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Zero-Norm Distance to Controllability of Linear Dynamic Networks
IEEE Transactions on Cybernetics
|October 8, 2024
Summary
This study introduces the zero-norm distance to controllability (ZNDC) for dynamical networks. We show ZNDC is NP-hard to compute but offer heuristic algorithms and bounds for practical applications.
Area of Science:
- Control Theory
- Network Science
- Systems Engineering
Background:
- Dynamical networks are often uncontrollable.
- Achieving controllability requires parameter perturbations.
- Existing distance metrics may not be suitable.
Purpose of the Study:
- Define and analyze the zero-norm distance to controllability (ZNDC).
- Investigate the computational complexity of ZNDC.
- Develop practical algorithms for ZNDC computation.
Main Methods:
- Formulated ZNDC for linear dynamical systems.
- Proved ZNDC is NP-hard, even for state matrix perturbations.
- Developed two heuristic algorithms: greedy selection and weighted norm relaxation with convex-concave procedure.
Main Results:
- Established the genericity of ZNDC, rendering other norms less relevant.
- Provided non-trivial lower and upper bounds for ZNDC.
- Demonstrated the performance of heuristic algorithms on multi-agent systems.
Conclusions:
- ZNDC is a crucial metric for network controllability.
- Heuristic algorithms offer practical solutions for computing ZNDC.
- The findings are applicable to uncontrollable networks in multi-agent systems.
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