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A new method for control of nonlinear networked systems

APPLIED SOFT COMPUTING 2016年 45卷 197-206页

作者： Rahmani, Behrooz Markazi, Amir H. D. Univ Yasuj Dept Mech Engn Yasuj Kohgiluyeh Va B Iran Iran Univ Sci & Technol Sch Mech Engn Tehran Iran

Networked control of a class of nonlinear systems is considered. For this purpose, the previously proposed variable selective control (VSC) methodology is extended to the nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set fuzzy-blended locally linearized subsystems, and further application of the VSC methodology to each subsystem. Using the idea of parallel distributed compensation (PDC) method, the closed-loop stability of the overall networked system is guaranteed, using new linear matrix inequalities (LMIs). For the real-time implementation, real-time control signals are constructed for every entry of pre-specified vector of time delays, which is selected based on the presumed upper-bound of the network time delay. Similar to the traditional packet-base control methodology, such control signals are then packed as a control-side packet and transmitted back to a time delay compensator (TDC) located on the plant-side of the network. According to the most recent network time delay, the TDC selects just one entry of the control vector and applies it to the actuator through a zero order hold element. A sufficient condition for closed-loop asymptotic stability is determined. Simulation studies on nonlinear benchmark problems demonstrate the effectiveness of the proposed method. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Nonlinear networked control system Nonlinear variable selective control Linear matrix inequality Takagi-Sugeno fuzzy modeling parallel distributed compensation

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l_∞-based stability criteria and its applications on FLC systems

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FUZZY SETS AND SYSTEMS 2003年第1期139卷 35-57页

作者： Liao, DZ Yeung, LF ASM Assembly Automat Ltd R&D Hong Kong Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China

In this paper, a new stability analysis and design method for the fuzzy logical systems described by the Takagi-Sugeno model is proposed. The proposed fuzzy controller is implemented by a parallel distributed compensation structure. The closed-loop system can be expressed as a linear time-variant system. A minimum transition matrix set can be determined by the fuzzy rule structure, so that it contains the transition matrices of the closed-loop system. Thus the stability of the system defined over the set is sufficient to ensure the stability of the closed-loop system. A common l(infinity) Lyapunov function method is employed for the stability analysis of the system defined over the transition matrix set. It is proved that the existence of the l(infinity) Lyapunov function is the sufficient and necessary stability condition of the system defined over the transition matrix set. Thus the l(infinity) Lyapunov function can be applied to more cases than quadratic Lyapunov functions. A convenient stability criterion based on l(infinity) Lyapunov function is also given in this paper. By using geometric properties of l(infinity) Lyapunov functions, an iterative algorithm is introduced to construct the required 1, Lyapunov function. (C) 2002 Elsevier B.V. All rights reserved.

关键词： fuzzy system stability analysis Lyapunov function variable structure control theory parallel distributed compensation

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Fuzzy dynamic output-feedback control of non-linear networked discrete-time system with missing measurements

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IET CONTROL THEORY AND APPLICATIONS 2015年第3期9卷 327-335页

作者： Li, Hongyi Wu, Chengwei Feng, Zhiguang Bohai Univ Coll Engn Jinzhou 121013 Liaoning Peoples R China Bohai Univ Coll Informat Sci & Technol Jinzhou 121013 Liaoning Peoples R China

This article studies the problem of H dynamic output-feedback control of non-linear networked discrete-time systems with data packet dropouts. Specifically, the data missing happens randomly from the sensor to the controller and the controller to the actuator. A sequence of independent variables obeying the Bernoulli random binary distribution is introduced to account for the measurement missing. The Takagi-Sugeno fuzzy model is used to describe the non-linear plant. In addition, the strategy of parallel distributed compensation is adopted to design the fuzzy dynamic output-feedback controller. Here, attention is focused on obtaining the sufficient conditions to guarantee the closed-loop system to be stochastically stable as well as the prescribed H performance. An approach based on fuzzy Lyapunov function is developed to solve it. To tackle the non-convex problem, the cone-complementarity linearisation procedure is adopted. Finally, a numerical example is employed to show the usefulness of the proposed result.

关键词： fuzzy control feedback control system synthesis nonlinear control systems networked control systems distributed parameter systems discrete time systems H control compensation closed loop systems asymptotic stability Lyapunov methods concave programming linearisation techniques fuzzy dynamic output-feedback controller design nonlinear networked discrete-time system data missing measurements H dynamic output-feedback control problem data packet dropouts independent variables Bernoulli random binary distributed Takagi-Sugeno fuzzy model nonlinear plant parallel distributed compensation closed-loop system asymptotic stability fuzzy Lyapunov function nonconvex problem cone-complementarity linearisation procedure

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TP transformation based dynamic system modeling for nonlinear control

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2005年第6期54卷 2191-2203页

作者： Baranyi, P Várkonyi-Kóczy, AR Hungarian Acad Sci Comp & Automat Res Inst H-1111 Budapest Hungary Integrated Intelligent Syst Japanese Hunagarian Lab H-1111 Budapest Hungary

The aim of this paper is to propose a numerical controller design methodology. This methodology is based on two steps. In the first step, the tensor product (TP) model transformation is applied, which is capable of transforming a given nonlinear state-space dynamic model into TP model form. Then, in the second step, the linear matrix inequality (LMI) theorems are used within the parallel distributed compensation (PDC) controller design frameworks. The main novelty of this paper is the TP model transformation of the first step. It is also capable of dealing with the tradeoff between complexity and accuracy of the resulting TP model. The TP model transformation is a numerical method that leads to the following advantages: it is capable of functioning with models given either by analytic explicit forms or by various soft-computing based identification techniques;it does not need problem dependent analytic derivations, but can be executed "automatically" by computers. Numerical simulations are used to provide empirical validation of the proposed control design methodology. In order to demonstrate the effectiveness of the TP model transformation a controller is derived for the prototypical aeroelastic wing section that exhibits limit cycle oscillation and chaotic behavior.

关键词： linear matrix inequality nonlinear control design parallel distributed compensation tensor product (TP) model

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Robust stabilizing controller design for Takagi-Sugeno fuzzy descriptor systems under state constraints and actuator saturation

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FUZZY SETS AND SYSTEMS 2017年 329卷 77-90页

作者： Quoc Viet Dang Vermeiren, Laurent Dequidt, Antoine Dambrine, Michel Univ Valenciennes & Hainaut Cambresis LAMIH UMR CNRS 8201 F-59313 Valenciennes France

The aim of this paper is to present a new framework for designing robust controllers for uncertain nonlinear systems described by Takagi-Sugeno fuzzy descriptor systems and subject to input and state constraints. For this, a novel structure of modified parallel distributed compensation control laws is proposed. The controller parameters can be obtained through the numerical resolution of an optimization problem with linear matrix inequality constraints derived from Lyapunov's stability theory and the choice of an original Lyapunov function. This ensures the stabilization of the closed-loop system and the respect of the state and input constraints regionally. The technique is illustrated through three numerical examples. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Takagi-Sugeno fuzzy descriptor systems Actuator saturation parallel distributed compensation Stability Linear matrix inequality

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Robust multi-objective H₂/H_∞ tracking control based on the Takagi-Sugeno fuzzy model for a class of nonlinear uncertain drive systems

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2012年第I8期226卷 1107-1118页

作者： Azimi, Vahid Nekoui, Mohammad A. Fakharian, Ahmad Islamic Azad Univ Fac Elect & Comp Engn Qazvin Branch Qazvin *** Iran Islamic Azad Univ Dept Elect Engn S Tehran Branch Qazvin *** Iran KN Toosi Univ Technol Fac Control Engn Tehran Iran

In this paper a robust H-2/H-infinity multi-objective state-feedback controller and tracking design are presented for a class of multiple input/multiple output nonlinear uncertain systems. First, some states (error of tracking) are augmented to the system in order to improve tracking control. Next, uncertain parameters and the quantification of uncertainty on physical parameters are defined by the affine parameter-dependent systems method. Then, to apply the H-2/H-infinity controller, the uncertain nonlinear system is approximated by the Takagi-Sugeno fuzzy model. After that, based on each local linear subsystem with augmented state, an H-2/H-infinity multi-objective state-feedback controller is designed by using a linear matrix inequalities approach. Finally, parallel distributed compensation is used to design the controller for the overall system and the total linear system is obtained by use of the weighted sum of the local linear subsystems. Several results show that the proposed method can effectively meet performance requirements such as robustness, good load disturbance rejection, good tracking and fast transient responses for a three-phase interior permanent magnet synchronous motor system.

关键词： Robust control Takagi-Sugeno fuzzy model linear matrix inequalities multi-objective H-2/H-infinity controller parallel distributed compensation three-phase interior permanent magnet synchronous motor

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Optimal fuzzy tracking control with obstacles avoidance for a mobile robot based on Takagi-Sugeno fuzzy model

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2019年第10期41卷 2772-2781页

作者： Akka, Khaled Khaber, Farid Setif Univ Fac Technol Dept Elect Engn QUERE Lab Setif 19000 Algeria

This paper presents a trajectory tracking control approach for a mobile robot in the presence of static obstacles on the reference trajectory. The tracking control is developed based on the fuzzy parallel distributed compensation scheme where the linear quadratic regulator is used as a state feedback controller for each subsystem. The obstacle avoidance task is accomplished by applying a linear quadratic regulator on the overall open loop Takagi-Sugeno (T-S) fuzzy system, in which the weighting matrices are adjusted dynamically using a fuzzy controller. A fuzzy fusion controller is designed to combine the tracking and the obstacle avoidance velocities in order to perform both tasks simultaneously. Simulation results illustrate the effectiveness of the proposed control strategy.

关键词： Tracking control linear quadratic regulator obstacle avoidance mobile robot fuzzy control T-S fuzzy model parallel distributed compensation

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Improvement on the problem of optimal fuzzy H_∞-tracking control design for non-linear systems

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IET CONTROL THEORY AND APPLICATIONS 2011年第18期5卷 2179-2190页

作者： Esfahani, S. H. Sichani, A. K. Shahrekord Univ Sch Elect Engn Shahr E Kord Iran

This study is concerned with the problem of output feedback fuzzy H-infinity-tracking control design for non-linear systems. The non-linear system is represented by using the Takagi and Sugeno fuzzy modelling scheme. The final controller takes the form of parallel distributed compensation. The final controller results in the stability of the closed-loop system and the H-infinity tracking of a bounded reference signal. Existing approaches to this problem available in the literature implement an observer-based output feedback controller. These approaches lead to a non-linear matrix inequality condition, which can be partially solved by applying a double-step algorithm. The approach presented in this study is based on a new structure for the controller. In this approach, the problem formulation and the method of finding the controller parameters involve a single-step linear matrix inequality form. Moreover, it is possible to easily find the optimal controller from the whole solution set. The approach is also extended to the case of non-linear time-delay systems. Finally, two examples are given to illustrate the effectiveness of the obtained results in comparison with the existing methods.

关键词： H∞ control nonlinear time-delay systems observer-based output feedback controller nonlinear matrix inequality condition output feedback optimal fuzzy H∞-tracking control design stability control system synthesis Stability in control theory Control system analysis and synthesis methods Nonlinear control systems Fuzzy control Takagi-Sugeno fuzzy modelling scheme closed loop systems double-step algorithm feedback closed-loop system stability Algebra delays nonlinear control systems fuzzy control Optimal control linear matrix inequalities reference signal parallel distributed compensation observers distributed parameter control systems single-step linear matrix inequality form

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Relaxed design conditions using Takagi-Sugeno fuzzy models and Lyapunov-Floquet transformation for controlling time-varying periodic systems

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JOURNAL OF VIBRATION AND CONTROL 2023年第19-20期29卷 4439-4454页

作者： Travassos, Marco A. Cardim, Rodrigo Teixeira, Marcelo Cm Assuncao, Edvaldo Sao Paulo State Univ Dept Elect Engn Ilha Solteira Brazil

This manuscript approaches the Takagi-Sugeno fuzzy control technique, the Lyapunov-Floquet transformation, and their applications for controlling linear time-varying systems. Each of the techniques is applied in the control of a linear time-varying periodic system in order to compare their effectiveness. A hybrid control method involving the Takagi-Sugeno fuzzy control and the Lyapunov-Floquet transformation is proposed. In this method, the stability of the closed-loop system is mathematically guaranteed. In addition, this new procedure can reduce the conservatism of time-varying periodic systems with uncertainties in the input matrix. Finally, an application of the hybrid method is presented in a time-varying periodic system considering a constraint on input and uncertainties on the input matrix.

关键词： fuzzy control Lyapunov-Floquet transformation time-varying periodic system parallel distributed compensation linear matrix inequalities

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Takagi-Sugeno Model-based Steering Control for Autonomous Vehicles with Actuator Saturation

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IFAC-PapersOnLine 2016年第5期49卷 206-211页

作者： Nguyen, Anh-Tu Sentouh, Chouki Popieul, Jean-Christophe Laboratory LAMIH UMR CNRS 8201 University of Valenciennes France

This paper is devoted to the development of a novel control law for an autonomous vehicle. The control goal is to perform lane keeping under multiple constraints, namely actuator saturation of the steering system, roads with unknown curvature, and uncertain lateral wind force. Such system constraints will be explicitly considered in the control design procedure. To achieve this goal, we propose a novel constrained Takagi-Sugeno control method using non-quadratic Lyapunov stability framework. The obtained non-parallel distributed compensation controller is not only able to handle various system constraints but also a large variation range of vehicle speed. Especially, by means of the well-known Taylor's approximation method we can significantly reduce the numerical complexity of the proposed control method to ease the real-time control implementation. The control synthesis conditions are expressed in terms of linear matrix inequalities which can be efficiently solved with available solvers. The effectiveness of the proposed method is demonstrated with different simulation scenarios. © 2016

关键词： Automobile steering equipment Actuators Feedback control Linear matrix inequalities Modal analysis Numerical methods Real time control Robustness (control systems) Steering Actuator saturations Autonomous Vehicles Lane keeping control Numerical complexity parallel distributed compensation Takagi Sugeno fuzzy systems Takagi Sugeno modeling Taylor's approximation

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