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Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation
Xiaoshuai Ding1, Jinde Cao2, Ahmed Alsaedi3
1School of Mathematics and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210096, China; School of Education, Xizang Minzu University, Xianyang 712082, China.
Summary
This study achieves fixed-time synchronization for complex-valued neural networks with uncertain parameters and discontinuous functions. A new control method ensures synchronization within a predictable time, independent of initial states.
Area of Science:
- Complex-valued neural networks
- Nonlinear control systems
- Synchronization theory
Background:
- Fixed-time synchronization is crucial for complex-valued neural networks (CVNNs) but challenging due to discontinuous activations and parameter uncertainties.
- Existing methods often lack guaranteed finite-time convergence or independent settling time bounds.
Purpose of the Study:
- To develop a novel control strategy for achieving fixed-time synchronization in CVNNs.
- To establish conditions for guaranteed synchronization within a finite, tunable time.
- To extend the methodology for fixed-time anti-synchronization.
Main Methods:
- Design of a novel feedback control procedure for slave CVNNs.
- Application of Filippov discontinuity theories to handle discontinuous activation functions.
- Utilization of Lyapunov stability theories to derive control parameters and settling time bounds.
Main Results:
- Sufficient conditions are established to guarantee fixed-time synchronization for the addressed CVNNs.
- A uniform upper bound for the settling time is derived, adjustable independently of initial conditions.
- Criteria for fixed-time anti-synchronization are also presented for the same system.
Conclusions:
- The proposed control method effectively achieves fixed-time synchronization and anti-synchronization for CVNNs.
- The finite settling time is controllable and independent of initial states, offering practical advantages.
- The theoretical findings are validated through a numerical example.