Controllability and observability in complex networks - the effect of connection types

Area of Science:

• Control theory
• Network science
• Dynamical systems analysis

Background:

• Network theory is widely applied to controllability and observability analysis.
• Current applications often focus on physical topologies, neglecting internal system dynamics.
• This overlooks the crucial role of state variable interactions in system behavior.

Purpose of the Study:

• To highlight the importance of internal dynamics in network-based system analysis.
• To introduce a novel approach by adding functional relationship edges to physical network topologies.
• To improve the accuracy of dynamical system modeling and analysis.

Main Methods:

• Redefining network topologies to include functional relationships between state variables.
• Analyzing benchmark networks with these reinterpreted topologies.
• Developing a workflow for network science-based dynamical system analysis.
• Introducing a method for optimizing sensor and actuator placement.

Main Results:

• The reinterpreted networks more accurately represent the dynamics of mass, momentum, and energy conservation.
• Functional network topologies alter the number of required sensors and actuators compared to physical topologies.
• A systematic workflow and optimization method for sensor/actuator placement are provided.

Conclusions:

• Incorporating functional relationships significantly enhances network-based dynamical system analysis.
• This approach leads to more accurate modeling and efficient control system design.
• The proposed methods offer a pathway to optimize sensor and actuator placement for complex systems.