  Previous approaches to constructing abstractions for control systems rely on
geometric conditions or, in the case of an interconnected control system, a
condition on the interconnection topology. Since these conditions are not
always satisfiable, we relax the restrictions on the choice of abstractions,
instead opting to select ones which nearly satisfy such conditions via
optimization-based approaches. To quantify the resulting effect on the error
between the abstraction and concrete control system, we introduce the notions
of practical simulation functions and practical storage functions. We show that
our approach facilitates the procedure of aggregation, where one creates an
abstraction by partitioning agents into aggregate areas. We demonstrate the
results on an application where we regulate the temperature in three separate
zones of a building.
