scholarly journals Robust and Passive Constrained Fuzzy Control for Discrete Fuzzy Systems with Multiplicative Noises and Interval Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Cheung-Chieh Ku ◽  
Zong-Guo Fu
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Linear Matrix ◽  
Weighting Matrix ◽  
Multiplicative Noises ◽  
Feedback Scheme

The passive fuzzy control for discrete-time uncertain Takagi-Sugeno (T-S) fuzzy models with multiplicative noises and time delay is investigated subject to robust asymptotical stability. Applying Jensen’s inequality and free-weighting matrix technique, less conservative sufficient conditions are derived via choosing Lyapunov function to analyze and synthesize the robust asymptotical stability and passivity of closed-loop system. The derived conditions are not strictly linear matrix inequality (LMI) problems, thus the cone complementarity technique is employed to propose a suboptimal technique to solve the proposed nonstrictly LMI problems. An algorithm is developed in this paper to design the fuzzy controller which can be accomplished by state-feedback scheme or output-feedback scheme. Finally, numerical examples are provided to demonstrate the feasibility and applicability of the proposed fuzzy controller design technique.

scholarly journals Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang
Keyword(s):  
Fuzzy Control ◽  
Control Method ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Lyapunov Theory ◽  
Linear Matrix ◽  
Multiplicative Noises ◽  
Ship Steering ◽  
The Matrix

The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

Design of State Feedback Controller for Discrete Systems with Time-Delay

2013 ◽  
Vol 347-350 ◽  
pp. 695-700
Author(s):  
Shuai Tian He ◽  
Zhi Chang Li
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
State Feedback ◽  
Controller Design ◽  
Dynamic Performance ◽  
Sufficient Conditions ◽  
Discrete Systems ◽  
Adjustable Parameter ◽  
Linear Matrix ◽  
Feedback Gain

The stability analysis and controller design of discrete linear systems with time-varying delay are addressed. Firstly, the uniformly asymptotical stability criterion with adjustable parameter is derived by Lyapunov-Razumikhin approach. Then, the stabilization approaches for linear systems with time delay by state feedback and observer based-on state feedback are also presented. Sufficient conditions for the existence of state feedback gain and the observer gain are derived through the numerical solution of a set of obtained linear matrix inequalities. Compared with methods in the references, the dynamic performance of systems, such as the overshoot and the convergence rate of the response, can be adjusted by changing the adjustable parameter. Lastly, an illustrative example is given to show the effectiveness of the proposed.

Passive Fuzzy Control via Fuzzy Integral Lyapunov Function for Nonlinear Ship Drum-Boiler Systems

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Wen-Jer Chang ◽  
Yao-Chung Chang ◽  
Cheung-Chieh Ku
Keyword(s):  
Lyapunov Function ◽  
Fuzzy Control ◽  
Fuzzy Controller ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Programming Algorithm ◽  
Linear Matrix ◽  
Line Integral ◽  
Drum Boiler ◽  
Fuzzy Lyapunov Function

The passive fuzzy control problem is studied in this paper via line-integral fuzzy Lyapunov function for nonlinear ship drum-boiler systems with multiplicative noises. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinearities of the multiplicative noised nonlinear ship drum-boiler systems. For stability analysis and synthesis, the sufficient conditions are derived via line-integral fuzzy Lyapunov functions. These conditions are transformed into the linear matrix inequality (LMI) forms which can be solved by the convex optimal programming algorithm. In addition, the passivity theory is employed to deal with the effect of external disturbance in the ship drum-boiler system. Finally, a numerical example is provided to show the applicability and effectiveness of the proposed fuzzy controller design approach.

Non-Fragile Robust Controller Design for Nonlinear Stochastic System with Time-Delay

2012 ◽  
Vol 443-444 ◽  
pp. 452-458 ◽  
Author(s):  
Ya Jun Li ◽  
Fei Qi Deng ◽  
Yun Jian Peng
Keyword(s):  
Time Delay ◽  
Stochastic System ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Nonlinear Stochastic System ◽  
Robust Controller ◽  
System With Time Delay ◽  
Robust Controller Design

The problem of non-fragile memoryless controller design for a class of uncertain nonlinear stochastic system with time-delay is considered. Based on Lyapunov candidate and the stochastic Lyapunov stability theory, the sufficient conditions making the closed-loop system robust stable are given and de-rived. All results are given by the form of linear matrix inequality (LMI) method. Numerical example is given to illustrate the effectiveness of the controller designed.

scholarly journals Stability Analysis and Robust Stabilization of Uncertain Fuzzy Time-Delay Systems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2441
Author(s):  
Chun-Tang Chao ◽  
Ding-Horng Chen ◽  
Juing-Shian Chiou
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Delay Dependent ◽  
Takagi Sugeno

New sufficient conditions for delay-independent and delay-dependent robust stability of uncertain fuzzy time-delay systems based on uncertain fuzzy Takagi-Sugeno (T-S) models are presented by using the properties of matrix and norm measurements. Further sufficient conditions are formulated, in terms of the linear matrix inequalities (LMIs) of robust stabilization, and are developed via the technique of parallel distributed compensation (PDC), and then the simplification of the conditions for the controller design of uncertain fuzzy time-delay systems. The proposed methods are simple and effective. Some examples below are presented to illustrate our results.

scholarly journals Design of Takagi-Sugeno Fuzzy Control Scheme for Real World System Control

2019 ◽  
Vol 11 (14) ◽  
pp. 3855 ◽  
Author(s):  
Chiu ◽  
Peng
Keyword(s):  
Fuzzy Control ◽  
Real World ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
World System ◽  
Linear Matrix ◽  
System Control ◽  
Ts Fuzzy Model ◽  
Control Scheme ◽  
Takagi Sugeno

In this study, a novelty dual Takagi-Sugeno (TS) fuzzy control scheme (DTSFCS) is proposed for real world system control. We propose using a ball robot (BR) system control problem, where the BR has the ability to move omnidirectionally. The proposed control scheme combines two fuzzy control approaches for a BR. In this fuzzy control approach, the TS fuzzy model was adopted for the fuzzy modeling of the BR. The concept of parallel distributed compensation (PDC) was utilized to develop a fuzzy control scheme from the TS fuzzy models. The linear matrix inequalities (LMIs) can formulate sufficient conditions. Moreover, in this study, the motors of the BR were mounted on two orthogonal axes. Then, the dual TS fuzzy controller was designed to independently operate without coupling. Finally, the efficiency of the proposed control scheme is illustrated by the experimental and simulation results that are presented in this study.

scholarly journals Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

2021 ◽  
Vol 11 (6) ◽  
pp. 2833
Author(s):  
Wen-Jer Chang ◽  
Ming-Hsuan Tsai ◽  
Chin-Lin Pen
Keyword(s):  
Discrete Time ◽  
Control Method ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Singular Systems ◽  
Lyapunov Theory ◽  
Linear Matrix ◽  
Feedback Scheme ◽  
The Stability

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

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