Abstract
This article proposes a synchronization technique for uncertain hyperchaotic systems in the modified function projective manner using integral fast terminal sliding mode (I-FTSM) and adaptive second-order sliding mode algorithm. The new I-FTSM manifolds are introduced with the aim of having the fast convergence speed. The proposed continuous controller not only results in the robustness and high-accuracy synchronization in the presence of unknown external disturbances and/or model uncertainties but also helps alleviating the chattering effect significantly. Numerical simulation results are provided to illustrate the effectiveness of the proposed control design technique and verify the theoretical analysis.
Highlights
Synchronization of chaotic or hyperchaotic systems (HPSs) has attracted enormous research efforts from the control community as the recent reports have shown the potential in many areas such as secure communications, image encryption, information processing, diagnosis and identification, power converters, chemical reaction and biological systems [1]–[6]
While the existing approaches either do not deal with external disturbances and uncertainties (EDaU) [8]–[10] or require the upper bounds of EDaU, our approach is able to successfully synchronize the HPSs against the unknown external disturbance and uncertainties. Compared to both classic adaptive control approaches [13]–[17] and finite-time control (FTC) ones [19]–[24] which replace sign(·) with some smooth approximation that only make modified function projective synchronization (MFPS) errors either bounded or enter into the neighbor centered at the origin, all MFPS errors is ensured to reach zero in finite time by our proposed one
Remark 7: If there are no effects of EDaU on the synchronized HPSs, the second-order sliding mode in (22) will be maintained from the beginning, which implies that the differential equation (12) exhibits the behavior of the closed-loop system
Summary
Synchronization of chaotic or hyperchaotic systems (HPSs) has attracted enormous research efforts from the control community as the recent reports have shown the potential in many areas such as secure communications, image encryption, information processing, diagnosis and identification, power converters, chemical reaction and biological systems [1]–[6]. While the existing approaches either do not deal with EDaU [8]–[10] or require the upper bounds of EDaU (see [11] and [12]), our approach is able to successfully synchronize the HPSs against the unknown external disturbance and uncertainties Compared to both classic adaptive control approaches [13]–[17] and FTC ones [19]–[24] which replace sign(·) with some smooth approximation that only make MFPS errors either bounded or enter into the neighbor centered at the origin, all MFPS errors is ensured to reach zero in finite time by our proposed one. The control action is established to exhibit the sliding motion in finite time and maintain such a motion
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