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This study introduces a novel feedback control strategy to precisely manage switching times in dynamical systems influenced by noise. The method effectively controls escape probabilities from stable states, even without knowing the noise intensity.

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Area of Science:

  • Nonlinear dynamics
  • Stochastic processes
  • Control theory

Background:

  • Dynamical systems with multiple equilibria are susceptible to noise-induced transitions.
  • Controlling stochastic switching times is crucial for system stability and predictability.
  • Existing methods often struggle with unknown noise intensities or complex system dynamics.

Purpose of the Study:

  • To develop a generalizable strategy for controlling mean stochastic switching times in multi-stable systems under Gaussian white noise.
  • To demonstrate the ability to enhance or abate escape probabilities from stable states.
  • To achieve precise control over switching behavior irrespective of unknown noise levels.

Main Methods:

  • A feedback control strategy is synthesized, adjusting system dynamics based on proximity to the boundary of the attraction region.
  • The controller actively modifies the system's response to external stochastic perturbations.
  • Analytical validation is performed on a one-dimensional system, followed by numerical simulations on relevant dynamical systems.

Main Results:

  • The proposed control strategy successfully regulates the mean stochastic switching times.
  • The controller can effectively increase or decrease the likelihood of escaping a stable equilibrium.
  • The method's robustness is shown by its effectiveness even when the noise strength is unknown.
  • Numerical simulations confirm the strategy's efficacy across various important dynamical systems.

Conclusions:

  • A robust and adaptable feedback control method for managing stochastic switching in multi-stable dynamical systems has been presented.
  • This strategy offers precise control over system transitions, enhancing predictability and stability.
  • The approach holds significant potential for applications in fields requiring reliable control of noisy systems.