scholarly journals H∞ Robust Control for Chaotic Motion of the Fractional-Order D-PMSG via the PDC Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Li Yang ◽  
Zijie Shen ◽  
Weitao Sheng ◽  
Tianmin Huang
Keyword(s):  
Fractional Order ◽  
Performance Index ◽  
Direct Method ◽  
External Disturbance ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Direct Drive ◽  
Parameter Uncertainties ◽  
Cauchy Matrix ◽  
Fuzzy State

The stability analysis and controller design problems for the fractional-order (FO) direct-drive permanent magnet synchronous generator (FOD-PMSG) wind turbine with parameter uncertainties and external disturbance are addressed. Takagi–Sugeno (T-S) model is used to approximate nonlinearities, and the parallel distributed compensation (PDC) technique is employed to construct the fuzzy state feedback controller. In order to suppress the external disturbance more effectively, the global Mittag-Leffler stability definition satisfying the H∞ performance index is proposed for the first time. Using the FO Lyapunov direct method, applying the Cauchy matrix inequality (CMI), and combining with the Schur complement lemma, the sufficient conditions of Mittag-Leffler stability meeting the H∞ performance index are given in the form of linear matrix inequalities (LMIs). Simulation results clearly show that the proposed control scheme can make the system get rid of the chaotic state quickly and have strong robustness under parameter uncertainties and external disturbance varying randomly.

scholarly journals Fuzzy Chaos Control of Fractional Order D-PMSG for Wind Turbine with Uncertain Parameters by State Feedback Design

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 7369
Author(s):  
Li Yang ◽  
Fuzhao Yang ◽  
Weitao Sheng ◽  
Kun Zhou ◽  
Tianmin Huang
Keyword(s):  
Wind Turbine ◽  
Fractional Order ◽  
Chaotic Motion ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Direct Drive ◽  
Chaotic Motions ◽  
Fuzzy State

To research the chaotic motion problem of the direct-drive permanent magnet synchronous generator (D-PMSG) for a wind turbine with uncertain parameters and fractional order characteristics, a control strategy established upon fuzzy state feedback is proposed. Firstly, according to the working mechanism of D-PMSG, the Lorenz nonlinear mathematical model is established by affine transformation and time transformation. Secondly, fractional order nonlinear systems (FONSs) are transformed into linear sub-model by Takagi–Sugeno (T-S) fuzzy model. Then, the fuzzy state feedback controller is designed through Parallel Distributed Compensation (PDC) control principle to suppress the chaotic motion. By applying the fractional Lyapunov stability theory (FLST), the sufficient conditions for Mittag–Leffler stability are formulated in the format of linear matrix inequalities (LMIs). Finally, the control performance and effectiveness of the proposed controller are demonstrated through numerical simulations, and the chaotic motions in D-PMSG can be eliminated quickly.

scholarly journals Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Shuo Zhang ◽  
Yongguang Yu ◽  
Wei Hu
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Robust Stability ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Neural System ◽  
Hopfield Neural Networks ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Theoretical Results

The issue of robust stability for fractional-order Hopfield neural networks with parameter uncertainties is investigated in this paper. For such neural system, its existence, uniqueness, and global Mittag-Leffler stability of the equilibrium point are analyzed by employing suitable Lyapunov functionals. Based on the fractional-order Lyapunov direct method, the sufficient conditions are proposed for the robust stability of the studied networks. Moreover, robust synchronization and quasi-synchronization between the class of neural networks are discussed. Furthermore, some numerical examples are given to show the effectiveness of our obtained theoretical results.

scholarly journals Performance Index Based Observer-Type Iterative Learning Control for Consensus Tracking of Uncertain Nonlinear Fractional-Order Multiagent Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Liming Wang ◽  
Guoshan Zhang
Keyword(s):  
Dimensional Analysis ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Performance Index ◽  
Sufficient Conditions ◽  
Iterative Learning ◽  
Linear Matrix ◽  
Two Dimensional ◽  
System Matrix ◽  
Monotonic Convergence

This paper is devoted to the perfect tracking problem of consensus and the monotonic convergence problem of input errors for the uncertain nonlinear fractional-order multiagent systems (FOMASs), where there exist the linear coupling relations between the fractional order, the perturbations of the system matrix, and input matrix. For the FOMASs including one leader agent and multiple follower agents, an observer-type fractional-order iterative learning consensus protocol is proposed. Based on the two-dimensional analysis for the FOMASs, a novel performance index, which can exhibit the monotonic convergence of the input errors, is constructed by using the definition of fractional integral. A Lyapunov-like method is applied to derive the sufficient conditions in terms of linear matrix inequalities, which can guarantee the perfect tracking of consensus and the monotonic convergence of input errors. Finally, the numerical simulation results including comparisons to traditional two-dimensional analysis are presented to demonstrate the effectiveness of the proposed methods.

Robust H2 Output Feedback Controller Design for Damping Power System Oscillations

2017 ◽  
Vol 6 (10) ◽  
pp. 8
Author(s):  
Kho Hie Kwee ◽  
Hardiansyah .
Keyword(s):  
Power System ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Worst Case ◽  
Output Feedback Controller ◽  
Power System Oscillations

This paper addresses the design problem of robust H2 output feedback controller design for damping power system oscillations. Sufficient conditions for the existence of output feedback controllers with norm-bounded parameter uncertainties are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design the output feedback controller which minimizes an upper bound on the worst-case H2 norm for a range of admissible plant perturbations. The technique is illustrated with applications to the design of stabilizer for a single-machine infinite-bus (SMIB) power system. The LMI based control ensures adequate damping for widely varying system operating.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

Guaranteed cost and finite-time event-triggered control of fractional-order switched systems

2021 ◽  
pp. 014233122110048
Author(s):  
Yilin Shang ◽  
Leipo Liu ◽  
Yifan Di ◽  
Zhumu Fu ◽  
Bo Fan
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Electrical Circuit ◽  
Linear Matrix ◽  
Current State ◽  
Guaranteed Cost ◽  
Event Triggered

This paper considers the problem of guaranteed cost and finite-time event-triggered control of fractional-order switched systems. Firstly, an event-triggered scheme including both the information of current state and an exponential decay function is proposed, and a novel cost function that adopts the characteristics of fractional-order integration is presented. Secondly, some sufficient conditions are derived to guarantee that the corresponding closed-loop system is finite-time stable with a certain cost upper bound, using multiple Lyapunov functions and average dwell time approach. Meanwhile, the event-triggered parameters and state feedback gains are simultaneously obtained via solving linear matrix inequalities. Moreover, Zeno behavior does not exist by finding a positive lower bound of the triggered interval. Finally, an example about fractional-order switched electrical circuit is provided to show the effectiveness of the proposed method.

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

2007 ◽  
Vol 17 (03) ◽  
pp. 207-218 ◽  
Author(s):  
BAOYONG ZHANG ◽  
SHENGYUAN XU ◽  
YONGMIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Neuron Activation ◽  
Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

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.

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