A model of hybrid systems and their transition dynamics

Hybrid systems (HS) provide a new formalism for dynamical systems and control theory which bridges a gap between continuous-time and discrete-event systems. In this paper, we examine phenomena arising in general systems for which hybrid systems would appear to be an appropriate formalism. A hybrid model is adopted that provides a means of capturing hybrid-type phenomena and behaviour of interest. This model couples a finite control automaton with a continuous-time plant through analog-to-digital and digital-to-analog converters, with the automaton and plant interacting only at fixed sample times. Within this modelling formalism, the following customizations are made: (i) the specification of three admissible control law classes, (ii) the provision of a setting to consider three forms of uncertainty referred to as transition dynamics, structural uncertainty, and parametric uncertainty. We introduce various models of transition dynamics that characterize varying levels of knowledge or certainty about the system dynamics during some transition period.