Hybrid Systems: Modeling and Supervisory Control

This paper presents elements of control-oriented models of hybrid systems with input and output signals. Models can be composed through standard block-diagram interconnections. Transition systems with inputs and outputs are introduced to deene the semantics for open-loop hybrid systems. Fixed-point iterations can then used to synthesize logical supervisory controllers. This is illustrated for the problem of designing a supervisor to keep the state of the hybrid system out of a speciied set of forbidden states. Recently developed tools for computer-aided modeling, simulation, and veriication of hybrid systems are reviewed brieey. The paper concludes with a discussion of open research issues and prospects for applications of the theory to problems of practical interest.