Abstract
In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based on backstepping and Lyapunov stability theory. The adaptive laws of the unknown parameters are derived by using the Lyapunov stability theory. To handle the effect caused by the input saturation, an auxiliary system is used to compensate the tracking error and synchronization error. The proposed adaptive tracking control and synchronization schemes ensure the effects of tracking and synchronization. Several examples have been detailed to illuminate the design procedure.
Highlights
Chaotic systems are extremely complex nonlinear systems highly sensitive to initial value and parametric uncertainties [1], they have been well known owing to their potential applications in communications, information, chemical reactions, lasers, biological systems, etc. [2]
To deal with the unknown parameters in chaotic system, T-S fuzzy system is used for modeling of chaotic systems [17], and fuzzy neural network is used for modeling of chaotic systems [18]
Compared with the above works, the main merits of this paper are listed as follows. (a) A systematic design scheme is presented for both synchronization and tracking control of chaotic systems. (b) The transient performance is adjustable by choosing proper design parameters and can be adjusted by choosing the initial value. (c) Both unknown parameters and input saturation are considered in this paper; the auxiliary system is designed to deal with saturation problem
Summary
Chaotic systems are extremely complex nonlinear systems highly sensitive to initial value and parametric uncertainties [1], they have been well known owing to their potential applications in communications, information, chemical reactions, lasers, biological systems, etc. [2]. The synchronization between two different chaotic systems with unknown parameters and external disturbances is realized by a robust adaptive sliding mode controller [21]. Considering the unmeasured states and unknown parameters, a novel neural network-based adaptive observer and an adaptive controller have been designed [23]. An adaptive controller based on fuzzy neural is given for uncertain chaotic systems, in which the auxiliary system is used to deal with saturation [28]. Motivated by the above works, both tracking and synchronization control for the Arneodo chaotic system with unknown parameters and input saturation is developed in this paper. (c) Both unknown parameters and input saturation are considered in this paper; the auxiliary system is designed to deal with saturation problem.
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