Stabilization bound of singularly perturbed switched nonlinear systems subject to actuator saturation using the Takagi–Sugeno fuzzy model

2020 ◽  
Author(s):  
Qianjin Wang ◽  
Lei Ma ◽  
Dongyang Wang ◽  
Xiaoping Ma
Keyword(s):  
Nonlinear Systems ◽  
Actuator Saturation ◽  
Fuzzy Model ◽  
Singularly Perturbed ◽  
Switched Nonlinear Systems ◽  
Takagi Sugeno

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

Sampled-data based asynchronous stabilization for switched systems with stochastic perturbations

2019 ◽  
Vol 42 (3) ◽  
pp. 439-450 ◽  
Author(s):  
Jianrong Zhao ◽  
Wen Wang ◽  
Dan Zhang
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Average Dwell Time ◽  
Sampling Interval ◽  
Switched Nonlinear Systems ◽  
Sampled Data ◽  
Stochastic Perturbations ◽  
Asynchronous Control ◽  
Mass Spring

This paper studies the sampled-data based asynchronous control problem for switched nonlinear systems subject to stochastic perturbations. Applying the T-S fuzzy model, the sampled-data based asynchronous stabilization is studied for switched nonlinear systems subject to stochastic perturbations. Combining the sampled-data dependent Lyapunov functional with the mode-dependent average dwell-time technique, a fuzzy controller is obtained to stabilize switched nonlinear systems in the mean-square sense. No more than one switching and multiple switchings are both discussed in one sampling interval to achieve more common results. At last, a simulation example about nonlinear mass-spring mechanical systems subject to stochastic perturbations is given to illustrate the effectiveness of proposed results.

Fault-tolerant controller design with fault estimation capability for a class of nonlinear systems using generalized Takagi-Sugeno fuzzy model

2019 ◽  
Vol 41 (15) ◽  
pp. 4218-4229 ◽  
Author(s):  
Alireza Navarbaf ◽  
Mohammad Javad Khosrowjerdi
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Wide Range ◽  
Satisfy Lipschitz Condition ◽  
Unknown Disturbances ◽  
Takagi Sugeno

In this paper, a new design approach to construct a fault-tolerant controller (FTC) with fault estimation capability is proposed using a generalized Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems in the presence of actuator faults and unknown disturbances. The generalized T-S fuzzy model consists of some local models with multiplicative nonlinear terms that satisfy Lipschitz condition. Besides covering a very wide range of nonlinear systems with a smaller number of local rules in comparison with the conventional T-S fuzzy model and hence having less computational burden, the existence of the multiplicative nonlinear term solves the uncontrollability issues that the other generalized T-S fuzzy models with additive nonlinear terms dealt with. A state/fault observer designed for the considered generalized T-S fuzzy model and then, a dynamic FTC law based on the estimated fault information is proposed and sufficient design conditions are given in terms of linear matrix inequalities (LMIs). It can be shown that the number of LMIs are less than that of previously proposed methods and then feasibility of our method is more likely. The effectiveness of the proposed FTC approach is verified using a nonlinear mass-spring-damper system.

scholarly journals T-S Fuzzy-Based Optimal Control for Minimally Invasive Robotic Surgery with Input Saturation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Faguang Wang ◽  
Hongmei Wang ◽  
Yong Zhang ◽  
Xijin Guo
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Invariant Ellipsoid ◽  
Minimally Invasive Robotic Surgery ◽  
Takagi Sugeno

A minimally invasive surgery robot is difficult to control when actuator saturation exists. In this paper, a Takagi-Sugeno fuzzy model-based controller is designed for a minimally invasive surgery robot with actuator saturation, which is difficult to control. The contractively invariant ellipsoid theorem is applied for the actuator saturation. The proposed scheme can be derived using the H-infinity control theorem and parallel distributed compensation. The result is rebuilt in the form of linear matrix inequalities for easier calculation by computer. Meanwhile, the uniformly ultimately bounded stable and the prescribed H-infinity control performance can be guaranteed. The proposed scheme is simulated in a Novint Falcon haptic device system.

Takagi–Sugeno Fuzzy Predictive Control for a Class of Nonlinear System With Constrains and Disturbances

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Bin Wang ◽  
Jianwei Zhang ◽  
Delan Zhu ◽  
Diyi Chen
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Predictive Control ◽  
Three Dimensional ◽  
Fuzzy Model ◽  
Control Input ◽  
Chen System ◽  
External Disturbances ◽  
Takagi Sugeno ◽  
Fuzzy Predictive Control

This paper investigates the fuzzy predictive control for a class of nonlinear system with constrains under the condition of noise. Based on the fuzzy linearization theory, a class of nonlinear systems can be described by the Takagi–Sugeno (T–S) fuzzy model. The T–S fuzzy model and predictive control are combined to stabilize the proposed class of nonlinear system, and the detailed mathematical derivation is given. Moreover, the designed controller has been optimized even if the system is constrained by output and control input, or perturbed by external disturbances. Finally, numerical simulations including three-dimensional Lorenz system, four-dimensional Chen system and five-dimensional nonlinear system with external disturbances are presented to demonstrate the universality and effectiveness of the proposed scheme. The approach proposed in this paper is simple and easy to implement and also provides reference for relevant nonlinear systems.

scholarly journals An interval observer design for uncertain nonlinear systems based on the T-S fuzzy model

2017 ◽  
Vol 27 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Yamina Menasria ◽  
Hichem Bouras ◽  
Nasreddine Debbache
Keyword(s):  
Nonlinear Systems ◽  
Estimation Error ◽  
Fuzzy Model ◽  
Observer Design ◽  
Pole Placement ◽  
Dynamic State ◽  
New Approach ◽  
Dynamic State Estimation ◽  
Interval Observer ◽  
Takagi Sugeno

AbstractA new approach to build an interval observer for nonlinear uncertain systems is presented in this paper. Nonlinear systems modeled in the Takagi-Sugeno (T-S) form are studied. A T-S proportional observer is first issued by pole-placement and LMI tools. Secondly, time-varying change of coordinates for each dynamic state estimation error is used to design an interval observer. The system state bounds are then directly deduced.

scholarly journals Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Chang Che ◽  
Jiayao Peng ◽  
Tao Zhao ◽  
Jian Xiao ◽  
Jie Zhou
Keyword(s):  
Nonlinear Systems ◽  
Integral Inequality ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Control Approach ◽  
State Delays ◽  
Lyapunov Stability Criterion ◽  
Takagi Sugeno

This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S) fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs) are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

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