SUPERVISORY CONTROL THEORY. W.M. Wonham Systems Control Group ECE Department University of Toronto firstname.lastname@example.org. MODELS AND METHODS. Workshop on Discrete-Event Systems Control Eindhoven 2003.06.24. WHAT’S BEEN ACCOMPLISHED?. Formal control theory
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Systems Control Group
University of Toronto
MODELS AND METHODS
Workshop on Discrete-Event Systems Control
Accepting that most of the interesting
problems are exponentially hard!
Automata versus Petri nets
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)
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
(Algebraically) hybrid state set
Q1 Q2 ··· Qm k l
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)
• 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, ...
•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