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New delay-dependent finite-time stabilization of Takagi-Sugeno fuzzy approaches for delayed nonlinear systems

ASIAN JOURNAL OF CONTROL 2024年第0期

作者： El Fezazi, Nabil Fahim, Mohamed Idrissi, Said Farkous, Rashid Alvarez, Teresa Tissir, El Houssaine Ibn Zohr Univ Higher Sch Technol Dakhla Morocco Sidi Mohammed Ben Abdellah Univ Fac Sci Dhar El Mehraz Dept Phys LISAC Lab Fes Morocco Ibn Tofail Univ Comp Sci Res Lab Kenitra Morocco Mohammed V Univ Higher Sch Technol Sale Rabat Morocco Univ Valladolid Ind Engn Sch Dr Mergelina S N Valladolid 47005 Spain

In this paper, the finite-time stability and stabilization of nonlinear systems with delays is studied, via a Takagi-Sugeno approach. By using a novel Lyapunov-Krasovskii functional and introducing some fuzzy free-weighting matrices, sufficient conditions are derived, for bounded and differentiable time-varying delays in terms of an upper bound of the delay derivatives. Then, we achieve closed-loop stabilization in finite time through an efficient parallel distributed compensation design. The sufficient conditions are formulated as linear matrix inequalities to achieve the desired performance. Finally, the proposed methodology is applied to various case studies, highlighting its significance.

关键词： finite-time stability nonlinear systems parallel distributed compensation T-S fuzzy approach

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Stability analysis and synthesis of fuzzy singularly perturbed systems

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2005年第2期13卷 273-284页

作者： Liu, HP Sun, FC Sun, ZQ Tsinghua Univ Dept Comp Sci & Technol State Key Lab Intelligent Technol & Syst Beijing 100084 Peoples R China

In this paper, we investigate the stability analysis and synthesis problems for both continuous-time and discrete-time fuzzy singularly perturbed systems. For continuous-time case, both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities (LMIs). For discrete-time case, only the analysis problem can be cast in LMIs, while the derived stability conditions for controller design are nonlinear matrix inequalities (NMIs). Furthermore, a two-stage algorithm based on LMI and iterative LMI (ILMI) techniques I'S developed to solve the resulting NMIs and the stabilizing feedback controller gains can be obtained. For both continuous-time and discrete-time cases, the reduced-control law, which is only dependent on the slow variables, is also discussed. Finally, an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures.

关键词： fuzzy systems linear matrix inequalities (LMIs) parallel distributed compensation singular perturbations

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Observer-based fuzzy covariance control for discrete nonlinear systems

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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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More Relaxed Non-quadratic Stabilization Conditions for TS Fuzzy Control Systems using LMI and GEVP

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2015年第4期13卷 995-1002页

作者： Vafamand, Navid Sadeghi, Mokhtar Sha Shiraz Univ Technol Elect & Elect Engn Fac Dept Control Engn Shiraz Fars Province Iran

In this paper, a new systematic approach is presented to further decrease the conservativeness in stability analysis condition and controller design. Non-quadratic Lyapunov function is utilized to derive stability conditions in terms of linear matrix inequalities. Also, the control problem is formulated in a generalized eigenvalue problem. Considering the concept of decay rate and control input constraint, a new systematic procedure is proposed to calculate a maximum bound for the upper bounds of the time derivatives of the membership functions. Moreover, some slack matrices are introduced that help to reduce conservativeness. The number of inequalities is few compared to the existing results in literature, which helps the feasibility in the case of large number of fuzzy rules. Simulation examples and comparison results demonstrate the merits of this method.

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

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A projection approach to stability analysis and design of fuzzy systems

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 2003年第6期33卷 766-771页

作者： Huang, CP Juang, YT Natl Cent Univ Dept Elect Engn Chungli 32054 Taiwan

The stability analysis and design of the systems, described in Takagi-Sugeno's (TS) fuzzy model, are discussed in this correspondence. Based on the alternating projection method, the stability issue can be extended to a prescribed stability region. And the projection algorithm is proposed for assuring the desired stability. By involving the controller, we further introduce the design issues for the closed-1oop system. Some numerical examples are given to demonstrate the validity and feasibility.

关键词： fuzzy system parallel distributed compensation pole assignment stability TS fuzzy model

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Fuzzy Tracking Control for Indirect Field-oriented Induction Machine Using Integral Action Performance

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IETE JOURNAL OF RESEARCH 2011年第5期57卷 443-451页

作者： Allouche, Moez Chaabane, Mohamed Souissi, Mansour Mehdi, Driss Univ Sfax Natl Schools Engn Sfax Lab Sci & Techn Automat & Comp Engn Sfax 3038 Tunisia LAII Lab Automat Informat Ind Super Sch Engn Poitiers F-86022 Poitiers France

This paper deals with the synthesis of fuzzy controller applied to the induction motor with a guaranteed H tracking performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy observer-based fuzzy tracking controller is designed to stabilize the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The rotor flux is unavailable for measurement and it is estimated by a fuzzy observer. An integral action is added to the new parallel distributed compensation fuzzy controller related to the tracking to avoid static errors. The gains of fuzzy control and fuzzy observer are obtained by solving a set of Linear Matrix Inequality. Finally, simulation result is given to demonstrate the controllers effectiveness.

关键词： H8734 performance Linear matrix inequality parallel distributed compensation Takagi-sugeno fuzzy model Tracking control

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Fuzzy controller and observer design for backing control of a trailer-truck

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 1997年第5期10卷 441-452页

作者： Tanaka, K Taniguchi, T Wang, HO Kanazawa Univ Dept Human & Mech Syst Engn Kanazawa Ishikawa 920 Japan Duke Univ Durham NC 27706 USA

This paper presents a fuzzy controller and observer design for backward movement control of a trailer-truck A nonlinear dynamic model of the trailer-truck is represented by a Takagi-Sugeno fuzzy model. The concept of parallel distributed compensation is employed to design a fuzzy controller and a fuzzy observer from the Takagi-Sugeno fuzzy model of the trailer-truck. Stability conditions of the fuzzy control system are derived, using the Lyapunov approach. It is shown that the stability conditions are characterized in terms of linear matrix inequalities (LMIs). Stability of the overall fuzzy control system, including a fuzzy controller and a fuzzy observer is guaranteed by using a convex optimization technique based on LMIs. Simulation and experimental results show that the fuzzy controller and the fuzzy observer effectively achieve backward movement control of the trailer-truck. (C) 1997 Published by Elsevier Science Ltd. All rights reserved.

关键词： fuzzy control fuzzy observers stability analysis linear matrix inequalities parallel distributed compensation

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Stability analysis and design of Takagi-Sugeno fuzzy systems

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INFORMATION SCIENCES 2006年第19期176卷 2817-2845页

作者： Ting, Chen-Sheng Natl Huwei Univ Sci & Technol Dept Elect Engn Huwei 632 Yunlin Taiwan

This work presents stable composite control criteria for multivariable Takagi-Sugeno (T-S) fuzzy systems. On the basis of the linear matrix inequality (LMI) control strategy and parametric optimization, the composite fuzzy control algorithms are derived. Unlike earlier studies of fuzzy-control systems on an LMI framework, this investigation develops a supervisory control approach, such that a fuzzy controller can be synthesized more efficiently. Moreover, a robust control scheme is applied to the T-S fuzzy model with parametric uncertainties. The sufficient conditions are deduced in the form of reduced LMIs and adaptive tuning rules. Finally, numeric simulations are given to validate the proposed approach. (C) 2005 Elsevier Inc. All rights reserved.

关键词： T-S fuzzy system parallel distributed compensation reduced stability conditions

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Modeling and PDC fuzzy control of planar parallel robot: A differential-algebraic equations approach

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2017年第1期14卷

作者： Allouche, Benyamine Dequidt, Antoine Vermeiren, Laurent Dambrine, Michel Univ Valenciennes & Hainaut Cambresis Valenciennes France

Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential-algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential-algebraic equations is given. The goal is to use the structural characteristics of the mechanical system to reduce the complexity of the nonlinear model. Therefore, a trajectory tracking control is achieved using the Takagi-Sugeno fuzzy model derived from the differential-algebraic equation forms and its linear matrix inequality constraints formulation. Simulation results show that the proposed approach based on differential-algebraic equations and Takagi-Sugeno fuzzy modeling leads to a better robustness against the structural uncertainties.

关键词： parallel manipulator Takagi-Sugeno model parallel distributed compensation differential-algebraic equations LMI

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Fuzzy distributed cooperative tracking for a swarm of unmanned aerial vehicles with heterogeneous goals

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2016年第16期47卷 3803-3811页

作者： Kladis, Georgios P. Menon, Prathyush P. Edwards, Christopher Univ Cyprus Dept Elect & Comp Engn KIOS Res Ctr Intelligent Syst & Networks CY-1678 Nicosia Cyprus Univ Exeter Ctr Syst Dynam & Control Exeter Devon England

This article proposes a systematic analysis for a tracking problem which ensures cooperation amongst a swarm of unmanned aerial vehicles (UAVs), modelled as nonlinear systems with linear and angular velocity constraints, in order to achieve different goals. A distributed Takagi-Sugeno (TS) framework design is adopted for the representation of the nonlinear model of the dynamics of the UAVs. The distributed control law which is introduced is composed of both node and network level information. Firstly, feedback gains are synthesised using a parallel distributed compensation (PDC) control law structure, for a collection of isolated UAVs;ignoring communications among the swarm. Then secondly, based on an alternation-like procedure, the resulting feedback gains are used to determine Lyapunov matrices which are utilised at network level to incorporate into the control law, the relative differences in the states of the vehicles, and to induce cooperative behaviour. Eventually stability is guaranteed for the entire swarm. The control synthesis is performed using tools from linear control theory: in particular the design criteria are posed as linear matrix inequalities (LMIs). An example based on a UAV tracking scenario is included to outline the efficacy of the approach.

关键词： Graph theory multi-agent systems consensus parallel distributed compensation Takagi-Sugeno fuzzy model linear matrix inequalities

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