SUPERVISORY CONTROL THEORY

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SUPERVISORY CONTROL THEORY

• MODELS AND METHODS

W.M. Wonham Systems Control Group ECE
Department University of Toronto wonham_at_control.ut
oronto.ca
Workshop on Discrete-Event Systems
Control Eindhoven 2003.06.24
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WHATS BEEN ACCOMPLISHED?

• Formal control theory
• Basis simple ideas about control and
  observation
• Some esthetic appeal
• Amenable to computation
• Admits architectural composition
• Handles real industrial applications

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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!
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MODEL FLEXIBILITY

• For instance

Automata versus Petri nets
or
batrakhomuomakhia
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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)

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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
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MODEL WITH THE BEST OF BOTH WORLDS ?
(Algebraically) hybrid state set
Q1 ? Q2 ? ? Qm ? ?k ? ?l

• Qi for (an unstructured) automaton component
• for a naturally additive component
  (buffer...)
• ? for a naturally boolean component (switch...)

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WHAT ABOUT LARGE SYSTEMS?
For architecture, need algebraic laws for
basic objects and operators
E.g. languages, prefix-closure, synchronous
product
_____
DES G nonblocking 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)
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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

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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

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AIP COMPUTATION

• Equivalent flat model 1024 states,
  intractable by extensional methods
• BDD controller 7 ? 104 nodes
• Intermediate node count lt 21 ? 104
• PC with Athlon cpu, 1GHz, 256 MB RAM
• Computation time 45 min

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CONCLUSIONS

• Base model flexibility, architectural variations
  among topics of current importance

Symbolic computation to play major role
Other topics p.o. concurrency models,
causality, lattice-theoretic ideas, ...
There is steady progress
There is lots to do