Adaptive Control for Nonlinear Singular Systems

Azarfar, Azita; Shandiz, Heydar Toossian; Shafiee, Masoud

doi:10.5755/j01.itc.43.2.4958

Cited by 5 publications

(9 citation statements)

References 18 publications

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“…1. The following first-order differential equations define the new four-dimensional hyperchaotic finance system: (2) where w is the new state variable that represents average profit margin, and d, k are new positive real constants [46]. The hyperchaotic varies of system (2) are analysed with demonstrating the bifurcation diagrams versus parameters c and k [46].…”

Section: The Hyperchaotic Finance Systemmentioning

confidence: 99%

“…For the control of hyperchaotic finance system to its equilibrium points, u 1 , u 2 , u 3 , and u 4 controllers are added to the system (2). Then, the controlled system becomes The error state dynamic equations of system (3) can be denoted as (4) Then, the error dynamics in system (4) become (5)…”

Section: The Passive Feedback Controlmentioning

confidence: 99%

“…Since the pioneer study of Ott et al in 1990 [29], several effective methods for the control of chaotic systems have been proposed. The chaos control approaches include linear feedback control [13,15,16,18,22,24,41,44,47], nonlinear feedback control [7], time-delayed feedback control [34], adaptive control [2,40], sliding mode control [22,12], passive control [8,22,28,33,45], backstepping design [12,32], and intelligent control [20] methods. Among them, the linear feedback control has been widely used due to its simplicity of implementation.…”

Section: Introductionmentioning

confidence: 99%

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Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

Kocamaz

Göksu

Uyaroğlu

et al. 2018

ITC

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In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness. Finally, the comparative findings are discussed.

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Section: The Hyperchaotic Finance Systemmentioning

confidence: 99%

Section: The Passive Feedback Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

Kocamaz

Göksu

Uyaroğlu

et al. 2018

ITC

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“…With the improvement of linear singular system theory, there are more and more research results on the nonlinear singular system. [2][3][4][5][6][7][8][9][10][11] The stabilization results of the T-S fuzzy singular system using the sliding mode control method are given in References 2-5. In Reference 6, the output regulation of the singular system is realized, and state jump is also suppressed at switching moments.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time adaptive stabilization and H∞$$ {H}_{\infty } $$ control for a class of nonlinear Hamiltonian singular systems with parametric perturbations

Jin,

Sun,

Yang

2024

Intl J Robust & Nonlinear

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This article addresses the finite‐time adaptive stabilization and finite‐time adaptive control problems of a class of nonlinear Hamiltonian singular systems with parametric perturbations. Under the suitable state feedback control scheme, a dissipative differential‐algebraic form of the nonlinear Hamiltonian singular system is obtained. According to this dissipative form, the finite‐time adaptive stabilization of the nonlinear Hamiltonian singular system with unknown parametric perturbations is investigated using the Hamiltonian function method. Then, considering the system with the external disturbances, a finite‐time adaptive controller is designed. Finally, the simulation results of the nonlinear singular circuit system demonstrate the efficacy of the controller designed in this article.

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“…It is known that the control problems for normal uncertain nonlinear systems can be solved to some extent by the advanced adaptive control theory. And the adaptive control theory has been extended to solve the admissibility problems for nonlinear singular systems in References 35-37. Nevertheless, for the more complex uncertain nonlinear singular systems, and more complex control problems, such as nonlinear tracking control, a better way should be developed.…”

Section: Introductionmentioning

confidence: 99%

Observer‐based adaptive neural control for a class of nonlinear singular systems

Chen

Lin

Zhang

2020

Intl J Robust & Nonlinear

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The problem of observer-based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse-free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed-loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method. K E Y W O R D S adaptive neural control, output feedback, singular system, uncertain nonlinear system 1 Int J Robust Nonlinear Control. 2020;30:4043-4058. wileyonlinelibrary.com/journal/rnc © 2020 John Wiley & Sons, Ltd. 4043 4044 CHEN et al.nonstrict feedback systems. 11 In addition, the Newton-based observer, 19 sliding-mode, 20 and Lyapunov-based observer 21 are designed for nonlinear systems. Singular systems have been extensively studied because it can better describe the physical systems, such as power systems, economics, biological systems, and other areas. 22,23 The study of singular systems is much more complicated than that of the state-space systems because not only the stability but also the regularity and impulse-free should be considered. Recently, the study of singular systems is mainly based on the linear system theory. The observer design is addressed in References 24-27. The problems of stability analysis for singular Markovian jump systems, 28 and the admissibility for singular T-S fuzzy model 29 are studied. In References 30 and 31 , the analysis and control synthesis for singular systems with time delays are discussed. All the above results are based on linear matrix inequality (LMI) techniques. The above methods are regarded as effective methods for linear singular systems. However, for nonlinear, or uncertain singular systems, the T-S fuzzy model-based methods 22,32-34 will bring much conservatism. It is known that the control problems for normal uncertain nonlinear systems can be solved to some extent by the advanced adaptive control theory. And the adaptive control theory has been extended to solve the admissibility problems for nonlinear singular systems in References 35-37. Nevertheless, for the more complex uncertain nonlinear singular systems, and more complex control problems, such as nonlinear tracking control, a better way should be developed.In this article, an observer-based neural control scheme via output feedback is proposed for a class of uncertain nonlinear singular systems for the first time. In the proposed scheme, a reduced-order observer is constructed to estimate the unmeasured state vari...

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Adaptive Control for Nonlinear Singular Systems

Cited by 5 publications

References 18 publications

Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

Finite‐time adaptive stabilization and H∞$$ {H}_{\infty } $$ control for a class of nonlinear Hamiltonian singular systems with parametric perturbations

Observer‐based adaptive neural control for a class of nonlinear singular systems

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