SUPERVISORY CONTROL THEORY

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SUPERVISORY CONTROL THEORY. W.M. Wonham Systems Control Group ECE Department University of Toronto wonham@control.utoronto.ca. MODELS AND METHODS. Workshop on Discrete-Event Systems Control Eindhoven 2003.06.24. WHAT’S BEEN ACCOMPLISHED?. Formal control theory

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SUPERVISORY CONTROL THEORY

W.M. Wonham

Systems Control Group

ECE Department

University of Toronto

wonham@control.utoronto.ca

MODELS AND METHODS

Workshop on Discrete-Event Systems Control

Eindhoven 2003.06.24

WHAT’S BEEN ACCOMPLISHED?
• Formal control theory
• Basis – simple ideas about control and observation
• Some esthetic appeal
• Amenable to computation
• Handles real industrial applications
WHAT MORE SHOULD BE ACCOMPLISHED?
• Flexibility of model type
• Flexibility of model architecture
• Transparency of model structure (how to view and understand a complex DES?)
• ...

Accepting that most of the interesting

problems are exponentially hard!

MODEL FLEXIBILITY

For instance

Automata versus Petri nets

or

batrakhomuomakhia

COMPUTATION OF SIMSUP

1.FMS = Sync (M1,M2,R) (20,34)

2. SPEC = Allevents (FMS) (1,8)

3. SUPER(.DES) = Supcon (FMS,SPEC) (15,24)

4. SUPER(.DAT) = Condat (FMS,SUPER)

5. SIMSUP = Supreduce (FMS,SUPER,SUPER)

(computes control congruence on SUPER)

(4,16)

COMPUTATION OF MONITORS

Based on “theory of regions”

1. Work out reachability graph of PN

(20 reachable markings, 15 coreachable)

2. Find the 6 “dangerous markings”

3. Solve the 6 “event/state separation” problems (each a system of 15 linear integer inequalities)

4. Implement the 3 distinct solutions as monitors

MODEL WITH THE BEST OF BOTH WORLDS ?

(Algebraically) hybrid state set

Q1 Q2 ··· Qm  k  l

• Qi for (an unstructured) automaton component
• for a naturallyadditive component (buffer...)

 for a naturally boolean component (switch...)

For architecture, need algebraic “laws” for basic objects and operators

E.g. languages, prefix-closure, synchronous product

_____

DES Gnonblocking if Lm(G) = L(G). Suppose G = G1 G2.

_____ ____________

Lm(G) Lm(G1)  Lm(G2) (computationally intensive!)

_____ _____

=? Lm(G1)  Lm(G2) = L(G1)  L(G2) =L(G)

TOP-DOWN MODELLING BY STATE TREES
• Adaptation of state charts to supervisory
• control
• • Transparent hierarchical representation
• of complex systems
• • Amenable to efficient control computation
• via BDDs
AIP CONTROL SPECIFICATIONS

• Normal production sequencing

Type1 workpiece: I/O  AS1 AS2  I/O

Type2 workpiece: I/O  AS2  AS1  I/O

• AS3 backup operation if AS1 or AS2 down

• Conveyor capacity bounds, ...

• Nonblocking

AIP COMPUTATION
• Equivalent “flat” model ~ 1024 states, intractable by extensional methods
• BDD controller ~ 7  104 nodes
• Intermediate node count < 21  104
• PC with Athlon cpu, 1GHz, 256 MB RAM
• Computation time ~ 45 min
CONCLUSIONS
• Base model flexibility, architecturalvariations among topics of current importance

•Symbolic computation to play major role

•Other topics: p.o. concurrency models,

causality, lattice-theoretic ideas, ...