Supervisory Control - The Unknown Component Problem: Theory and Applications - page 240

The automaton is incomplete (2 states) and deterministic.
2 inputs 8 states 13 transitions
Inputs = { i, E }

s0

a -

s1

a -

s2

b -

s3 b -

a - b - b -

s4 s5

b - a -

a -

s6

b -

b -

DC - -

Fig. 15. 3 Graphical output of BALM showing the automaton x.aut of the largest controller
C M D .P [ S/

Pref

for the full controllability problem of Example 15.11 and Fig. 15.2

a deadlock or a livelock may occur in the closed-loop composition of the plant with
the supervisor. To exclude these situations one introduces the notion of a progressive
(i.e., non-blocking) supervisor. 1
Definition 15.2.2. A supervisor

is compositionally progressive or simply
progressive or non-blocking if the automaton

C

P \ C is trim.

Theorem 15.12. If the equation P \ X D S is solvable then Pref .S / is a

progressive solution.

1 Another definition of progressive or non-blocking solution is reported in the literature, see [38,
78, 102, 104], by which a non-blocking controller C cannot block in the product P \ C any action

that is allowed by the specification.