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A new approach for global controllability of higher order Boolean control network
Summary
Researchers analyzed control sequences for higher-order Boolean control networks, providing a method to ensure systems reach desired states while avoiding specific sets. This work establishes conditions for global controllability and fixed-time control.
Area of Science:
- Control Theory
- Discrete Mathematics
- Network Science
Background:
- Higher-order Boolean control networks (HOBNCs) are complex systems requiring robust control strategies.
- Controlling HOBNCs to reach specific states while avoiding undesirable states is a critical challenge.
- Existing methods may not fully address the nuances of global reachability and avoidance sets in HOBNCs.
Purpose of the Study:
- To investigate the global control problem for HOBNCs with an avoidance set.
- To determine the number of control sequences for state transition while avoiding a specified set.
- To establish conditions for global controllability and fixed-time global controllability of HOBNCs.
Main Methods:
- Employed the semi-tensor product (STP) for analyzing HOBNC dynamics.
- Utilized classical nonnegative matrix theory to derive controllability conditions.
- Developed a framework for quantifying control sequences and establishing reachability criteria.
Main Results:
- Provided a method to count control sequences driving HOBNCs from initial to destination states, avoiding a given set.
- Defined and presented necessary and sufficient conditions for the global controllability of HOBNCs with avoidance sets.
- Obtained a sufficient condition for k-fixed-time global controllability, enhancing temporal control precision.
Conclusions:
- The study offers a comprehensive approach to controlling HOBNCs with avoidance constraints.
- The derived conditions for global and fixed-time controllability are crucial for designing reliable HOBNC systems.
- The presented example validates the theoretical findings and demonstrates practical applicability.
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