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Summary: 2036 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 48, NO. 11, NOVEMBER 2003
Synthesis of Supervisors Enforcing General Linear
Constraints in Petri Nets
Marian V. Iordache and Panos J. Antsaklis
Abstract--Efficient techniques exist for the design of supervisors
enforcing constraints consisting of linear marking inequalities. This note
shows that without losing the benefits of the prior techniques, the class of
constraints can be generalized to linear constraints containing marking
terms, firing vector terms, and Parikh vector terms. We show that this
extended class of constraints is more expressive. Furthermore, we show
that the extended constraints can describe any supervisor consisting of
control places arbitrarily connected to the transitions of a plant Petri net
(PN). The supervisor design procedure we propose is as follows. For PNs
without uncontrollable and unobservable transitions, a direct method for
the design of a PN supervisor that is least restrictive is given. For PNs with
uncontrollable and/or unobservable transitions, we reduce the problem to
the design of supervisors enforcing linear marking inequalities.
Index Terms--Linear constraints, Petri nets (PNs), supervisory control.
I. INTRODUCTION
Efficient methods have been proposed in [1][4] for the design of
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