Supervisory Control - The Unknown Component Problem: Theory and Applications - page 252

24

m 5

m 4

23

c 3

m 6

c 2

04

20

c 1 c 4

c 10

34

14

c 7 c 9

54 64

c 8

Fig. 15.13 Supervisory controller for cat and mouse from Problem 15.1

Fig. 15.14 Plant P from

a

Problem 15.2

a

b

15.2. (More) Supervisory Control under Partial Controllability
Consider the plant

Df a; b g ,

˙ u c Df b g , P shown in Fig. 15.14 from [77], where ˙

P Df a ? ba ? g .
(a) Suppose that the specification is

, i.e., it is required
that the closed-loop system produces prefixes of words with an equal number
of occurrences of

S D Pref . f a k ba k ;k 0 g /

. Check whether
there exists a supervisor for this specification, and if so specify it and describe
its control strategy.
(b) Repeat the problem in (a) with the marked language of the specification given
by

a before and after the single occurrence of b

S Df a k ba k ;k 0 g . Is there a non-blocking supervisor?
(c) Repeat the problem in (a) with the marked language of the specification given
by S Df a k ba l ;k l 0 g . Is there a non-blocking supervisor?