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Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints
Ahmad Taher Azar1,2, Fernando E Serrano3,4, Quanmin Zhu5
1College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
Entropy (Basel, Switzerland)
|September 28, 2021
Summary
This study introduces a new chaotic system, achieving robust stabilization and synchronization using a novel controller. The system
Area of Science:
- Nonlinear Dynamics
- Control Theory
- Chaos Theory
Background:
- Chaotic systems exhibit complex, unpredictable behavior.
- Stabilization and synchronization are crucial for controlling chaotic dynamics.
- Sigmoidal functions can be used to generate chaotic behavior.
Purpose of the Study:
- To present a novel chaotic system utilizing a sigmoidal function.
- To design a robust controller for stabilizing the chaotic system.
- To achieve synchronization between drive and response chaotic systems.
Main Methods:
- Bifurcation analysis to identify stability regions.
- Design of a robust controller using a control Lyapunov function.
- Implementation of an extra state for tractable saturated input conditions.
Main Results:
- The novel chaotic system demonstrates controllable chaotic behavior.
- The robust controller successfully drives system variables to equilibrium in finite time.
- Synchronization of the chaotic system is achieved by driving the error to zero.
Conclusions:
- The proposed robust control strategy effectively stabilizes and synchronizes the novel chaotic system.
- The inclusion of an extra state ensures mathematical tractability of control law design.
- Numerical simulations validate the theoretical findings.
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