  This paper provides a compositional scheme based on dissipativity approaches
for constructing finite abstractions of continuous-time continuous-space
stochastic control systems. The proposed framework enjoys the structure of the
interconnection topology and employs a notion of stochastic storage functions,
that describe joint dissipativity-type properties of subsystems and their
abstractions. By utilizing those stochastic storage functions, one can
establish a relation between continuous-time continuous-space stochastic
systems and their finite counterparts while quantifying probabilistic distances
between their output trajectories. Consequently, one can employ the finite
system as a suitable substitution of the continuous-time one in the controller
design process with a guaranteed error bound. In this respect, we first
leverage dissipativity-type compositional conditions for the compositional
quantification of the distance between the interconnection of continuous-time
continuous-space stochastic systems and that of their discrete-time (finite or
infinite) abstractions. We then consider a specific class of stochastic affine
systems and construct their finite abstractions together with their
corresponding stochastic storage functions. The effectiveness of the proposed
results is demonstrated by applying them to a temperature regulation in a
circular network containing 100 rooms and compositionally constructing a
discrete-time abstraction from its original continuous-time dynamic. The
constructed discrete-time abstraction is then utilized as a substitute to
compositionally synthesize policies keeping the temperature of each room in a
comfort zone.
