Identification of hybrid systems

Hybrid or continuous/discrete systems have attracted increased scientific attention in recent years. In fact, most technical systems consist of physical (sub)systems which are governed by continuous dynamics, continuous or discrete-time controllers, and logical systems which react to and trigger events in the continuous parts. Hybrid systems also arise from modeling of physical phenomena alone, e.g. in evaporation and other processes with phase transitions or in mechanical systems. Beginning with Tavernini´s work (1987), several rather theoretical modeling paradigms for such systems have been introduced. The dynamics of a hybrid system can simply be described as follows: Starting from an initial point the systems trajectory evolves in state space. Due to the discrete actions (phase transitions, control inputs, etc.) there exist switching manifolds in the state space. If the trajectory reaches one of these switching manifolds, the continuous dynamics of the system changes. After such a mode-change, a reinitialization of the continuous variables may be necessary, e.g. when conservation laws have to be considered. Thus the trajectory of a general hybrid dynamical system shows blips and/or jumps. In this contribution, we propose an approach to identify a model of a hybrid dynamical system from measured data