Observability Research Papers - Academia.edu (original) (raw)

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. Y. Y. Liu et al. started a new trend in network science when they become the first to analyse complex networks as dynamical systems with the maximum matching algorithm 1. They considered nodes as state variables, interpreted networks as linear multivariable dynamical systems and studied the controllability and observability of these models 2. Based on these principles Yan et al. analysed the required energy for controlling a system 3 , Ruths & Ruths determined control profiles for cluster networks 4 , Pósfai, Liu, Slotine & Barabási examined how the degree correlation influences the required inputs 5 , and the robustness of an input configuration was also improved by X. Liu et al. 6. The application of the proposed method is also widespread, for example, Penn, Knight, Chalkias, Velenturf & Lloyd applied this approach on fuzzy cognitive maps as well 7. These studies impressively show the benefits of network science-based analysis of dynamical systems. Despite the groundbreaking successes, some critiques have also been received. Müller & Schuppert determined that in transcriptional networks the method drastically overestimates the number of necessary inputs 8. Sun, Cornelius, Kath & Motter also highlighted that the methodology needs further clarification because the method gives incorrect results for non-linear systems even for small examples 9. This fact has also been evinced by Dunne, Williams, & Martinez 10. Another problem is that researchers examined the correlation between necessary inputs generated by the proposed method, and structural properties, like degree distribution, but they did not take into account that the result of the maximum matching algorithm is not unique 11. The most contestable point of the network-based analysis is that it is based on a static and structural view of the system. We wish to offer a solution to the previously mentioned problems by examining how system dynamics should be represented realistically. The usage of proper topology is important and a crucial part of network analysis, as this is the only way to emphasise dynamics in statical representations. We introduce connection types according to the typical relationships of the state variables. To analyse how the determined connection types influence the controllability and observability of dynamical systems we developed a MATLAB toolbox. We examined 35 example networks used in articles and found that 27 do not represent dynamical systems. By comparing them with 18 independently selected dynamical systems, we revealed significant differences. 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.