its time derivatives, which allow the introduction of some slack matrices to facilitate the stability analysis. Stability conditions in terms of linear matrix inequalities are derived to aid the design of stable fuzzy-model-based control systems. Simulation examples are given to illustrate the effectiveness of the proposed non-PDC fuzzy control schemes.
Hirokazu Nishitani - One of the best experts on this subject based on the ideXlab platform.
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multilayer minimum projection method for nonsmooth strict control Lyapunov Function design
Systems & Control Letters, 2010Co-Authors: Hisakazu Nakamura, Yoshiro Fukui, Nami Nakamura, Hirokazu NishitaniAbstract:Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. To address this problem, we had proposed the minimum projection method to design nonsmooth control Lyapunov Functions. This method, however, has some problems: difficult etale-surjection design, undesirable resulting control Lyapunov Functions, etc. In this paper, we propose a new nonsmooth control Lyapunov Function design method called the ‘Multilayer minimum projection method’ for nonsmooth control Lyapunov Function design on general manifolds. The method considers many simple-structured smooth manifolds associated with the original manifold by etale mappings, and then a Function on the original manifold is obtained by projecting control Lyapunov Functions defined on the simple-structured manifolds onto the original manifold. In this paper, we prove that the resulting Function by the proposed method is a nonsmooth control Lyapunov Function on the original manifold. Moreover, we prove that if all control Lyapunov Functions defined on simple-structured manifolds are strict, the control Lyapunov Function on the original manifold is a strict control Lyapunov Function. Finally, the effectiveness of the proposed method and the advantage over the conventional minimum projection method are confirmed by an example.
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minimum projection method for nonsmooth control Lyapunov Function design on general manifolds
Systems & Control Letters, 2009Co-Authors: Hisakazu Nakamura, Yuh Yamashita, Hirokazu NishitaniAbstract:Abstract Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. On the other hand, an important fact is every control system that is globally asymptotically stabilizable at a desired equilibrium must have nonsmooth control Lyapunov Functions. This paper considers the problem of construction of nonsmooth control Lyapunov Functions on general manifolds, and we propose a nonsmooth control Lyapunov Function design method called the ‘Minimum Projection Method’. The proposed method considers a simple-structured smooth manifold associated with the original manifold by a surjective immersion, and then a control Lyapunov Function defined on the simple-structured manifold is projected to the original manifold. A Function on the original manifold is thus obtained. In this paper, we prove that the control system on another manifold associated with a surjective immersion is determined uniquely, and the resulting Function by the proposed method is a nonsmooth control Lyapunov Function on the original manifold. The effectiveness of the proposed method is confirmed by examples.
Hisakazu Nakamura - One of the best experts on this subject based on the ideXlab platform.
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global nonsmooth control Lyapunov Function design for path following problem via minimum projection method
IFAC-PapersOnLine, 2016Co-Authors: Hisakazu NakamuraAbstract:Abstract: Path-following and trajectory-tracking problems are important control problems. For the path-following problem the paper proposes a locally semiconcave path-following control Lyapunov Function (PF-CLF). Moreover, the paper proposes the minimum projection method for PF-CLF design by using tracking control Lyapunov Function. Furthermore, a static feedback controller for a path-following problem is proposed. Finally, we confirm the effectiveness of the proposed method by computer simulation.
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asymptotic stabilization of two wheeled mobile robot via locally semiconcave generalized homogeneous control Lyapunov Function
SICE journal of control measurement and system integration, 2015Co-Authors: Shunsuke Kimura, Hisakazu Nakamura, Yuh YamashitaAbstract:A locally semiconcave control Lyapunov Function exists for every globally asymptotically controllable system; however for nonholonomic systems, the issue of a locally semiconcave generalized homoge...
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control of two wheeled mobile robot via homogeneous semiconcave control Lyapunov Function
IFAC Proceedings Volumes, 2013Co-Authors: Shunsuke Kimura, Hisakazu Nakamura, Yuh YamashitaAbstract:Abstract Semiconcave control Lyapunov Functions for globally asymptotic stabilizing control-lable systems are available. However, a semiconcave control Lyapunov Function for nonholonomic systems has not been proposed yet. For a two-wheeled mobile robot, we construct a homogeneous semiconcave control Lyapunov Function and a control law with the Function. The advantages of the proposed method are confirmed by computer simulation.
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multilayer minimum projection method for nonsmooth strict control Lyapunov Function design
Systems & Control Letters, 2010Co-Authors: Hisakazu Nakamura, Yoshiro Fukui, Nami Nakamura, Hirokazu NishitaniAbstract:Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. To address this problem, we had proposed the minimum projection method to design nonsmooth control Lyapunov Functions. This method, however, has some problems: difficult etale-surjection design, undesirable resulting control Lyapunov Functions, etc. In this paper, we propose a new nonsmooth control Lyapunov Function design method called the ‘Multilayer minimum projection method’ for nonsmooth control Lyapunov Function design on general manifolds. The method considers many simple-structured smooth manifolds associated with the original manifold by etale mappings, and then a Function on the original manifold is obtained by projecting control Lyapunov Functions defined on the simple-structured manifolds onto the original manifold. In this paper, we prove that the resulting Function by the proposed method is a nonsmooth control Lyapunov Function on the original manifold. Moreover, we prove that if all control Lyapunov Functions defined on simple-structured manifolds are strict, the control Lyapunov Function on the original manifold is a strict control Lyapunov Function. Finally, the effectiveness of the proposed method and the advantage over the conventional minimum projection method are confirmed by an example.
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minimum projection method for nonsmooth control Lyapunov Function design on general manifolds
Systems & Control Letters, 2009Co-Authors: Hisakazu Nakamura, Yuh Yamashita, Hirokazu NishitaniAbstract:Abstract Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. On the other hand, an important fact is every control system that is globally asymptotically stabilizable at a desired equilibrium must have nonsmooth control Lyapunov Functions. This paper considers the problem of construction of nonsmooth control Lyapunov Functions on general manifolds, and we propose a nonsmooth control Lyapunov Function design method called the ‘Minimum Projection Method’. The proposed method considers a simple-structured smooth manifold associated with the original manifold by a surjective immersion, and then a control Lyapunov Function defined on the simple-structured manifold is projected to the original manifold. A Function on the original manifold is thus obtained. In this paper, we prove that the control system on another manifold associated with a surjective immersion is determined uniquely, and the resulting Function by the proposed method is a nonsmooth control Lyapunov Function on the original manifold. The effectiveness of the proposed method is confirmed by examples.
