Abstract
For synchronization of a class of chaotic systems in the presence of nonvanishing uncertainties, a novel time-varying gain observer-based sliding mode control is proposed. First, a novel time-varying gain disturbance observer (TVGDO) is developed to estimate the uncertainties. Then, by using the output of TVGDO to modify sliding mode control (SMC), a new TVGDO-based SMC scheme is developed. Although the observation and control precision of conventional fixed gain disturbance observer-based control (FGDOC) for chaotic systems can be guaranteed by a high observer gain, the undesirable spike problem may be caused by the high gain if the initial values of estimate and true states are not equal. The most attractive feature of this work is that the newly proposed TVGDO can eliminate the spike problem by developing a time-varying gain scheme. Finally, the effectiveness of the proposed method is demonstrated by the numerical simulation.
Highlights
In the past decades, with the development of theoretical analysis methods of chaos, many chaos systems such as the Lorenz system [1], Rossler system [2], and Chen system [3] have been wildly studied. ese theoretical advancements of chaotic systems have been influentially applicated in many fields, such as power electrical systems [4, 5], robotics [6], lasers [7], and secure communications [8]
To improve the robustness of chaos synchronization in allusion to uncertainties, many modern robust control theories have been applied to design synchronization controllers, including H∞ robust control [10, 11], adaptive control [12, 13], neural network control [14, 15], observerbased control [16, 17], and sliding mode control (SMC) [18,19,20,21,22]
In [28,29,30], the SMC schemes were proposed by employing the disturbance observer (DO) to estimate the uncertainties in chaotic systems
Summary
With the development of theoretical analysis methods of chaos, many chaos systems such as the Lorenz system [1], Rossler system [2], and Chen system [3] have been wildly studied. ese theoretical advancements of chaotic systems have been influentially applicated in many fields, such as power electrical systems [4, 5], robotics [6], lasers [7], and secure communications [8]. The chattering problem of conventional SMC can be eliminated by using the estimation of uncertainties to replace the discontinuous control terms of SMC. In [28,29,30], the SMC schemes were proposed by employing the disturbance observer (DO) to estimate the uncertainties in chaotic systems. A new time-varying gain disturbance observer (TVGDO) is proposed to estimate the lumped uncertainties of the chaotic system. (1) Compared with conventional DO and ESO used in the uncertain chaotic systems, the most attractive feature of the proposed TVGDO is that the spike problem can be eliminated on the condition of the initial values of estimate and true states are not equal. Let ‖ · ‖ denote the Euclidean norm of a vector and its induced norm of a matrix
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