Asymptotic Feedback Stabilization of Boolean Control Networks With Random Impulsive Disturbances

Area of Science:

• Control Theory
• Network Science
• Discrete Mathematics

Background:

• Boolean control networks (BCNs) are essential for modeling complex systems.
• Random impulsive disturbances pose challenges to network stability.
• Existing models often lack methods for handling such stochastic dynamics.

Purpose of the Study:

• To investigate asymptotic feedback set stabilization for BCNs with random impulsive disturbances.
• To develop a novel framework for analyzing and controlling these systems.
• To design state feedback controllers for guaranteed convergence to a target set.

Main Methods:

• Utilizing a hybrid-index model and assuming independent and identically distributed (i.i.d.) intervals between impulses.
• Converting random impulsive BCNs (RI-BCNs) into impulsive-interval driven probabilistic BCNs (ID-PBCNs) using semi-tensor product (STP).
• Constructing the input-state transition probability matrix (IS-TPM) and analyzing convergence in hybrid and time domains.

Main Results:

• Establishing necessary and sufficient conditions for asymptotic feedback set stabilizability.
• Developing a state feedback controller design algorithm based on state-space partition.
• Demonstrating efficient convergence to a target set with minimal impulsive intervals.

Conclusions:

• The proposed methods effectively stabilize RI-BCNs with random impulsive disturbances.
• The controller design ensures asymptotic convergence to a specified target set.
• Simulation results validate the theoretical findings and the controller's performance.