An indirect Lyapunov approach to the observer-based robust control for fractional-order complex dynamic networks

Lan, Yong‐Hong; Gu, Haibo; Chen, Caixue; Zhou, Yan; Luo, Yiping

doi:10.1016/j.neucom.2014.01.009

Cited by 55 publications

(31 citation statements)

References 31 publications

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“…Based on the principle of separation, the nonlinear observer-based control is designed in [35]. Reference [36] concerns observer-based robust control problem for a class of fractional-order complex dynamical networks. In [37], by using the properties of Mittag-Leffler function and the Gronwall-Bellman inequality, two sufficient conditions on the global asymptotic stability for a class of nonlinear FOS with the fractional-orders 0 < < 1 and 1 < < 2 are derived, respectively.…”

Section: Introductionmentioning

confidence: 99%

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Qiu

2017

Mathematical Problems in Engineering

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We discuss the observer-based robust controller design problem for a class of nonlinear fractional-order uncertain systems with admissible time-variant uncertainty in the case of the fractional-order satisfying 0 < < 1. Based on direct Lyapunov approach, a sufficient condition for the robust asymptotic stability of the observer-based nonlinear fractional-order uncertain systems is presented. Employing Finsler's Lemma, the systematic robust stabilization design algorithm is then proposed in terms of linear matrix inequalities (LMIs). The efficiency and advantage of the proposed algorithm are finally illustrated by two numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Qiu

2017

Mathematical Problems in Engineering

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“…The other reason is that fractional controller has shown that it has more potential and more design freedom comparing to the standard integer order controller [18,25]. For more details on fractional calculus, please refer to [1,3,6,8,11,12,15,17,20,22,30].…”

Section: Introductionmentioning

confidence: 99%

“…In [30], the authors used the eigenvalue analysis to stabilize a linearized FONSs. Another attempt by Lan et al [11] was to investigate robust stabilization of fractional order nonlinear complex network using the Lyapunov indirect approach. For more details and examples, please see in [2,10,29,30].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

Hanan¹,

Ahmad²,

Fadhel³

2017

J. Nonlinear Sci. Appl.

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This paper focuses on the application of fractional backstepping control scheme for nonlinear fractional partial differential equation (FPDE). Two types of fractional derivatives are considered in this paper, Caputo and the Grünwald-Letnikov fractional derivatives. Therefore, obtaining highly accurate approximations for this derivative is of a great importance. Here, the discretized approach for the space variable is used to transform the FPDE into a system of fractional differential equations. The convergence of the closed loop system is guaranteed in the sense of Mittag-Leffler stability. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme.

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“…In practical control applications, it is impatient duty to have a systematic method of ensuring the stability of the overall system. Recently, many NN methods are introduced based on the Lyapunov stability theory, [16][17][18][19] but what we need to resolve and focus on is the determination of the assumptions and adaptive learning laws. With the above-mentioned motivations, the radial basis function (RBF) NN with a selfrecurrent and variable structure (VS) not only guarantees the stability of the control system, 19 but also does not need the constrained conditions and knowledge of the controlled system.…”

Section: Introductionmentioning

confidence: 99%

Adaptive complementary fuzzy self-recurrent wavelet neural network controller for the electric load simulator system

Wang

Gao

Hou

et al. 2016

Advances in Mechanical Engineering

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Due to the complexities existing in the electric load simulator, this article develops a high-performance nonlinear adaptive controller to improve the torque tracking performance of the electric load simulator, which mainly consists of an adaptive fuzzy self-recurrent wavelet neural network controller with variable structure (VSFSWC) and a complementary controller. The VSFSWC is clearly and easily used for real-time systems and greatly improves the convergence rate and control precision. The complementary controller is designed to eliminate the effect of the approximation error between the proposed neural network controller and the ideal feedback controller without chattering phenomena. Moreover, adaptive learning laws are derived to guarantee the system stability in the sense of the Lyapunov theory. Finally, the hardware-in-the-loop simulations are carried out to verify the feasibility and effectiveness of the proposed algorithms in different working styles.

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An indirect Lyapunov approach to the observer-based robust control for fractional-order complex dynamic networks

Cited by 55 publications

References 31 publications

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Observer‐Based Robust Controller Design for Nonlinear Fractional‐Order Uncertain Systems via LMI

Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations

Adaptive complementary fuzzy self-recurrent wavelet neural network controller for the electric load simulator system

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