Statistical Evaluation of Minimal Node Cardinality Disturbance Decoupling over Networks
Tomasz Jakub Mazurek
Avancerad (30hp)
kl 13:15, Transformen (In English)
[Abstract]This report investigates how different graph topologies affect the performance of the minimal node cardinality disturbance decoupling algorithms. Disturbance decoupling refers to the problem of designing control laws that prevent disturbances from specified nodes from propagating to specified target nodes in a network. Three approaches are studied: state feedback, output feedback, and dynamical feedback. The algorithms are systematically tested on both randomly generated graphs, including Erdós-Rényi, Watts Strogatz, and scale free models, and on a wide range of real-world networks, taken from different open-source database.
Results show that network topology has a strong influence on decoupling cost, that we measure as the number of control nodes and measurements nodes required to the disturbance decoupling problem, and the occurrence of trivial solutions, where the minimal cost solution corresponds to choosing to place the controls directly on the targets. Graphs with hubs and hierarchical structures, such as scale free and animal networks, are generally cheaper to decouple, while dense Erdós-Rényi and certain small-world configurations are more expensive. State feedback consistently achieves the lowest costs but assumes full state availability. Output feedback provides a more realistic setting but results in higher costs, whereas dynamical feedback improves performance relative to output feedback. These findings highlight the importance of structural properties such as degree distribution, clustering, and connectivity when designing control strategies for networked systems |