A control problem for hybrid systems with discrete inputs and outputs

We address the control synthesis of hybrid systems with discrete inputs and outputs. The control objective is to ensure that the events of the closed-loop system belong to the language of the control requirements. The controller is sampling-based and it is representable by a finite-state machine. We formalize the control problem and provide a theoretically sound solution based on finite-state abstractions of the symbolic behavior of the plant. In addition, we identify classes of hybrid systems for which a suitable finite-state abstraction can be computed and we sketch the corresponding algorithms