Timed Petri nets in Hybrid Systems: Stability and Supervisory Control
X.D. Koutsoukos K.X. He, M.D. Lemmon and P.J. Antsaklis
Journal of Discrete Event Dynamic Systems: Theory and Applications
8(2), 137-173, 1998.
Abstract -- In this paper, timed Petri nets are used to model
and control hybrid systems. Petri nets are used instead of finite
automata primarily because of the advantages they offer in dealing
with concurrency and complexity issues. A brief overview of existing
results on hybrid systems that are based on Petri nets is first presented.
A class of timed Petri nets named programmable timed Petri nets (PTPN)
is then used to model hybrid systems. Using the PTPN, the stability
and supervisory control of hybrid systems are addressed and efficient
algorithms are introduced. In particular, we present sufficient
conditions for the uniform ultimate boundness of hybrid systems composed
of multiple linear time invariant plants which are switched between
using a logical rule described by a Petri net. This paper also examines
the supervisory control of a hybrid system in which the continuous
state is transferred to a region of the state space in a way that
respects safety specifications on the plant's discrete and continuous
dynamics.
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