  We consider a security setting in which the Cyber-Physical System (CPS) is
composed of subnetworks where each subnetwork is under ownership of one
defender. Such CPS can be represented by an attack graph where the defenders
are required to invest (subject to a budget constraint) on the graph's edges in
order to protect their critical assets (where each defender's critical asset
has a certain value to the defender if compromised). We model such CPS using
Hybrid Input-Output Automaton (HIOA) where each subnetwork is represented by a
HIOA module. We first establish the building blocks needed in our setting. We
then present our model that characterizes the continuous time evolution of the
investments and discrete transitions between different states (where each state
represents different condition and/or perturbation) within the system. Finally,
we provide a real-world CPS example to validate our modeling.

Systems and Control;Systems and Control