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Observer-based fuzzy covariance control for discrete nonlinear systems

JOURNAL OF MARINE SCIENCE AND TECHNOLOGY-TAIWAN 2007年第3期15卷 255-264页

作者： Chang, Wen-Jer Yeh, Yi-Lin Natl Taiwan Ocean Univ Dept Marine Engn Chilung 202 Taiwan

In this paper, the practical covariance control theory is applied to incorporate the concept of variance constrained control for the discrete nonlinear systems using T-S fuzzy models. This paper focuses on the control problem of finding observed-state feedback gains for the discrete fuzzy controllers, which can achieve the common state covariance assignment. Finally, a numerical example will be used to show the simulation results of the present fuzzy control method and usefulness of the proposed approach.

关键词： Takagi-Sugeno fuzzy models parallel distributed compensation observed-state feedback gains and covariance control

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Modelling and control of flexible joint robot based on Takagi-Sugeno fuzzy approach and its stability analysis via sum of squares

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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS 2013年第3期19卷 250-262页

作者： Hosseinpour, M. Nikdel, P. Badamchizadeh, M. A. Akbari, M. A. Univ Tabriz Fac Elect & Comp Engn Tabriz Iran Islamic Azad Univ Fac Elect Engn Ahar Branch Tabriz Iran

This article proposes a Takagi-Sugeno (T-S) fuzzy model of single-link rotary flexible joint robot. The proposed control method is based on parallel distributed control. The parameters of T-S controller are improved by distributed population genetic algorithm (GA) with chaos GA. Using Hermite-Biehler theorem in distributed population, GA is made to have a fast convergence. Dividing search space into several sub-spaces causes a better response, and chaos disturbance helps the whole algorithm to reach a best answer. The stability of the controller is analysed via the sum of squares programming, and finally, it is implemented on the plant.

关键词： Takagi-Sugeno flexible joint robots chaos distributed population genetic algorithm parallel distributed compensation sum of squares

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More Relaxed Non-Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

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ASIAN JOURNAL OF CONTROL 2017年第2期19卷 467-481页

作者： Vafamand, Navid Shasadeghi, Mokhtar Shiraz Univ Technol Dept Elect Engn Shiraz Iran

This paper proposes more relaxed stabilization conditions based on a non-quadratic Lyapunov function (NQLF) and parallel distributed compensator (PDC) controller. The conditions are derived in terms of linear matrix inequalities (LMIs) by introducing three slack matrices based on the properties of TS membership functions, an open loop system and a PDC controller. These slack matrices are utilized to decouple the LMI variables from the TS system and the input matrices. Therefore, the proposed approach greatly reduces the number of LMI conditions and improves feasibility by providing more degrees of freedom compared to recently published studies. Moreover, local stability and stabilization conditions are considered to handle the time derivatives of membership functions appearing in the stabilization synthesis of the TS closed-loop system with PDC controller. Finally, several examples are presented to demonstrate the advantages of the proposed approaches.

关键词： Linear matrix inequality parallel distributed compensation relaxed stability conditions Takagi-Sugeno fuzzy model local stability analysis

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Dissipative Control for Single Flexible Joint Robotic System via T–S Fuzzy Modelling Approach ⁎

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IFAC-PapersOnLine 2022年第1期55卷 637-642页

作者： Rupak Datta Rajeeb Dey Nabanita Adhikari Department of Electrical Engineering National Institute of Technology Silchar 788010 India

The dissipativity analysis for single flexible joint robotic system via Takagi–Sugeno (T–S) fuzzy modelling technique is the main focus of this paper. Our aim is to design a delayed state feedback controller by using parallel distributed compensation (PDC) so that the considered system is asymptotically stable with a (Φ 1 , Φ 2 , Φ 3 )-γ- dissipative performance index. A delay-range-dependent strictly (Φ 1 , Φ 2 , Φ 3 ) -γ- dissipativity condition is derived in terms of linear matrix inequality (LMI) framework by constructing an appropriate Lyapunov– Krasovskii functional (LKF) and using higher order polynomial based integral inequality (HOPBII) to estimate its derivative. Finally, numerical simulation result is given to show the effectiveness of the proposed theoretical method.

关键词： Dissipativity analysis Takagi Sugeno fuzzy modelling parallel distributed compensation linear matrix inequality Lyapunov Krasovskii functional

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Robust Positively Invariant Polyhedral Sets and Constrained Control using Fuzzy T-S Models: a Bilinear Optimization Design Strategy ⁎

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IFAC-PapersOnLine 2020年第2期53卷 8013-8018页

作者： Carlos E.T. Dórea Eugenio B. Castelan Jackson G. Ernesto Universidade Federal do Rio Grande do Norte UFRN-CT-DCA 59078-280 Natal RN Brazil Universidade Federal de Santa Catarina UFSC-DAS FlorianÓpolis SC Brazil

We propose a numerical method to compute stabilizing state feedback control laws and associated polyhedral invariant sets for nonlinear systems represented by Fuzzy Takagi-Sugeno (T-S) models, subject to state and control constraints, and persistent disturbances. Sufficient conditions are derived under which a given polyhedral set is positively invariant under a parallel distributed compensation (PDC), in the form of bilinear algebraic inequalities. Then, a bilinear programming (BP) problem is proposed to compute the state feedback gains and an associated positively invariant polyhedron, with predefined complexity, which solve a constrained regulation problem for the Fuzzy T-S system. A numerical example illustrates the effectiveness of the method.

关键词： Fuzzy T-S models parallel distributed compensation Constrained Control Invariant Sets Bilinear Programming

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Guaranteed Cost Control For Constrained Takagi-Sugeno Fuzzy Systems

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IFAC Proceedings Volumes 2009年第19期42卷 325-330页

作者： Carlos Ariño Emilio Pérez Antonio Sala Department of Industrial Systems Engineering and Design Universitat Jaume I Avenida Vicent Sos Baynat s/n. 12071 Castelló de la Plana Spain Dept. of Systems Engineering & Control at the Technical University of Valencia E-46022 Valencia Spain

Abstract This paper presents a novel control design technique in order to obtain a Guaranteed Cost Fuzzy Controller subject to constraints on the input channel. This Guaranteed cost control law is obtained via multi-parametric Quadratic Programming. The result is a piecewise fuzzy control law where the state partition is defined by fuzzy inequalities. The parameters of the Lyapunov function can be obtained previously using linear matrix inequalities optimization.

关键词： Takagi-Sugeno fuzzy control LMI quadratic stability parallel distributed compensation piecewise control multi-parametric Quadratic Programming Constrained Control

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Complexity relaxation of the tensor product model transformation for higher dimensional problems

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ASIAN JOURNAL OF CONTROL 2007年第2期9卷 195-200页

作者： Baranyi, Peter Petres, Zoltan Korondi, Peter Yam, Yeung Hashimoto, Hideki Hungarian Acad Sci Comp & Automat Res Inst H-1117 Budapest Hungary Budapest Univ Technol & Econ Dept Telecommun & Media Informat H-1117 Budapest Hungary Budapest Univ Technol & Econ Integrated Intelligent Syst Japanese Hungarian La H-1117 Budapest Hungary Chinese Univ Hong Kong Dept Automat & Comp Aided Engn Shatin Hong Kong Peoples R China Univ Tokyo Inst Ind Sci Tokyo 1538505 Japan

The Tensor Product (TP) model transformation method was proposed recently as an automated gateway between a class of non-linear models and linear matrix inequality based control design. The core of the TP model transformation is the higher order singular value decomposition of a large sized tensor, which requires high computational power that is usually outside of a regular computer capacity in cases of higher dimensionality. This disadvantage restricts the utilization of the TP model transformation to models having smaller dimensionality. The aim of this paper is to propose a computationally relaxed version of the TP model transformation. The paper also presents a 6 dimensional example to show the effectiveness of the modified transformation.

关键词： non-linear control design TP model transformation parallel distributed compensation linear matrix inequality

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Stable Fault Tolerant Controller Design for Takagi-Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

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ENERGIES 2019年第11期12卷

作者： Patel, Himanshukumar R. Shah, Vipul A. Dharmsinh Desai Univ Fac Technol Dept Instrumentat & Control Nadiad 387001 Gujarat India

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi-Sugeno (T-S) fuzzy models. Takagi-Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T-S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T-S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi-Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T-S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

关键词： actuator fault fuzzy control linear matrix inequalities T-S model-based fuzzy control parallel distributed compensation stability condition system component fault three conical tank Takagi-Sugeno fuzzy model

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H ∞ Control for T–S Fuzzy System via Delayed State Feedback: Application to Two-Link Robotic System ⁎

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IFAC-PapersOnLine 2022年第1期55卷 777-782页

作者： Rupak Datta Rajeeb Dey Nabanita Adhikari Jason Gu Umar Farooq Muhammad Usman Asad Department of Electrical Engineering National Institute of Technology Silchar 788010 India Department of Electrical & Computer Engineering Dalhousie University Halifax Canada

This paper introduces a fuzzy control design method for nonlinear systems with H ∞ performance index. First, the Takagi–Sugeno (T–S) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a parallel distributed compensation (PDC) based delayed fuzzy controller is developed. The advantage of the proposed control design is that only a simple fuzzy controller is used in our approach without the feedback linearization technique. By constructing a suitable Lyapunov–Krasovskii functional (LKF) and using the Wirtinger-based inequality method, the proposed fuzzy control problem is designed in terms of linear matrix inequality (LMI) problem. Finally, the simulation result is presented to show the effectiveness of the proposed condition.

关键词： Fuzzy control Takagi–Sugeno fuzzy model parallel distributed compensation Lyapunov–Krasovskii functional Linear matrix inequality

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LMI static output feedback design of fuzzy power system stabilisers

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2011年第4期12卷 328-340页

作者： Soliman, M. Bendary, F. Mansour, W. Elshafei, Abdel-Latif Benha Univ Elect Power & Machines Dept 108 Shubra StPO 11240 Cairo Egypt Cairo Univ Elect Power & Machines Dept Giza Egypt

The design of a model-free fuzzy power system stabiliser (PSS) lacks systematic stability analysis and performance guarantees. This paper provides a step towards the design of a model-based fuzzy PSS that guarantees not only stability, but also performance specifications of power systems. A new practical and simple design based on static output feedback is proposed. The design guarantees robust pole clustering in an acceptable region in the complex plane for a wide range of operating conditions. A power system design model is approximated by a set of Takagi-Sugeno (T-S) fuzzy models to account for non-linearities, uncertainties and large-scale power systems. The proposed PSS design is based on parallel distributed compensation (PDC). Sufficient design conditions are derived as linear matrix inequalities (LMIs). The design procedure leads to a tractable convex optimisation problem in terms of the stabiliser gain matrix. Simulations results of both single machine and multimachine power systems confirm the effectiveness of the proposed PSS design.

关键词： power system stability robustness linear matrix inequality LMI Takagi-Sugeno fuzzy models parallel distributed compensation PDC static output feedback

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