Topology Control is one of principal questions in network design. Tree-decompositions with bags of small diameter models networks, and were used to construct compact routing schemes. Over time, the bags must change to reflect the changes in the network topology as nodes move around, or links failure. It must be possible to restore the service when there is a failure of an edge or a node in the network. In order to preserve the advantages of this structure, we propose to study the case where a node or edge is added to (resp. is removed from) the network and its effects on some invariants of a tree decomposition.