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Disturbance Decoupling in Graphs

Seuren, F.M. (2017) Disturbance Decoupling in Graphs.

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Abstract:A graph can be interpreted as a discrete time system where information moves from a vertex to the neighbors at each step. Disturbances can change the information at these vertices. Can such a disturbance occurring in one or multiple vertices of a graph be coun- teracted by controlling another vertex? In this report we study this so-called disturbance decoupling problem, and the recursive algorithm that can solve it for discrete time systems. We rewrite simple graph structures as discrete systems and solve the problem for these basic examples. By observing what happens in the graph in each step of the recursive algorithm we are able to form hypotheses on the relation between disturbance decoupling and the graph structure. Based on these hypotheses we proved theorems that solved the problem for certain types of graphs, like graphs where each vertex has no more than one incoming edge. For other graphs, where vertices may have multiple incoming edges, we have a strong suspicion on how to solve the disturbance decoupling problem.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics BSc (56965)
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