1. A work cell consists of two machines M1 and M2 and an automated guided vehicle AGV. The automaton models of these three components are shown in the figure below. The complete system is G = M1 M2 AGV.

(a) Find G.(b) Is G blocking or non-blocking?

0 0

0

1 1

1 2

M1 M2

readyat1

loadat1

giveto2

loadat2

giveto2

giveout

loadat2

loadat1

AGV

2. Build the observer of the nondeterministic automaton shown in the figure below.

a, b

0 1

3 5

42

b

a

b

b

a

a

3. Build the diagnoser of unobservable event event e for the nondeterministic automaton shown in figure below. (All the events are

observable but e.)

1

2

3 4 5

7 11 12

8 9 10 6

t

t

e

ab

g

ae

b g

bg

d

d

4. A simple manufacturing process involves two machines, M1 and M2, and a Buffer B in between. There is an infinite supply of parts to M1. When a part is processed at M1, it is placed in B, which has a capacity of one part only. The part is subsequently processed by M2. Let us suppose that we build the uncontrolled model of Mi, i = 1, 2, as follows. Each machine has three states: Idle (the initial state), Processing, and Down. Each machine has four transitions: event START from Idle to Processing, event END from Processing to Idle, event BREAKDOWN from Processing to Down, and event REPAIR from Down to Idle. The behavior of the system need to be restricted to satisfy the following rules:(i) M1 can only begin processing if the buffer is empty;(ii) M2 can only begin processing if the buffer is full;(iii) M1 cannot begin processing if M2 is down;(iv) If both machines are down, then M2 gets repaired first.

Answer the following questions.(a) Construct an automaton that represents the admissible behavior, as captured by (i) to (iv) above. This automaton should generate a sublanguage of L(M1 M2).(b) Suppose that the events START and REPAIR of each machine can be controlled (that is, enabled or disenabled) by a controller. For each state of your automaton in (a) above, identify which feasible events in M1 and M2 the controller should disable.

5. Consider the pump-valve-controller system discussed in Example 2.24 in the handout (Ch. 2, Cassandras and Lafortune, pp. 118-119). Build the diagnosers for the complete system model depicted in Fig. 2.29 (page 120) for the two faults STUCK_CLOSED and STUCK_OPEN. Are these faults diagnosable?