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.

scholarly journals Fuzzy Static Output Control of T-S Fuzzy Stochastic Systems via Line Integral Lyapunov Function

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 697
Author(s):  
Cheung-Chieh Ku ◽  
Yun-Chen Yeh ◽  
Yann-Hong Lin ◽  
Yu-Yen Hsieh
Keyword(s):  
Lyapunov Function ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Stochastic Systems ◽  
Line Integral ◽  
Output Control ◽  
Static Output

Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic differential equations and membership functions, is applied to represent nonlinear stochastic systems. Parallel distributed compensation (PDC) technology is used to construct the static output controller. A line-integral Lyapunov function (LILF) is used to derive some sufficient conditions for guaranteeing the asymptotical stability in the mean square. From the LILF, a potential conservatism produced by the derivative of the membership function is eliminated to increase the relaxation of sufficient conditions. Furthermore, those conditions are transferred into linear matrix inequality (LMI) form via projection lemma. According to the convex optimization algorithm, the feasible solutions are directly obtained to establish the static output fuzzy controller. Finally, a numerical example is applied to demonstrate the effectiveness and usefulness of the proposed design method.

Observer-based robust H∞ control for uncertain Markovian jump systems via fuzzy Lyapunov function

2018 ◽  
Vol 41 (3) ◽  
pp. 657-667 ◽  
Author(s):  
Jun Chen ◽  
Tieqing He ◽  
Fei Liu
Keyword(s):  
Lyapunov Function ◽  
External Disturbance ◽  
Optimization Techniques ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Congruent Transformation ◽  
Fuzzy Lyapunov Function ◽  
Jump Systems ◽  
Takagi Sugeno

This paper investigates the problem of observer-based robust [Formula: see text] control for a class of continuous-time nonlinear Markovian jump systems (MJSs) with uncertainties, external disturbance and unavailable states that can be represented by Takagi-Sugeno (T-S) fuzzy models. Based on a mode-dependent fuzzy Lyapunov function and by introducing slack matrix variables, a sufficient condition for the existence of the state observer and observer-based robust [Formula: see text] controller for such MJSs are derived by constructing an augmented fuzzy system. Further, by means of congruent transformation in matrix and linear matrix inequality (LMI) method, the results are given in the form of LMIs that can be easily solved by using the convex optimization techniques. Moreover, we also give the result obtained via common stochastic Lyapunov function to compare with the proposed approach. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

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 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 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 Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

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.

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

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