A mathematical approach to discrete-event dynamic modelling of hybrid systems

Presently, design of supervisory control systems is based on ad hoc design methods. This project attempts to approach the design of supervisory controllers using the structure of continuous and sampled systems. The approach builds on process models, incorporates performance specifications and constraints imposed by the plant and otherwise and synthesises the controller by partial inversion of the process model. This paper describes a modelling technology derived for hybrid systems. The hybrid system consists of a continuous plant forced by commands from the supervisory control system and observed through event detectors. The event detectors generate the "measurements" used as inputs to the supervisory control system. The modelling technology quantises the state space systematically and leads to discrete-event dynamic process models that depend on the discrete inputs and the effects of the environments of the plant. Modelling and control of a simple plant is discussed. The resulting controlled systems are analysed for undesirable effects.