1. 1 SUPERVISORY CONTROL THEORY MODELS AND METHODS W.M. Wonham Systems Control Group ECE Department University of Toronto wonham@control.utoronto.ca Workshop on Discrete-Event Systems Control Eindhoven 2003.06.24

2. 2 WHAT’S 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

3. 3 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!

4. 4 MODEL FLEXIBILITY For instance Automata versus Petri nets batrakhomuomakhia or

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7. 7 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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10. 10 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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15. 15 MODEL WITH THE BEST OF BOTH WORLDS ? Q 1  Q 2  · · ·  Q m   k   l (Algebraically) hybrid state set Q i for (an unstructured) automaton component Í for a naturally additive component (buffer...)  for a naturally boolean component (switch...)

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17. 17 WHAT ABOUT LARGE SYSTEMS? For architecture, need algebraic “laws” for basic objects and operators _____ DES G nonblocking if L m (G) = L(G). Suppose G = G 1  G 2. _____ ____________ L m (G)  L m (G 1 )  L m (G 2 ) (computationally intensive!) _____ _____ =? L m (G 1 )  L m (G 2 ) = L(G 1 )  L(G 2 ) =  L(G) E.g. languages, prefix-closure, synchronous product

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19. 19 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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26. 26 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

27. 27 AIP COMPUTATION Equivalent “flat” model ~ 10 24 states, intractable by extensional methods BDD controller ~ 7  10 4 nodes Intermediate node count < 21  10 4 PC with Athlon cpu, 1GHz, 256 MB RAM Computation time ~ 45 min

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30. 30 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