In this paper, based on adaptive control and terminal sliding mode control method, we introduce a new four-dimensional fractional-order (4-D FO) Rösslor hyperchaotic system with uncertainty and external disturbances, and design a new controller to study its synchronization problem. First, a fractional order sliding surface is designed to make the error dynamics converge to near zero in finite time on the sliding surface, and then, a new sliding controller with adaptive updating laws is designed , which eliminates the effect of nonlinear terms in the systems and makes the error system converge to zero quickly , this results in synchronized of the drive and response systems, finally, based on the 4-D FO Rösslor chaotic system, numerical simulations show that the controller based on adaptive control and terminal sliding mode designed in this paper has good practicality and feasibility.
Adaptive backstepping sliding mode control method is used to synchronize two Volta’s chaotic systems with external disturbances. The hyperbolic tangent function is adopted to replace the sign function in the sliding mode controller, to weaken the chatter problem caused by the sign function. Using Lyapunov theory and Barbalat's Lemma to prove the asymptotic convergence of the proposed control system. The numerical simulation demonstrates the effectiveness of the designed controller.
To study the chaotic phenomenon of fractional-order permanent magnet synchronous motor (FOPMSM) and its control problem, a strategy of decoupled adaptive backstepping chaotic control is proposed based on feedback decoupling control for fractional-order permanent magnet synchronous motor (FOPMSM) system to reduce the order, and the adaptive backstepping method is used to design the chaotic controller according to the decoupled system. The fractional-order permanent magnet synchronous motor (FOPMSM) system's stability is analyzed using the Mittag-Leffler stability theorem. The simulation results show that the decoupled adaptive backstepping control can bring the permanent magnet synchronous motor (FOPMSM) out of the chaotic state quickly and with a fast response.
Xinlei An first proposed the An-System in 2010, which has been studied by many scholars, but there are few control studies based on the fractional-order An-System. In this paper, by utilizing the fractional calculus theory and adaptive finite time control method, dynamics of the fractional-order An-System are studied. In order to eliminate the chaotic behavior in the An-System, an adaptive finite-time controller is designed. Then we prove its rationality by Chaos Control Theory. Finally, numerical simulation is applied to verify the effectiveness, convergence and robustness of the controller.
We discuss the problem of the projection synchronization of fractional-order chaotic system in this paper, which has different orders and parameters identification. We also design a new controller of adaptive projection synchronization and identification parameter law. By using the J function criterion, we prove that the synchronization system can be achieved. Finally, from the numerical simulation, we can obtain that the controller we introduced and parameter identification are highly effective.
In recent years, Bhalekar-Gejji system has been widely studied for their wealthy dynamic behavior and application background, however, synchronization of fractional-order Bhalekar-Gejji systems has been very little studied. In this paper, the synchronization problem of fractional-order Bhalekar-Gejji system is studied, and the controller and parameter updating method are designed based on fractional calculus theory, backstepping method and adaptive sliding mode control method. Finally, the effectiveness and robustness of the scheme are verified by numerical simulation.
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