Abstract
Network theory based controllability and observability analysis have become widely used techniques. We realized that most applications are not related to dynamical systems, and mainly the physical topologies of the systems are analysed without deeper considerations. Here, we draw attention to the importance of dynamics inside and between state variables by adding functional relationship defined edges to the original topology. The resulting networks differ from physical topologies of the systems and describe more accurately the dynamics of the conservation of mass, momentum and energy. We define the typical connection types and highlight how the reinterpreted topologies change the number of the necessary sensors and actuators in benchmark networks widely studied in the literature. Additionally, we offer a workflow for network science-based dynamical system analysis, and we also introduce a method for generating the minimum number of necessary actuator and sensor points in the system.
Highlights
To analyse how the determined connection types influence the controllability and observability of dynamical systems we developed a MATLAB toolbox
After a brief introduction to the network science-based analysis of dynamical systems, we present how the functional relationships of state variables define different types of connections, and propose a workflow to evaluate how these connection types influence the number of necessary actuators and sensors that ensure controllability and observability
We conclude that in most of the articles dealing with network science-based controllability and observability analysis mainly the physical topologies of the systems are studied, while the analysis of the realistic state-transition matrix-based topologies can lead to significantly different conclusions
Summary
To analyse how the determined connection types influence the controllability and observability of dynamical systems we developed a MATLAB toolbox. While in dynamical systems the number of inputs and outputs does not change when the proper topology of the model is studied, in the case of other networks more than 95% of inputs and outputs disappeared because of the determined connection types.
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