scholarly journals A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Ting-Ting Gang ◽  
Jun Yang ◽  
Qing Gao ◽  
Yu Zhao ◽  
Jianbin Qiu
Keyword(s):  
Nonlinear Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Dynamic Feedback ◽  
Stabilization Problem ◽  
Fuzzy Models ◽  
Quadratic Lyapunov Functions ◽  
Affine Nonlinear Systems ◽  
Semiglobal Stabilization ◽  
Approximation Capability

This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

scholarly journals Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

2021 ◽  
Author(s):  
Fujin Jia ◽  
Junwei Lu ◽  
Yong-Min Li ◽  
Fangyuan Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Control Algorithm ◽  
Lyapunov Analysis ◽  
Stabilization Problem ◽  
Analysis Method ◽  
Control Approach ◽  
Affine Nonlinear Systems ◽  
Simulation Results ◽  
Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

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.

Robust Stabilization for a Class of Switched Nonlinear Systems

2012 ◽  
Vol 490-495 ◽  
pp. 1536-1540
Author(s):  
Cai Yun Wu ◽  
Ben Niu
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Switched Nonlinear Systems ◽  
Closed Loop System ◽  
Multiple Lyapunov Functions ◽  
Switching Law ◽  
Nonlinear Part ◽  
State Dependent

This paper addresses the stabilization problem for a class of switched nonlinear systems with Lipschitz nonlinearities using the multiple Lyapunov functions (MLFs) approach. A state feedback controller and a state dependent switching law are proposed to asymptotic stabilization the switched system via linear matrix inequalities (LMI). The developed control strategy ensures asymptotic stability of the closed-loop system even if the nonlinear part . Finally, the feasibility of the proposed method is illustrated through a simulation example

Gelig’s Averaging Method For Local Stabilization Of A Class Of Nonlinear Systems By A Pulse-Width Modulated Control

2020 ◽  
pp. 129-135
Author(s):  
Alexander N. Churilov
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Pulse Width ◽  
Averaging Method ◽  
Domain Of Attraction ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Pulse Width Modulated ◽  
Zero Equilibrium

A stabilization problem for a nonlinear system with a sector bound nonlinearity and a pulse-width modulated (PWM) feedback is considered. The linear matrix inequalities (LMI) technique is used to estimate the domain of attraction for the zero equilibrium of the closed system.

scholarly journals Robust Stabilization for Continuous Takagi-Sugeno Fuzzy System Based on Observer Design

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yassine Manai ◽  
Mohamed Benrejeb
Keyword(s):  
Robust Stabilization ◽  
Uncertain System ◽  
Observer Design ◽  
Linear Matrix ◽  
State Variables ◽  
Fuzzy Models ◽  
Distributed Controller ◽  
Numeric Simulation ◽  
Stabilization Condition ◽  
Takagi Sugeno

This paper investigates the influence of a new parallel distributed controller (PDC) on the stabilization region of continuous Takagi-Sugeno (T-S) fuzzy models. Using a nonquadratic Lyapunov function, a new sufficient stabilization criterion is established in terms of linear matrix inequality. The criterion examines the derivative membership function; an approach to determine state variables is given based on observer design. In addition, a stabilization condition for uncertain system is given. Finally, numeric simulation is given to validate the developed approach.

scholarly journals Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Zaiyue Yang ◽  
C. W. Chan ◽  
Yiwen Wang
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Robust Stabilization ◽  
Control Coefficient ◽  
Control Performance ◽  
Stabilization Problem ◽  
Asymptotic Stabilization

This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.

FUZZY LYAPUNOV METHOD FOR STABILITY CONDITIONS OF NONLINEAR SYSTEMS

2006 ◽  
Vol 15 (02) ◽  
pp. 163-171 ◽  
Author(s):  
CHENG-WU CHEN ◽  
WEI-LING CHIANG ◽  
CHUNG-HUNG TSAI ◽  
CHEN-YUAN CHEN ◽  
MORRIS H. L. WANG
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Lyapunov Method ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Asymptotic Stable ◽  
Fuzzy Lyapunov Function ◽  
Quadratic Lyapunov Functions

This paper proposes a fuzzy Lyapunov method for stability analysis of nonlinear systems represented by Tagagi-Sugeno (T-S) fuzzy model. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Based on fuzzy Lyapunov functions, some stability conditions are derived to ensure nonlinear systems are asymptotic stable. By using parallel distributed compensation (PDC) scheme, we design a nonlinear fuzzy controller for the nonlinear system. This control problem will be reformulated into linear matrix inequalities (LMI) problem.

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