Time-optimal open-loop set stabilization of Boolean control networks

Area of Science:

• Control Theory
• Discrete Dynamical Systems
• Boolean Networks

Background:

• Boolean control networks (BCNs) are widely used to model complex biological systems.
• Stabilization of BCNs with unobservable initial states presents unique challenges.
• The equivalence of open-loop and closed-loop control for BCN stabilization is questioned.

Purpose of the Study:

• To demonstrate the nonequivalence of open-loop and closed-loop control for BCNs with unobservable initial states.
• To explore and establish criteria for open-loop set stabilization in such systems.
• To derive time-optimal open-loop set stabilizers.

Main Methods:

• Illustrative example to show control nonequivalence.
• Derivation of mathematical criteria for open-loop set stabilization.
• Development of algorithms for time-optimal control sequence generation.

Main Results:

• Open-loop and closed-loop control are not equivalent for BCN stabilization with unobservable initial states.
• Criteria for open-loop set stabilization are formally derived.
• Time-optimal open-loop set stabilizers are proposed for stabilizable BCNs.

Conclusions:

• The findings highlight the importance of considering control strategy when initial states are unobservable.
• The derived criteria and proposed stabilizers offer practical tools for BCN control.
• This work advances the understanding of control in discrete dynamical systems with incomplete state information.