scholarly journals Bifurcation Analysis and  H∞ Control of a Stochastic Competition Model with Time Delay

2021 ◽  
Author(s):  
Yue Zhang ◽  
Jing Zhang
Keyword(s):  
Time Delay ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Competition Model ◽  
Linear Matrix ◽  
Singular Boundary ◽  
Center Manifold Reduction ◽  
Bifurcation Phenomenon

Abstract In this paper, we study a stochastic competition model with time delay and harvesting.We first simplify it through the stochastic center manifold reduction principle and stochastic averaging method as a one-dimensional Markov diffusion process. Singular boundary theory and an invariant measure are applied to analyze stochastic stability and bifurcation. The T-S fuzzy model of the system is constructed, and the H∞ fuzzy controller is designed to eliminate the bifurcation phenomenon through a linear matrix inequality approach. Numerical simulation is used to demonstrate our results.

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.

scholarly journals H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cheng Gong ◽  
Yi Zeng
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Singular Systems ◽  
Fuzzy Model ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Delay Dependent ◽  
Jump Systems

This paper investigates theH∞filtering problem of discrete singular Markov jump systems (SMJSs) with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition onH∞-disturbance attenuation is presented, in which both stability and prescribedH∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependentH∞filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

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.

DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1095-1105 ◽  
Author(s):  
XINGWEN LIU ◽  
XIN GAO
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed State Feedback ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Compensation Design ◽  
Hyperchaotic Systems ◽  
Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

Takagi-Sugeno Fuzzy Load-Following Control of Nuclear Reactors Based on Reactor Point Kinetics Equations

2014 ◽  
Author(s):  
Xiuchun Luan ◽  
Jie Zhou ◽  
Yu Zhai
Keyword(s):  
Control System ◽  
Linear Models ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Neutron Density ◽  
Load Following ◽  
Wide Range ◽  
Takagi Sugeno ◽  
Operating Points

A state differential feedback control system based Takagi-Sugeno (T-S) fuzzy model is designed for load-following operation of nonlinear nuclear reactor whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy controller is designed via using the parallel distributed compensation (PDC) scheme with the relative neutron density at the equilibrium point as the premise variable. Last the stability analysis is given by means of linear matrix inequality (LMI) approach, thus the control system is guaranteed to be stable within a large range. The simulation results demonstrate that the control system works well over a wide region of operation.

scholarly journals Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
R. C. Hu ◽  
Q. F. Lü ◽  
X. F. Wang ◽  
Z. G. Ying ◽  
R. H. Huan
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Random Time ◽  
Nonlinear Stochastic System ◽  
Control Force ◽  
Markov Jump ◽  
Optimal Control Strategy ◽  
Vibrating Systems

A probability-weighted optimal control strategy for nonlinear stochastic vibrating systems with random time delay is proposed. First, by modeling the random delay as a finite state Markov process, the optimal control problem is converted into the one of Markov jump systems with finite mode. Then, upon limiting averaging principle, the optimal control force is approximately expressed as probability-weighted summation of the control force associated with different modes of the system. Then, by using the stochastic averaging method and the dynamical programming principle, the control force for each mode can be readily obtained. To illustrate the effectiveness of the proposed control, the stochastic optimal control of a two degree-of-freedom nonlinear stochastic system with random time delay is worked out as an example.

SYNCHRONIZATION OF TIME-DELAYED T–S FUZZY CHAOTIC SYSTEMS VIA SCALAR OUTPUT VARIABLE

2005 ◽  
Vol 15 (08) ◽  
pp. 2593-2601 ◽  
Author(s):  
JAE-HUN KIM ◽  
HYUNSEOK SHIN ◽  
EUNTAI KIM ◽  
MIGNON PARK
Keyword(s):  
Time Delay ◽  
Fuzzy Model ◽  
Order System ◽  
Linear Matrix ◽  
Output Variable ◽  
First Order ◽  
Scalar Output ◽  
The Stability ◽  
Takagi Sugeno ◽  
System With Time Delay

It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi–Sugeno (T–S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T–S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov–Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.

scholarly journals T-S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Weidong Zhang ◽  
Xianlin Huang ◽  
Xiao-Zhi Gao
Keyword(s):  
Attitude Control ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Attitude Dynamics ◽  
Approximation Accuracy ◽  
Fuzzy Modelling ◽  
Original Plant ◽  
Operating Points

This paper addresses the T-S fuzzy modelling and H∞ attitude control in three channels for hypersonic gliding vehicles (HGVs). First, the control-oriented affine nonlinear model has been established which is transformed from the reentry dynamics. Then, based on Taylor’s expansion approach and the fuzzy linearization approach, the homogeneous T-S local modelling technique for HGVs is proposed. Given the approximation accuracy and controller design complexity, appropriate fuzzy premise variables and operating points of interest are selected to construct the T-S homogeneous submodels. With so-called fuzzy blending, the original plant is transformed into the overall T-S fuzzy model with disturbance. By utilizing Lyapunov functional approach, a state feedback fuzzy controller has been designed based on relaxed linear matrix inequality (LMI) conditions to stable the original plants with a prescribed H∞ performance of disturbance. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed H∞ T-S fuzzy controller for the original attitude dynamics; the superiority of the designed T-S fuzzy controller compared with other local controllers based on the constructed fuzzy model is shown as well.

scholarly journals T-S Fuzzy Model-Based Approximation and Filter Design for Stochastic Time-Delay Systems with Hankel Norm Criterion

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanhui Li ◽  
Xiujie Zhou
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Fuzzy Model ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Hankel Norm ◽  
Error System ◽  
Stochastic Time

This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S) fuzzy model. Motivated by the parallel distributed compensation (PDC) technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance levelγ. Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs). The effectiveness of the proposed method is demonstrated via a numerical example.

Fuzzy Passivity Non-Fragile Control of Flexible Joint Robot

2013 ◽  
Vol 448-453 ◽  
pp. 3571-3575
Author(s):  
Bin Zhang
Keyword(s):  
Robot Control ◽  
Simulation Experiment ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Flexible Joint ◽  
Control Approach ◽  
Compensation Principle ◽  
The Stability

The paper proposes a fuzzy passivity non-fragile control approach for flexible joint robot. The T-S fuzzy model is applied to approximate the flexible joint robot at first, and then the fuzzy controller is developed based on parallel distributed compensation principle. The passivity non-fragile performance of controller is also employed to limit the influence of model error. The conditions for the stability of the flexible joint robot control system are proposed by using Lyapunov function, and linear matrix inequality is applied to resolve the controller parameter. The simulation experiment results show the effectiveness of the proposed method.

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