  In decentralized systems, branching behaviors naturally arise due to
communication, unmodeled dynamics and system abstraction, which can not be
adequately captured by the traditional sequencing-based language equivalence.
As a finer behavior equivalence than language equivalence, bisimulation not
only allows the full set of branching behaviors but also explicitly specifies
the properties in terms of temporal logic such as CTL* and mu-calculus. This
observation motivates us to consider the decentralized control of discrete
event systems (DESs) for bisimulation equivalence in this paper, where the
plant and the specification are taken to be nondeterministic and the supervisor
is taken to be deterministic. An automata-based control framework is
formalized, upon which we develop three architectures with respect to different
decision fusion rules for the decentralized bisimilarity control, named a
conjunctive architecture, a disjunctive architecture and a general
architecture. Under theses three architectures, necessary and sufficient
conditions for the existence of decentralized bisimilarity supervisors are
derived respectively, which extend the traditional results of supervisory
control from language equivalence to bisimulation equivalence. It is shown that
these conditions can be verified with exponential complexity. Furthermore, the
synthesis of bisimilarity supervisors is presented when the existence condition
holds.
