We address the control synthesis of hybrid systems with discrete inputs, disturbances 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. The solution is based on solving a discrete-event control problem for a finite-state abstraction of the plant. We propose a specific construction for the finite-state abstraction. This construction is not based on discretizing the state-space, but rather on converting the continuous-time hybrid system to a discrete-time one based on sampling. The construction works only for a specific class of hybrid systems. We describe this class of systems and we provide an example of such a system, inspired by an industrial use-case.

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International Federation of Automatic Control
A. Giua , M. Silva (Manuel) , J. Zaytoon
Computational Topology for Systems and Control
IFAC Conference on Analysis and Design of Hybrid Systems
Scientific Computing

Petreczky, M., van Beek, D. A., Rooda, J., Collins, P., & van Schuppen, J. (2009). Sampled-data control of hybrid systems with discrete inputs and outputs. In A. Giua, M. Silva, & J. Zaytoon (Eds.), Proceedings of the 3rd IFAC Conference on Analysis and Design of Hybrid Systems. International Federation of Automatic Control.