Discrete synchronization of hybrid systems

Control theory is currently faced with new paradigms and challenges that fall beyond traditional problems. Nowadays applications tend to be distributed, and require partial synchronization among their various subsystems. In this paper, we give initial steps towards discrete synchronization problems for systems which are compositions of several, possibly distributed, hybrid systems. Such problems arise frequently in the coordination of multi-agent systems, where each agent is modeled as a hybrid system. This results in control problems where the model is the composition of decoupled subsystems, but the specification is coupled across subsystems. A centralized solution to this problem requires computing the product hybrid system resulting in state explosion. We alternatively consider decentralized solutions to such discrete synchronization problems. Partially decentralized synchronization is achieved if each subsystem is allowed to communicate with the subsystems it needs to partially synchronize with. The required communication between agents is provided by modeling abstractions of the remaining agents. These abstractions, which are property-dependent, are then used to derive local controllers using global, but minimal, observations.