Hybrid Control Systems Using Timed Petri Nets: Supervisory Control Design Based on Invariant Properties
X.D. Koutsoukos and P.J. Antsaklis
In Hybrid Systems V,
P. Antsaklis, W. Kohn, M. Lemmon, A. Nerode, S. Sastry Eds., Vol. 1567,
Lecture Notes in Computer Science (LNCS), pp. 142-162,
Springer-Verlag, 1999.
Abstract -- In this paper, a class of timed Petri nets named
programmable timed Petri nets is used fot supervisory control of
hybrid systems. In particular, the transfer of the continuous state
to a region of the state space under safety specifications on the
discrete and continuous dynamics is addressed. The switching policy
is embedded in the dynamics of the underlying Petri net structure and
the supervisors are described by Petri nets. The discrete specifications
are expressed in terms of linear constraints on the marking vector
and are satisfied by applying supervisory control of Petri nets based
on place invariants. The hybrid system switches from a subsystem
to another, in a way that the state gradually progresses from one
equilibrium to another towards the desired target equilibrium. The
supervisory control alorithm is designed to allow switchings to occur
only on the intersection of the invariant manifolds. Finally, in the
case when the continuous dynamics are described by first order
integrators, the design algorithm is formulated as a linear programming
problem.
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