Create Presentation
Download Presentation

Download Presentation
## SUPERVISORY CONTROL THEORY

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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 • Admits architectural composition • 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...)**WHAT ABOUT LARGE SYSTEMS?**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, ... •There is steady progress •There is lots to do