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Eric S. Kim, Murat Arcak, Sanjit A. Seshia.  2017.  Symbolic control design for monotone systems with directed specifications. Automatica. 83:10-19.

We study the control of monotone systems when the objective is to maintain trajectories in a directed set (that is, either upper or lower set) within a signal space. We define the notion of a directed alternating simulation relation and show how it can be used to tackle common bottlenecks in abstraction-based controller synthesis. First, we develop sparse abstractions to speed up the controller synthesis procedure by reducing the number of transitions. Next, we enable a compositional synthesis approach by employing directed assume-guarantee contracts between systems. In a vehicle traffic network example, we synthesize an intersection signal controller while dramatically reducing runtime and memory requirements compared to previous approaches.