809 research outputs found

    Robust adaptive synchronization of a class of uncertain chaotic systems with unknown time-delay

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    In this paper, a robust adaptive control strategy is proposed to synchronize a class of uncertain chaotic systems with unknown time delays. Using Lyapunov theory and Lipschitz conditions in chaotic systems, the necessary adaptation rules for estimating uncertain parameters and unknown time delays are determined. Based on the proposed adaptation rules, an adaptive controller is recommended for the robust synchronization of the aforementioned uncertain systems that prove the robust stability of the proposed control mechanism utilizing the Lyapunov theorem. Finally, to evaluate the proposed robust and adaptive control mechanism, the synchronization of two Jerk chaotic systems with finite non-linear uncertainty and external disturbances as well as unknown fixed and variable time delays are simulated. The simulation results confirm the ability of the proposed control mechanism in robust synchronization of the uncertain chaotic systems as well as to estimate uncertain and unknown parameters

    Stabilizing Unstable Periodic Orbit of Unknown Fractional-Order Systems via Adaptive Delayed Feedback Control

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    This paper presents an adaptive nonlinear delayed feedback control scheme for stabilizing the UPO of unknown fractional-order chaotic systems. The proposed control scheme uses the Lyapunov approach and sliding mode control technique to ensure that the closed-loop control system is asymptotically stable on a periodic trajectory sufficiently close to the UPO of the fractional-order chaotic system. It is guaranteed that the closed-loop system will be robust to external disturbances with unknowable bounds. Finally, the proposed method is used to stabilize the UPO of the fractional-order Duffing and Gyro systems, and extensive simulation results are used to evaluate its performance

    Gain-scheduled sliding-mode-type iterative learning control design for mechanical systems

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    In this paper, a novel gain-scheduled sliding-mode-type (SM-type) iterative learning (IL) control approach is proposed for the high-precision trajectory tracking of mechanical systems subject to model uncertainties and disturbances. Based on the SM variable, the proposed controller is synthesized involving a feedback regulation item, a feedforward learning item, and a robust switching item. The feedback regulation item is adopted to regulate the position and velocity tracking errors, the feedforward learning item is applied to handle the model uncertainties and repetitive disturbance, and the robust switching item is introduced to compensate the nonrepetitive disturbance and linearization residual error. Moreover, the gain-scheduled mechanism is employed for both the feedback regulation item and feedforward learning item to enhance the convergence speed. Convergence analysis illustrates that the position and velocity tracking errors can eventually regulate to zero under the proposed controller. By combining the advantages of both SM control and IL control, the proposed controller has strong robustness against model uncertainties and disturbances. Lastly, simulations and comparisons are provided to evaluate the efficiency and excellent performance of the proposed control approach

    Risk Control for Synchronizing a New Economic Model

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    Risk analysis in control problems is a critical but often overlooked issue in this research area. The main goal of this analysis is to assess the reliability of designed controllers and their impact on applied systems. The chaotic behavior of fractional-order economical systems has been extensively investigated in previous studies, leading to advancements in such systems. However, this chaotic behavior poses unpredictable risks to the economic system. This paper specifically investigates the reliability and risk analysis of chaotic fractional-order systems synchronization. Furthermore, we present a technique as a new mechanism to evaluate controller performance in the presence of obvious effects. Through a series of simulation studies, the reliability and risk associated with the proposed controllers are illustrated. Ultimately, we show that the suggested technique effectively reduces the risks associated with designed controllers

    Robust fractional-order fast terminal sliding mode control with fixed-time reaching law for high-performance nanopositioning

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    Open Access via the Wiley Agreement ACKNOWLEDGEMENTS This work is supported by the China Scholarship Council under Grant No. 201908410107 and by the National Natural Science Foundation of China under Grant No. 51505133. The authors also thank the anonymous reviewers for their insightful and constructive comments.Peer reviewedPublisher PD

    Adaptive fractional order terminal sliding mode control of a doubly fed induction generator- based wind energy system

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    The dynamic model of a doubly fed induction generator (DFIG)-based wind energy system is subjected to nonlinear dynamics, uncertainties, and external disturbances. In the presence of such nonlinear effects, a high-performance control system is required to guarantee the smooth and maximum power transfer from the wind energy system to the ac grids. This paper proposes a novel fractional order adaptive terminal sliding mode control system for both the rotor and grid side converters of the DFIG system. The stability of the closed loop is ensured using the fractional order Lyapunov theorem. Numerical results are presented to show the superiority of the proposed control method over the classical sliding mode control system and the proportional integral controllers

    The global sliding mode tracking control for a class of variable order fractional differential systems

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    In this paper, a novel variable order fractional control approach is proposed for tracking control of both of variable order fractional and constant order fractional order system with uncertain and external disturbance terms. In term of the global sliding mode control theory and terminal sliding mode control method, the system states are guaranteed to stay on the switching surface from the initial time, and then converge to the origin by the designed controllers which are continuous input signals. Such controllers avoid the undesirable chattering and remove the effects of uncertain and external disturbance completely. Finally, the comparison between the variable order fraction controller and the constant order fractional controller is given by numerical simulation, furthermore, numerical results on the effects of the tracking control are provided.This paper has been supported by National Natural Science Foundation of China (No.12002194; No.12072178; No.11732005), Natural Science Foundation of Shandong Province (No.ZR2020QA037; No.ZR2020MA054), Ministerio de Ciencia, Innovación y Universidades (No. PGC2018-097198-B-I00) and Fundación Séneca de la Región de Murcia (No.20783/PI/18)

    Disturbance observer-based adaptive sliding mode synchronization control for uncertain chaotic systems

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    The synchronization control problem of a class of chaotic systems with unknown uncertainties and outside perturbation is addressed in this article by employing an innovative adaptive sliding mode controller (SM, SMC) constructed using a disturbance observer (DO). For the synchronous error system, the external disturbances estimated by the disturbance observer cannot be measured directly. If the appropriate gain matrix is chosen, the DO can approximate the unknown external disturbances well. Then a continuous adaptive SM controller based on the DO's output is designed by using adaptive techniques and the system dimensional expansion method. The Duffing-Holmes chaotic system is finally selected to numerically test the efficiency of the suggested strategy

    Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties

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    This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system
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