scholarly journals Aperiodic Sampled-Data Control for Chaotic System Based on Takagi–Sugeno Fuzzy Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Minjie Zheng ◽  
Shenhua Yang ◽  
Lina Li
Keyword(s):  
Chaotic System ◽  
Fuzzy Model ◽  
Sampling Period ◽  
Linear Matrix ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Mean Square Exponential Stability ◽  
Data Controller ◽  
Takagi Sugeno

This paper investigates the aperiodic sampled-data control for a chaotic system. Firstly, Takagi–Sugeno (T-S) fuzzy models for the chaotic systems are established. The lower and upper bounds of the sampling period are taken into consideration. Then, the criteria for mean square exponential stability analysis and aperiodic sampled-data controller synthesis are provided by means of linear matrix inequalities. And the real sampling patterns can be fully captured by constructing suitable Lyapunov functions. Finally, an illustrative example shows that the proposed method is effective to guarantee that the system’s states are stable with aperiodic sampled data.

Dissipativity-Based Reliable Sampled-Data Control With Nonlinear Actuator Faults

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Srimanta Santra ◽  
R. Sakthivel ◽  
B. Kaviarasan
Keyword(s):  
Sufficient Conditions ◽  
Control Design ◽  
Delay Systems ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Actuator Faults ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Data Controller

In this paper, the problem of reliable sampled-data control design with strict dissipativity for a class of linear continuous-time-delay systems against nonlinear actuator faults is studied. The main objective of this paper is to design a reliable sampled-data controller to ensure a strictly dissipative performance for the closed-loop system. Based on the linear matrix inequality (LMI) optimization approach and Wirtinger-based integral inequality, a new set of sufficient conditions is established for reliable dissipativity analysis of the considered system by assuming the mixed actuator fault matrix to be known. Then, the proposed result is extended to unknown fault matrix case. Also, the reliable sampled-data controller with strict dissipativity is designed by solving a convex optimization problem which can be easily solved by using standard numerical algorithms. Finally, a numerical example based on liquid propellant rocket motor with a pressure feeding system model is presented to illustrate the effectiveness of the developed control design technique.

scholarly journals State-Feedback Sampled-Data Control Design for Nonlinear Systems via Passive Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Chengming Yang ◽  
Qi Zhou ◽  
H. R. Karimi ◽  
Huanqing Wang
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Sampled Data ◽  
Control Approach ◽  
Synthesis Conditions ◽  
Data Control ◽  
Sampled Data Control ◽  
Data Controller

This paper investigates the problem of passive controller design for a class of nonlinear systems under variable sampling. The Takagi-Sugeno (T-S) fuzzy modeling method is utilized to represent the nonlinear systems. Attention is focused on the design of passive controller for the T-S fuzzy systems via sampled-data control approach. Under the concept of very-strict passivity, a novel time-dependent Lyapunov functional is constructed to develop passive analysis criteria and passive controller synthesis conditions. A new sampled-data controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. These conditions are formulated in the form of linear matrix inequalities (LMIs), which can be solved by convex optimization approach. Finally, an application example is given to demonstrate the feasibility and effectiveness of the proposed results.

Exponentially Stable Sampled-Data Control for Uncertain Systems

2014 ◽  
Vol 981 ◽  
pp. 551-554
Author(s):  
Li Ying Fan
Keyword(s):  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Control Input ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control ◽  
Exponentially Stable ◽  
Data Controller ◽  
Continuous Time System

In this paper, the problem of the exponentially stable sampled-data control was investigated for a class of uncertain systems. Based on the input delay approach, the system was modeled as a continuous-time system with the delayed control input. Attention was focused on the design of a state feedback sampled-data controller which guarantees the exponential stability of the closed-loop system for all admissible parametric uncertainties. Using linear matrix inequality (LMI) approach, sufficient conditions are obtained. Simulation example was given to demonstrate the effectiveness and correctness of the proposed method.

Sampled-data control for nonlinear singular systems based on a Takagi–Sugeno fuzzy model

2018 ◽  
Vol 40 (14) ◽  
pp. 4027-4036 ◽  
Author(s):  
Zheng Minjie ◽  
Zhou Yujie ◽  
Yang Shenhua ◽  
Li Lina
Keyword(s):  
Singular Systems ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Sampled Data ◽  
Nonlinear Singular Systems ◽  
Stability Theorems ◽  
Data Control ◽  
Admissible Condition ◽  
Data Controller ◽  
Takagi Sugeno

The sampled-data admissibility problem for nonlinear singular systems in Takagi–Sugeno fuzzy models is discussed. By adding some novel terms, a novel fuzzy time-dependent Lyapunov–Krasovskii functional is proposed to fully capture the available characteristics of the actual sampling pattern. Sufficient conditions are derived to determine the regularity, absence of impulses and asymptotic stability of the system by using Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analysing the admissible condition. One practical example involving a truck–trailer system is considered. It is shown that the proposed method and the designed controller for the system are effective and that less conservativeness can be obtained.

STABILIZATION OF CHAOTIC SYSTEMS USING LINEAR SAMPLED-DATA CONTROLLER

2007 ◽  
Vol 17 (06) ◽  
pp. 2021-2031 ◽  
Author(s):  
H. K. LAM ◽  
F. H. F. LEUNG
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Design Procedure ◽  
Sampling Period ◽  
Feedback Gain ◽  
Sampled Data ◽  
Lyapunov Approach ◽  
And Performance ◽  
Data Controller

This paper proposes a linear sampled-data controller for the stabilization of chaotic system. The system stabilization and performance issues will be investigated. Stability conditions will be derived based on the Lyapunov approach. The findings of the maximum sampling period and the feedback gain of controller, and the optimization of system performance will be formulated as a generalized eigenvalue minimization problem. Based on the analysis result, a stable linear sampled-data controller can be realized systematically to stabilize a chaotic system. An example of stabilizing a Lorenz system will be given to illustrate the design procedure and effectiveness of the proposed approach.

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