scholarly journals Fuzzy-Model-Based Robust Control of Markov Jump Nonlinear Systems With Incomplete Transition Probabilities and Uncertain Packet Dropouts

2021 ◽  
Author(s):  
Zeyuan Xu ◽  
Meng Joo Er
Keyword(s):  
Nonlinear Systems ◽  
Transition Probabilities ◽  
Fuzzy Model ◽  
Mode Switching ◽  
Robot Arm ◽  
Markov Jump ◽  
Packet Dropouts ◽  
Complex Nonlinear Systems ◽  
Interval Type ◽  
System Mode

Abstract Interval type-2 fuzzy Markov jump systems (IT2FMJSs) have received much attention because they can better describe complex nonlinear systems with uncertainties and stochastic system mode switching. Over the past decade, many excellent results of fuzzy MJSs (FMJSs) have been reported. However, the transition probabilities which govern the dynamic behaviour of MJSs have been assumed to be completely known, limiting real-world applications of existing results. Different from the previous studies, transition probabilities between system modes switching are partly unknown, and packet dropouts of data transmission are uncertain in this study. The main contributions of this work are: (1) To analyze stochastic stability and reduce conservatism, a novel Lyapunov function which both depends on system mode and fuzzy basis function is constructed; (2) The existence of a mode-dependent and fuzzy-basis-dependent state-feedback controller is investigated; (3) The closedloop system is stochastically stable with a desired H∞ performance, thereby addressing the problem of incomplete transition probabilities and uncertain packet dropouts. An illustrative example of a robot arm is used to demonstrate the effectiveness and practicality of the proposed approach. By virtue of the proposed approach, the effects of incomplete transition probabilities and uncertain packet dropouts on IT2FMJSs are alleviated.

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.

Modeling and Control of Complex Nonlinear Systems Based on TS Model

2013 ◽  
Vol 380-384 ◽  
pp. 417-420
Author(s):  
Yu Chi Zhao ◽  
Jing Liu
Keyword(s):  
System Theory ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Modeling And Control ◽  
Linear Control Theory ◽  
Complex Nonlinear Systems ◽  
And Control

The current theory of nonlinear systems is still not perfect. The modeling and control of nonlinear system problem has always been the difficulty. In a variety of methods of its study, fuzzy system theory because of having the language descriptive way similar to the human mind, can obtain and deal with the qualitative information intelligently. The theory itself also has non-linear characteristics. Therefore the use of fuzzy systems theory to establish the fuzzy model of nonlinear system can well describe the nonlinear characteristics. T-S fuzzy systems, due to the combination of the good performance of the fuzzy system to deal with nonlinear problems with the simple linear expressions, are not only suitable for modeling the nonlinear system, but also use T-S fuzzy model and the linear control theory method to design the controller. So it has been widely used in nonlinear system control problems, and has also greatly developed the T-S fuzzy system theory, appearing a lot of methods of structural and parameter identification. However, this study of T-S fuzzy rules makes us have to face the difference of different ways to select the number of rules as well as online self-adaptability of the number of rules which off-line method lacks when using T-S fuzzy model to deal with nonlinear system modeling and control problem. In view of this, this paper researches on modeling and controlling of complex nonlinear systems based on TS model from different perspectives.

Fuzzy-model-based tracking control of Markov jump nonlinear systems with incomplete mode information

2021 ◽  
Vol 358 (7) ◽  
pp. 3633-3650
Author(s):  
Dan Cui ◽  
Yue Wang ◽  
Hongye Su ◽  
Zhaowen Xu ◽  
Haoyi Que
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
Fuzzy Model ◽  
Markov Jump ◽  
Model Based
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