State feedback control of timed hybrid Petri nets

A system in which discrete variables and continuous variables are mixed is called a hybrid system. Many models have been proposed for the description of hybrid systems. A model graphically describing the causality relationship between the variables is the hybrid Petri net (HPN). A model in which the concept of time is introduced into the HPN is the timed HPN (THPN). In this paper, with regard to the THPN with an external input place (THPNIP), state feedback control is discussed in the case where the control specifications are given by a predicate on the reachable set. In THPNIP, in general there is no guarantee that the maximum permissive feedback, which is the maximum element in the set of the state feedback satisfying the control specification, will exist. Hence, the necessary and sufficient conditions are presented for the existence of the maximum permissive feedback. (C) 2003 Wiley Periodicals, Inc.