Set Stabilization of Probabilistic Boolean Control Networks: A Sampled-Data Control Approach

Area of Science:

• Control Theory
• Network Science
• Computer Science

Background:

• Probabilistic Boolean Control Networks (PBCNs) are complex systems requiring robust control strategies.
• Sampled-data (SD) state-feedback control introduces challenges in system stabilization due to discrete time observations.
• Achieving set stabilization is crucial for ensuring predictable system behavior.

Purpose of the Study:

• To investigate set stabilization of PBCNs under SD state-feedback control.
• To develop criteria and controllers for finite and infinite time stabilization.
• To analyze the influence of sampled periods on stabilization.

Main Methods:

• Algorithms for identifying sampled point sets and control invariant sets.
• Development of necessary and sufficient criteria for finite-time set stabilization.
• Design of time-optimal SD state-feedback controllers.
• Derivation of criteria for infinite-time set stabilization using reachable sets.

Main Results:

• A necessary and sufficient criterion for finite-time global set stabilization is established.
• A time-optimal controller is designed for finite-time stabilization.
• The significant impact of sampled period on stabilization time and feasibility is demonstrated.
• A criterion for infinite-time global set stabilization is obtained, along with methods to find all possible controllers.

Conclusions:

• The proposed methods effectively achieve set stabilization for PBCNs under SD state-feedback control.
• The findings provide valuable insights into the design and analysis of control systems with sampled data.
• The study confirms the critical role of sampled period in the successful stabilization of PBCNs.