Robust adaptive finite‐time and fixed‐time synchronization of chaotic systems with smooth control

Wu, Jie; Ma, Ru-ru

doi:10.1002/rnc.5750

Cited by 21 publications

(10 citation statements)

References 47 publications

(134 reference statements)

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“…Chaotic systems exhibit highly nonlinear and unpredictable behavior. Therefore, the control of chaos has been an appealing and challenging topic for researchers 5–8 . Traditional control theory tends to linearize chaotic systems, which can lead to failure under several unexpected conditions.…”

Section: Introductionmentioning

confidence: 99%

Proximal policy optimization‐based controller for chaotic systems

Yau,

Kuo,

Luan

et al. 2023

Intl J Robust & Nonlinear

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Deep reinforcement learning (DRL) algorithms are suitable for modeling and controlling complex systems. Methods for controlling chaos, a difficult task, require improvement. In this article, we present a DRL‐based control method that can control a nonlinear chaotic system without any prior knowledge of the system's equations. We use proximal policy optimization (PPO) to train an agent. The environment is a Lorenz chaotic system, and our goal is to stabilize this chaotic system as quickly as possible and minimize the error by adding extra control terms to the chaotic system. Therefore, the reward function accounts for the total triaxial error. The experimental results demonstrated that the trained agent can rapidly suppress chaos in the system, regardless of the system's random initial conditions. A comprehensive comparison of different DRL algorithms indicated that PPO is the most efficient and effective algorithm for controlling the chaotic system. Moreover, different maximum control forces were applied to determine the relationship between the control forces and controller performance. To verify the robustness of the controller, random disturbances were introduced during training and testing, and the empirical results indicated that the agent trained with random noise performed better. The chaotic system has highly nonlinear characteristics and is extremely sensitive to initial conditions, and DRL is suitable for modeling such systems.

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Section: Introductionmentioning

confidence: 99%

Proximal policy optimization‐based controller for chaotic systems

Yau,

Kuo,

Luan

et al. 2023

Intl J Robust & Nonlinear

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show abstract

“…Although the FxS and control of chaotic systems have been successfully applied into many fields, such as power systems [15], PMSMs [18], memristor chaotic circuits [29], FWS [30], and so forth, there are few results for the chaotic finance systems. Zhao et al…”

Section: Introductionmentioning

confidence: 99%

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

et al. 2022

Nonlinear Dyn

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This paper concerns the problem of fixed-time synchronization(FxS) of masterslave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand.Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.

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“…A combination–combination synchronization is established in Khan and Mittal (2018) for time-delay chaotic systems using a robust adaptive sliding mode control law. In Wu and Ma (2021), the authors suggested a stochastic adaptive synchronization approach for chaotic systems with noise perturbations. Although the results are noticeable, the parametric uncertainties in this work have not been taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the singular perturbation theory, an observer-based adaptive neural network projective chaos synchronization method is designed in this work. The considered class of chaotic systems is relatively general and includes both disturbances and uncertainties, in contrast to some existing synchronization approaches that consider the master–slave systems to be almost known (Du et al, 2009; Harb and Zohdy, 2009; Wu et al, 2017) or those in which the effects of disturbances and uncertainties are neglected (Asadollahi et al, 2020; Ren and Zhang, 2019; Wu and Ma, 2021). 2.…”

Section: Introductionmentioning

confidence: 99%

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

Boubakir

Labiod

2022

Journal of Vibration and Control

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This paper addresses the design of an observer-based adaptive neural network chaos synchronization scheme for a general class of uncertain chaotic systems. The controller consists of an adaptive neural network control law and an extended state observer. The parameterization of the designed extended observer and the sufficient stability conditions are derived in the light of the singular perturbation theory. The extended observer is incorporated into the controller to reconstruct the synchronization error vector as well as to estimate the error between an ideal control law and the actual control. These estimated error signals are utilized in the adaptation mechanism of the neural network weight vector. In the presented chaos synchronization method, the knowledge of the models of the master–slave systems is not required and the controller only needs the projective synchronization error for its implementation. Numerical simulations are performed along with a comparative study to demonstrate the efficiency and effectiveness of the suggested chaos synchronization approach.

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Robust adaptive finite‐time and fixed‐time synchronization of chaotic systems with smooth control

Cited by 21 publications

References 47 publications

Proximal policy optimization‐based controller for chaotic systems

Proximal policy optimization‐based controller for chaotic systems

Adaptive fixed-time synchronization of Lorenz systems with application in chaotic finance systems

Observer-based adaptive neural network control design for projective synchronization of uncertain chaotic systems

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