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This paper formulates and studies the concepts of approximate (alternating)bisimulation relations characterizing equivalence relations betweeninterconnected systems and their abstractions. These equivalence relationsguarantee that the symbolic model conserves the original model's dynamics. Wedevelop a compositional approach for abstraction-based controller synthesis byrelying on the notions of approximate composition and incrementalinput-to-state stability. In particular, given a large-scale system consistingof interconnected components, we provide conditions under which the concept ofapproximate (alternating) simulation relation is preserved when going from thesubsystems to the large-scale interconnected system. The engineering relevanceof the theoretical results has been evaluated through an application in trafficcongestion control.

Compositional Approximately Bisimilar Abstractions of Interconnected Systems