Abstract
This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the abstraction preserves the dynamics of the original model. We develop a compositional approach to abstraction-based controller synthesis based on the notions of approximate composition and incremental input-to-state stability. In particular, given a large system consisting of interconnected components, we provide conditions under which the notion of approximate (alternating) simulation relation is preserved when moving from the subsystems to the large interconnected system. The effectiveness of the proposed results has been evaluated through traffic congestion control.
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