scholarly journals Stabilizing Fuzzy Output Control for a Class of Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Output Control ◽  
Output Controller ◽  
Control Scheme ◽  
Lyapunov Matrix ◽  
Takagi Sugeno

The paper presents new conditions suitable in design of a stabilizing output controller for a class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the fuzzy control scheme relating to the parallel distributed output compensators, the sufficient design conditions are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and guarantees global stability of the system. Simulation result illustrates the design procedure and demonstrates the performances of the proposed design method.

scholarly journals Optimal Fuzzy Control for a Class of Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stabilizing Controllers ◽  
Simulation Results ◽  
Takagi Sugeno ◽  
Slack Matrices

The paper presents conditions suitable in design giving quadratic performances to stabilizing controllers for given class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Based on extended Lyapunov function and slack matrices, the design conditions are outlined in the terms of linear matrix inequalities to possess a stable structure closest to LQ performance, if premise variables are measurable. Simulation results illustrate the design procedure and demonstrate the performances of the proposed control design method.

scholarly journals Improved RobustH∞Filtering Approach for Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jun Chen ◽  
Haiqiao Sun
Keyword(s):  
Nonlinear Systems ◽  
Filter Design ◽  
Fuzzy Model ◽  
Design Procedure ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Matrix Variable ◽  
Lyapunov Matrix ◽  
Improved Design ◽  
Takagi Sugeno

An improved design approach of robustH∞filter for a class of nonlinear systems described by the Takagi-Sugeno (T-S) fuzzy model is considered. By introducing a free matrix variable, a new sufficient condition for the existence of robustH∞filter is derived. This condition guarantees that the filtering error system is robustly asymptotically stable and a prescribedH∞performance is satisfied for all admissible uncertainties. Particularly, the solution of filter parameters which are independent of the Lyapunov matrix can be transformed into a feasibility problem in terms of linear matrix inequalities (LMIs). Finally, a numerical example illustrates that the proposed filter design procedure is effective.

scholarly journals H∞Control of Pairwise Distributable Large-Scale TS Fuzzy Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Anna Filasová ◽  
Dušan Krokavec
Keyword(s):  
Fuzzy Systems ◽  
Large Scale ◽  
Tuning Parameter ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Bounded Real Lemma ◽  
Control Scheme ◽  
State Controller ◽  
Lyapunov Matrix ◽  
Takagi Sugeno

The paper presents new conditions suitable in design of the stabilizing state controller for a class of continuous-time nonlinear systems, which are representable by pairwise distributable Takagi-Sugeno models. Taking into account the affine properties of the TS model structure and applying the pairwise subsystems fuzzy control scheme relating to the parallel distributed output compensators, the extended bounded real lemma form and the sufficient design conditions for pairwise decentralized control are outlined in terms of linear matrix inequalities. The proposed procedure decouples the Lyapunov matrix and the system parameter matrices in the LMIs and, using free tuning parameter, provides the way to obtain global stability of such large-scale TS systems and optimizes subsystems interactionH∞norm bounds.

scholarly journals Design of a Takagi-Sugeno Fuzzy Regulator for a Set of Operation Points

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Máira P. A. Santim ◽  
Marcelo C. M. Teixeira ◽  
Wallysonn A. de Souza ◽  
Rodrigo Cardim ◽  
Edvaldo Assunção
Keyword(s):  
Control System ◽  
Design Method ◽  
Linear Matrix ◽  
Control System Design ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Single Controller ◽  
Fuzzy Regulator ◽  
Nonlinear Plants ◽  
Takagi Sugeno

The paper proposes a new design method based on linear matrix inequalities (LMIs) for tracking constant signals (regulation) considering nonlinear plants described by the Takagi-Sugeno fuzzy models. The procedure consists in designing a single controller that stabilizes the system at operation points belonging to a certain range or region, without the need of remaking the design of the controller gains at each new chosen equilibrium point. The control system design of a magnetic levitator illustrates the proposed methodology.

scholarly journals Delay-Dependent RobustH∞Filtering of the Takagi-Sugeno Fuzzy Stochastic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Ze Li ◽  
Xin-Hao Yang
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Mean Square Stability ◽  
Error System ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper is concerned with the problem of the robustH∞filtering for the Takagi-Sugeno (T-S) fuzzy stochastic systems with bounded parameter uncertainties. For a given T-S fuzzy stochastic system, this paper focuses on the stochastically mean-square stability of the filtering error system and theH∞performance level of the output error and the disturbance input. The design method for delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed methods is substantiated with an illustrative example.

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

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

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.

A Simple, Natural and Effective Framework of Nonlinear Systems Control and its Application to Aerial Robots

2014 ◽  
Vol 26 (2) ◽  
pp. 140-147 ◽  
Author(s):  
Motoyasu Tanaka ◽  
◽  
Hiroshi Ohtake ◽  
Kazuo Tanaka ◽  
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Design Problems ◽  
Model Based Control ◽  
Aerial Robots ◽  
Control Framework ◽  
Systems Control ◽  
Takagi Sugeno

This paper presents a simple, natural and effective framework of nonlinear systems control and its application to aerial robots. First, we present a framework of Takagi-Sugeno fuzzy model-based control and also discuss its feature. Next, a number of design problems for the control framework are formulated as numerically feasibility problems of representing in terms of linear matrix inequalities. Finally, we provide two applications of the control framework to aerial robots. The control results of aerial robots show the utility of the control framework.

scholarly journals LMI based fuzzy observer design for Takagi-Sugeno models containing vestigial nonlinear terms

2014 ◽  
Vol 24 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Continuous Time ◽  
Observer Design ◽  
System Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Observer ◽  
Quadratic Inequalities ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

Abstract The paper deals with the problem of full order fuzzy observer design for the class of continuous-time nonlinear systems, represented by Takagi-Sugeno models containing vestigial nonlinear terms. On the basis of the Lyapunov stability criterion and the incremental quadratic inequalities, two design conditions for this kind of system model are outlined in the terms of linear matrix inequalities. A numerical example is given to illustrate the procedure and to validate the performances of the proposed approach.

Stable and Optimal Controller Design for Takagi-Sugeno Fuzzy Model Based Control Systems via Linear Matrix Inequalities

2016 ◽  
Vol 14 (3) ◽  
pp. 31-40 ◽  
Author(s):  
M. Namazov ◽  
A. Alili
Keyword(s):  
Nonlinear System ◽  
Control Systems ◽  
Linear Matrix Inequalities ◽  
Linear Models ◽  
Fuzzy Model ◽  
Design Procedure ◽  
Optimal Performance ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Takagi Sugeno

AbstractThis paper deals with a systematic design procedure that guarantees the stability and optimal performance of the nonlinear systems described by Takagi-Sugeno fuzzy models. Takagi-Sugeno fuzzy model allows us to represent a nonlinear system by linear models in different state space regions. The overall fuzzy model is obtained by fuzzy blending of these linear models. Then based on this model, linear controllers are designed for each linear model using parallel distributed compensation. Stability and optimal performance conditions for Takagi-Sugeno fuzzy control systems can be represented by a set of linear matrix inequalities which can be solved using software packages such as MATLAB’s LMI Toolbox. This design procedure is illustrated for a nonlinear system which is described by a two-rule Takagi-Sugeno fuzzy model. The fuzzy model was built in MATLAB Simulink and a code was written in LMI Toolbox to determine the controller gains subject to the proposed design approach.

scholarly journals An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults An

2015 ◽  
Vol 25 (3) ◽  
pp. 547-559 ◽  
Author(s):  
Ali Ben Brahim ◽  
Slim Dhahri ◽  
Fayçal Ben Hmida ◽  
Anis Sellami
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode ◽  
Design Method ◽  
Estimation Error ◽  
Sliding Mode Observer ◽  
Linear Matrix ◽  
Sensor Faults ◽  
Fault Reconstruction ◽  
The Stability ◽  
Takagi Sugeno

Abstract This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer

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