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Controllability of networked higher-dimensional systems with one-dimensional communication
Lin Wang1,2, Xiaofan Wang3,2, Guanrong Chen4
1Department of Automation, Shanghai Jiao Tong University, Ministry of Education, Shanghai, People's Republic of China wanglin@sjtu.edu.cn.
Summary
State controllability of networked systems is analyzed, considering topology and node dynamics. Findings reveal complex interactions affecting overall system control, with implications for designing robust networked dynamical systems.
Area of Science:
- Control Theory
- Networked Dynamical Systems
- Cybernetics
Background:
- Networked systems are increasingly complex, requiring analysis of state controllability.
- Understanding influences on controllability is crucial for system design and stability.
- Linear time-invariant (LTI) systems with one-dimensional connections present unique challenges.
Purpose of the Study:
- To investigate state controllability in higher-dimensional LTI networked systems.
- To analyze the impact of network topology, node dynamics, and control inputs.
- To establish necessary and sufficient conditions for network controllability.
Main Methods:
- Analysis of state controllability for general network topologies.
- Examination of specific topologies like cycles and chains.
- Development of theoretical conditions for controllability based on node and network properties.
Main Results:
- Observability of node systems is generally necessary for network controllability.
- Controllability of node systems is necessary for chain topologies but not always for cycles.
- Examples demonstrate that uncontrollable nodes can form controllable networks, and vice-versa.
Conclusions:
- Network topology and node dynamics significantly influence overall system controllability.
- The relationship between node and network controllability is non-trivial and topology-dependent.
- Findings provide insights for designing and controlling complex networked dynamical systems.
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