システム制御研究室...Discrete-Event Systems (c. 1980) •Practical problems – inventory,...

システム制御研究室

准教授蔡凱

2020.08.11

つぁいかい

1

One of the main research topics of our lab is “Supervisory Control of Discrete-Event Systems (SCDES)”

In this lecture, we introduce a brief history of SCDES

2

Applications of SCDES• Communication protocol specification [Rudie,Wonham 90]

• Rapid thermal multiprocessor [Balemi et al 93]

• Robotic agents [Kosecka,Bajcsy 94]

• AIP automated manufacturing system [Brandin,Charbonnier 94],[Leduc et al 01],[Ma,Wonham 05]

• Telephone feature interaction [Thistle et al 97]

• Chemical process control [Sanchez 96],[Alsop et al 96]

• Truck dispatching [Blouin et al 01]

• Telephone directory assistance call center [Seidl 04]

• Electrical power flow control [Afzalian et al 09]

• MRI scanner patient support system [Theunissen et al 10]3

Agenda

• 1980 – 1987: birth

• 1987 – 2017: growth

• 2017 – 2030: future4

Discrete-Event Systems (c. 1980)

• Practical problems –inventory, traffic, database, logistics

• Not amenable to differential techniques

• System simulation for analysis and optimization (SIMULA, SIMSCRIPT)

[Fishman 78]5

Discrete-Event Systems (c. 1980) Theoretical approaches:• Queues, Markov chains, Petri nets,

boolean transition structures• Semaphores, path expressions • Pseudo-code based cut-and-try design• Formal approach: process algebras

(CSP, CCS, Dutch school)• Process behaviors[Dijkstra 65],[Arnold,Nivat 80],[Peterson 81],[Ben-Ari 82],[Hoare 85],[Milner 89]

6

Control problems implicit in the literature- enforcement of resource constraints- synchronization- guarantee of deadlock-freeness or liveness…


7

But• Emphasis on modeling, simulation,

performance measurement, verification• Little formalization of control synthesis• Absence of control-theoretic ideas• No standard model or approach to control• No clear separation of controller and

uncontrolled plant


8

State space framework well-established:

FeedbackStabilityControllability ObservabilityOptimality (Quadratic, Lvarious, H¥)

Systems Control Concepts (c. 1980)

e.g. [Athans,Falb 66]9

Qualitative synthesis via geometric concepts:

- lattice of linear subspaces(partial order: subspace inclusion)

- controllability subspaces - supremal controllability subspaces

Systems Control Concepts (c. 1980)

[Wonham 85],[BasileMarro 91]10

Needed (1980): DES Control TheorySystem model

Discrete in time and (usually) space

Asynchronous (event-driven)

Nondeterministic- support transitional choices

11

Needed (1980): DES Control Theory

• Amenable to formal control synthesis- exploit control concepts

• Applicable: manufacturing, traffic, database management, communications, logistic

• Accessible to practitioners and students

12

Proposed (1982):Supervisory Control Theory (SCT)

(P.J. Ramadge & W.M. Wonham)

• Automaton representation- internal state descriptions for concrete modeling and computation

• Language representation- external i/o descriptions for

implementation-independentconcept formulation

• Simple ‘control technology’ 13

From ‘Standard’ Control To Supervisory Control• Standard dynamics: dx/dt = f(t,x,u) �

Supervisory control dynamics: automaton with labeled transitions (events), some of which are controllable

• Standard output: y(t) = g[x(s),u(s)|s ≤ t]�

Supervisory control output: sequence of transition labels = string in a language 14

“AUTOMATON” = “SELF-MOVER”

Homer’s Iliad - 18, lines 373-377Twenty tripods [Hephaistos] crafted, to stand around … his house. At the base of each he placed golden wheels, so these self-movers [hoi automatoi] might enter the divine assembly, and return back to the house, a wonder to behold!

15

Automaton Dynamics

•••

16

SCT Base Model

• Automaton

MACHIdle

Down

µab

l• Control Technology

uncontrollable

controllable

Work

17

SCT Languages• Closed and Marked Behaviors

L(MACH) = all strings generable from initial state I

= {e, a, ab, al, aba, alµ, …}

= closed behavior of MACH

Lm(MACH) = all generable strings hitting some marker state

= {e, ab, alµ, …}

= marked behavior of MACH

_________• Liveness (Nonblocking): L(MACH) = Lm (MACH)

prefix closure

I

W Da

l

µb

18

Synchronous Product

• Builds a more complex automaton

b

g

a

g b

a

ashared

bg

19

SCT Complex Plant• Complex plant

= sync product of simple plant components

PLANT = M1 || M2 || TU

Transfer Line TL

M1 B1 M2 B2 TU1 2 3 4 5 6

8

[Al-Jaar,Desrochers 88]

20

SCT Complex (Safety) Specification• Complex specification

= sync product of partial specifications

SPEC = B1 || B2

B24

5

B12, 8 2,8

3 33

2, 8

21

General Control Issues

• Is there a control that enforces bothsafety, and liveness (nonblocking),which is maximally permissive ?

• If so, can its design be automated ?

• If so, with acceptable computing effort ?

22

SCT Synthesis - Problem

1. Safety:Lm(ConTL) Í Lm(PLANT) Ç Lm(SPEC)

2. Liveness (nonblocking):¾¾¾¾¾Lm(ConTL) = L(ConTL)

3. Maximal permissiveness:

Lm(ConTL) = maximum

subject to safety and liveness

E.g. for TL, let ConTL = ‘TL under control’Must guarantee

23

Language Controllability

24

SCT Synthesis - Solution

Fundamental result:

There exists a (unique) supremal controllablesublanguage

Ksup Í Lm(PLANT) Ç Lm(SPEC)

Furthermore Ksup can be effectively computed.

[Ramadge,Wonham 87]

25

SCT Synthesis Lattice

Lm(PLANT) Ç Lm(SPEC)

S* (all strings)

Lm(SPEC)Lm(PLANT)

optimizationKsup (optimal)

K" (suboptimal)K'

Æ (no strings) 26

‘Monolithic’ SCT Implementation• Given PLANT and SPEC, compute Ksup

SUP = supcon (PLANT, SPEC)Ksup = Lm(SUP)

• Given SUP, implement Ksup

PLANT

SUP

Ksupenable/disableevents in Sc

(feedback loop)

27

Agenda

• 1980 – 1987: birth

• 1987 – 2017: growth

• 2017 – 2030: the future28

1987-2017:

• SCT control architectures - for large and complex systems

• Partial-observation SCT

• Other topics

29

Control Architectures• Centralized• Decentralized (horizontal)• Hierarchical (vertical)• Heterarchical (horizontal+vertical)• Distributed (flat)

- computational challenge- transparent control logic 30

Centralized Architecture

PLANT

SUP

PLANT = sync (PLANT.1, … , PLANT.n)

SPEC = sync (SPEC.1, … , SPEC.m)

SUP = supcon (PLANT, SPEC)

State size of SUP ~ (Constant) n+mExponential state space explosion!

31

Transfer Line

PLANT = sync (M1, M2, TU)

SPEC = sync (B1, B2)

SUP = supcon (PLANT, SPEC)

M1 B1 M2 B2 TU1 2 3 4 5 6

8

32

Transfer Line

SUP

M1 M2 TU 33

Transfer Line

SUP

M1 M2 TU

3,5

5

53

1,31,5

33,5

[Su,Wonham 04]

34

Decentralized Architecture

PLANT

SUP.i

For each SPEC.i (i=1,…,m)

PLANT.i = sync (PLANT.i1, … , PLANT.ik)

SUP.i = supcon (PLANT.i, SPEC.i)

SUP.m

[Ramadge,Wonham 87]35

Transfer Line

M1 B1 M2 B2 TU1 2 3 4 5 6

8

36

B24

5

B12, 8 2,8

3 33

2, 8

Transfer Line

M1 M2 TU

SUP.1 SUP.2

37

Centralized vs Decentralized

PLANT

SUP

PLANT

SUP.i SUP.m

38

Hierarchical Architecture

PLANT

SUP.hi

PLANT.hi

PLANT = sync (PLANT.1, … , PLANT.n)PLANT.hi = higen (PLANT)SUP.hi = supcon (PLANT.hi, SPEC.hi)

[Zhong,Wonham 90],[Wong,Wonham 96]

39

Hierarchical Consistency

SUP.hi(MANAGER)

SUP.lo(OPERATOR)

PLANT.hi

PLANT.lo

plan

control

reportcommand

plan = report � (control � command)?

40

M1 B1 M2 B2

�

Event � = ‘TU returns faulty workpiece for re-working’

For hierarchical control, bring inmanager’s high-level alphabet T with events �, ...

TU

Transfer Line

41

t

tTransfer Line

42

SPEC.hi

fail (t)

pass

fail (t) pass

SUP.hi

pass

pass

Transfer Line

fail (t) fail (t)

43

Transfer Line

SUP.hi

M1 M2 TU

Plant.hi

SUP.hipass

pass

fail (t) fail (t)

44

Centralized vs Hierarchical

PLANT

SUP

PLANT

SUP.hi

PLANT.hi

45

Heterarchical Architecture

PLANT

SUP.1 SUP.m

SUP.1.hi SUP.m.hi

Coordinator

[Feng,Wonham 08],[Schmidt et al 08],

46

Transfer Line

M1 M2 TU

SUP.1 SUP.2

47

Transfer Line

M1 M2 TU

SUP.1 SUP.2

SUP.1.hi SUP.2.hi

48

Transfer Line

M1 M2 TU

SUP.1 SUP.2

SUP.1.hi SUP.2.hi

Coordinator

49

Centralized vs Heterarchical

PLANT

SUP

PLANT

SUP.1 SUP.m

SUP.1.hi SUP.m.hi

Coordinator

50

Distributed Architecture

SUP.1 SUP.n

PLANT.1 PLANT.n

Supervisor localization:

{SUP.1,…,SUP.n} = localize (PLANT.1,…,PLANT.n, SUPX)

[Cai,Wonham 10]

51

Transfer Line

M1 M2 TU

SUP.1 SUP.2 SUP.3

531

42

5,86

52

Centralized vs Distributed

PLANT

SUP SUP.1 SUP.n

PLANT.1 PLANT.n

53

PLANT

SUP

PLANT

SUP.i SUP.m

PLANT

SUP.hi

PLANT.hi

PLANT

SUP.1 SUP.m

SUP.1.hi SUP.m.hi

Coordinator

SUP.1 SUP.n

PLANT.1 PLANT.n

localization

Architecture Summary

localization54

1987-2017



• Other topics

55

Partial-Observation with Control Architectures

• Centralized• Decentralized (horizontal)• Hierarchical (vertical)• Heterarchical (horizontal+vertical)• Distributed (modular, flat)

[Lin,Wonham 88],[Cieslak et al 88]

[Rudie,Wonham 92],[Yoo,Lafortune 02]

[Kim et al 03]

[Zhang et al 16]

[Feng,Wonham 08],[Schmidt et al 08],

56

PLANT

SUPO

Observation Channel

Centralized Architecture with Partial Observation

57

Language Observability

58

Language Observability

59

Necessity of Observability


60

Partial-Observation SCT Problem

Observability is not closed under set unions.

There need not exist a unique supremalobservable (and controllable) sublanguage

Ksup Í Lm(PLANT) Ç Lm(SPEC)

61

Partial-Observation SCT Synthesis Lattice

Lm(PLANT) Ç Lm(SPEC)

S* (all strings)

Lm(SPEC)Lm(PLANT)

K1 K2

K2'K1'

Æ (no strings) 62

Partial-Observation SCT Synthesis – Approximate Solutions


[Cai,Wonham 15]

[Yin,Lafortune 16]

(Other relevant work [Takai,Ushio 03],[Cho,Marcus 89],[Brandt et al 90])63

PLANT

SUPO.1

Decentralized Architecture with Partial Observation

SUPO.m64

Coobservability

[Rudie,Wonham 92],[Yoo,Lafortune 02,04]65

Approximate Solutions

(Other relevant work [Takai et al 05],[Tripakis 04],[Rudie,Willems 95]) 66

If K fails to be coobservable, can decentralized supervisors exist to synthesize K by allowing them to communicate with each other?

Communicating Decentralized Supervisors

PLANT

SUPO.1

SUPO.m67

Communication protocol design and the state disambiguation problem

State-dependent (dynamic) observation and sensor activation, network bandwidth minimization, network security preservation problems

Communicating Decentralized Supervisors

[Rudie et al 03],[Wang et al 08]

[Thorsley,Teneketzis 07],[Sears,Rudie 16]

68

1987-2017



• Other topics- Timed models (timed automata, BW, temporal logic)- State models (EFSM, vector DES, STS)

69

Real-Time DES Models

• Clock automata• Timed transition models• Timed automata• Timed state automata• Timed DES• omega-languages, temporal logic• Timed Petri nets

[Brave,Heymann 88]

[Ostroff 90]

[Alur,Dill 90],[Wong-Toi,Hoffman 91]

[Cassandras 93]

[Brandin,Wonham 94]

[Thistle,Wonham 94][Cofer,Garg 96]

70

Brandin & Wonham Model

• BW = RW + time = logic + timing

• BW retains central concepts of RW controllability, observability, maximally permissive nonblocking supervision

• Supervisor: event disabling + tick preempting71

State-based models

• Extended FSM• Extended FSM + BDD/IDD• State tree structures:

state chart + BDD• Vector DES• SCT based on Petri nets

[Chen,Lin 00],[Skoldstam et al 07]

[Ma,Wonham 05]

[Li,Wonham 94]

[Uzam,Wonham 06]

[Miremadi et al 11]

72

Agenda

• 1980 – 1987: birth

• 1987 – 2017: growth

• 2017 – 2030: future 73

SCT in New Applications

Use SCT as a standard framework to address modeling and control for new applications 74

Warehouse automation

No collisionsNo deadlocks

75

Family of control architectures

Centralized control architectureDecentralized control architectureHierarchical control architectureHeterarchical control architectureDistributed control architecture

Given a specific application at hand, which architecture is best suited?

76

?

Use STOP signs or traffic light?

77

Leader-following or individual autonomy?

Kiva systems (www.businessinsider.com) 78

Centralized, hierarchical, or distributed?

8-hour air traffic in one picture (www.fliup.com)79

Theory of control architecture?

• Provides quantitative tradeoff comparisonsamong competing architectures

• Finds the “best” architecture for organizingcontrol, information, and feedback loops

80

81

2019 SCDES Book provides a comprehensive account of the theory

システム制御研究室...Discrete-Event Systems (c. 1980) •Practical problems – inventory,...

Documents

Transcript of システム制御研究室...Discrete-Event Systems (c. 1980) •Practical problems – inventory,...