scholarly journals Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Fengjiao Wu ◽  
Guitao Zhang ◽  
Zhengzhong Wang
Keyword(s):  
Fuzzy Control ◽  
Fractional Order ◽  
Matrix Theory ◽  
Control Method ◽  
Interval Matrix ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequalities ◽  
Random Disturbances ◽  
The Stability

The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.

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.

Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications

2017 ◽  
Vol 40 (10) ◽  
pp. 3078-3087 ◽  
Author(s):  
Xiaona Song ◽  
Shuai Song ◽  
Bo Li ◽  
Ines Tejado Balsera
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Hybrid Control ◽  
Control Strategies ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Secure Communications ◽  
Uncertain Parameters ◽  
Matrix Inequalities

In this paper, the adaptive projective synchronization of time-delayed fractional-order neural networks is considered. Using the active control and adaptive control methods, efficient hybrid control strategies are designed for time-delayed fractional-order neural networks with uncertain parameters. Based on a new version of fractional-order Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities, which is easily checked and applied to practical systems. Finally, numerical simulations and application of the proposed methods to secure communications have been presented to validate the synchronization method.

D-Stability Based LMI Criteria of Stability and Stabilization for Fractional Order Systems

2015 ◽  
Author(s):  
XueFeng Zhang ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Feasible Solution ◽  
Order System ◽  
Linear Matrix ◽  
Fractional Order Systems ◽  
Matrix Inequalities ◽  
Integer Order ◽  
Stability And Stabilization ◽  
The Stability ◽  
Conditions Of Stability

This paper considers the stability and stabilization of fractional order systems (FOS) with the fractional order α: 0 < α < 1 case. The equivalence between stability of fractional order systems and D–stability of a matrix A in specific region is proven. The criteria of stability and stabilization of fractional order system are presented. The conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily calculated with standard feasible solution problem in MATLAB LMI toolbox. When α = 1, the results reduce to the conditions of stability and stabilization of integer order systems. Numerical examples are given to verify the effectiveness of the criteria. With the approach proposed in this paper, we can analyze and design fractional order systems in the same way as what we do to the integer order system state-space models.

Completeness on the stability criterion of fractional order LTI systems

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Yiheng Wei ◽  
Yuquan Chen ◽  
Songsong Cheng ◽  
Yong Wang
Keyword(s):  
Fractional Order ◽  
Stability Criterion ◽  
Positive Definite Matrix ◽  
Order System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
The Stability ◽  
Definition Of ◽  
And Control

AbstractThe importance of the concept of stability in fractional order system and control has been recognized for some time now. Recently, it has become evident that many conclusions were drawn, but little consensus was reached. Consequently, there is an urgent need for a much deeper understanding of such a concept. With the definition of fractional order positive definite matrix, a set of equivalent and elegant stability criteria are developed via revisiting a stability criterion we proposed before. All the results are formed in terms of linear matrix inequalities. Afterwards, a series of interesting properties of these criteria are revealed profoundly, including completeness, singularity, conservatism, etc. Eventually, a simulation study is provided to validate the effectiveness of the obtained results.

Fuzzy Passivity Control of Flexible Joint Robot

2013 ◽  
Vol 834-836 ◽  
pp. 1229-1233
Author(s):  
Bin Zhang
Keyword(s):  
Control Method ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Model Error ◽  
Stability Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Flexible Joint ◽  
Single Link ◽  
The Stability

This paper researches a fuzzy control method for passive flexible joint robot. Stability control method applying T-S fuzzy model is employed for single-link flexible joint robot. T-S fuzzy model is used to approximate the flexible joint robot firstly, and then fuzzy controller is developed based on the principle of parallel distributed compensation. The fuzzy controller is also applied to the passive properties of model error. The stability conditions are proposed by Lyapunov function and linear matrix inequalities are also applied to solve the controller parameters. Simulation results show that the proposed method of application value.

Chaos, Sliding Mode Control between Two Different Fractional-Order Hyperchaotic Systems with Uncertain Parameters

2012 ◽  
Vol 424-425 ◽  
pp. 318-323
Author(s):  
Hong Zhang ◽  
Dao Yin Qiu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Control Method ◽  
Sliding Mode ◽  
Order System ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Mode Control ◽  
Short Period ◽  
The Stability

This work investigates chaos synchronization between two different fractional-order hyperchaotic system (FOHS)s with uncertain parameters. The Chen FOHS is controlled to be synchronized with a new FOHS. The analytical conditions for the synchronization of different FOHSs are derived by utilizing the stability theory of fractional-order system. Furthermore, synchronization between two different FOHSs is achieved by utilizing sliding mode control method in a quite short period and both remain in chaotic states. Numerical simulations are used to verify the theoretical analysis using different values of the fractional-order parameter

Mittag–Leffler stability and finite-time control for a fractional-order hydraulic turbine governing system with mechanical time delay: An linear matrix inequalitie approach

2021 ◽  
pp. 107754632199759
Author(s):  
Peng Chen ◽  
Bin Wang ◽  
Yuqiang Tian ◽  
Ying Yang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Control Method ◽  
Hydraulic Turbine ◽  
System Stability ◽  
Linear Matrix ◽  
Time Control ◽  
Governing System ◽  
The Stability

This article mainly studies the Mittag–Leffler stability and finite-time control of a time-delay fractional-order hydraulic turbine governing system. First, properties of the Riemann–Liouville derivative and some important lemmas are introduced. Second, considering the mechanical time delay of the main servomotor, the mathematical model of a fractional-order hydraulic turbine governing system with mechanical time delay is presented. Then, based on Mittag–Leffler stability theorem, a suitable sliding surface and finite-time controller are designed for the hydraulic turbine governing system. The system stability is confirmed, and the stability condition is given in the form of linear matrix inequalities. Finally, the traditional proportional–integral–derivative control method and an existing sliding mode control method are selected to verify the effectiveness and robustness of the proposed method. This study also provides a new approach for the stability analysis of the time-delay fractional-order hydraulic turbine governing system.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

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