Abstract
In this paper, first, a nonlinear feedback controller for achieving chaos control of a novel multi-wing chaotic system is presented. The nonlinear feedback controller has two parts. The first part is used to compensate an equilibrium point for the multi-wing chaotic system. The second part is a linear state feedback controller. The nonlinear feedback controller can globally asymptotically stabilize the multi-wing chaotic system to the equilibrium point. Stability conditions are given by using the Barbashin–Krasovskii theorem. Then, a linear state feedback controller for achieving chaos synchronization of the multi-wing chaotic system is presented. The linear state feedback controller can asymptotically stabilize the chaos synchronization error system to the origin. Stability conditions are given by using the passivity-based theory. Finally, a multi-frequency weak signal detection method is presented based on chaos control of the multi-wing chaotic system. The detection method can detect the frequencies of the weak signal and does not need to determine the critical point.
Highlights
Chaos control states the use of controllers to improve the characteristics of a chaotic system so that the system becomes stable at a chosen position or tracks a desired trajectory
This paper studies chaos control, chaos synchronization, and application of the smooth multi-wing chaotic system
The smooth multi-segment nonlinear function is constructed by using the smooth bounded nonlinear function
Summary
Chaos control states the use of controllers to improve the characteristics of a chaotic system so that the system becomes stable at a chosen position or tracks a desired trajectory. Some methods have been presented to achieve chaos control and chaos synchronization, such as timedelayed feedback control, act-and-wait time-delayed feedback control, state feedback control, composite linear control, semilinear control, output-feedback control, proportion integral control, composite nonlinear feedback based integral sliding mode control, coupling control, and dynamic control.12 These methods were successfully used in some general chaotic systems and were not extended to the multi-wing chaotic system. The linear state feedback controller can synchronize two identical multi-wing chaotic systems that start from different initial values.
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