Multitasking PlugIn

Detailed Description

The multitasking plug-in allows to examine colored marking generators (CMGs). Generators can be created in the same way as in the standard implementation, the identifier is MtcSystem. In addition to the standard implementation that is based on the classical theory, colored markings can be applied to single states. The class faudes::TmtcGenerator implements various methods to handle CMGs. Furthermore, functions for making CMGs deterministic or strongly coaccessible, for computing the parallel composition or an projection, are provided.

The libFAUDES multitasking plugin allows to develop descrete event systems using the classical, monolithic approach. Additionally, it is suitable for their modular or hierarchical development. For more information to the modular proceeding see

"Modular Multi-tasking Supervisory Control of Composite Discrete Event Systems", M.H. de Queiroz and J.E.R. Cury, IFAC World Congress, 2005.

Further information to the hierarchical proceeding can be found in

"Hierarchical and Decentralized Multitasking Control of Discrete Event Systems", K. Schmidt, M. H. Queiroz, and J. E. R. Cury, IEEE Conference on Decision and Control, 2007.

License

The implementation of the multitasking plug-in was part of Matthias Singers' student project, supervised by Klaus Schmidt. The code is distributed with libFAUDES and under the terms of the LGPL.




Copyright (c) 2008, Matthias Singer.

Classes

class  faudes::AttributeColoredState
 State attributes for multitasking automata. More...
 
class  faudes::ColorSet
 Container for colors: this is a NameSet with its own static symboltable. More...
 
class  faudes::TmtcGenerator< GlobalAttr, StateAttr, EventAttr, TransAttr >
 Allows to create colored marking generators (CMGs) as the common five tupel consisting of alphabet, stateset, transition relation, initial states, marked states, and attributes for state and event properties. More...
 

Functions

Idx faudes::calcNaturalObserver (const MtcSystem &rGen, EventSet &rHighAlph)
 Calculate a colored natural observer by extending a given high-level alphabet. More...
 
void faudes::mtcParallel (const MtcSystem &rGen1, const MtcSystem &rGen2, MtcSystem &rResGen)
 Parallel composition of two colored marking generators, controllability status is observed. More...
 
void faudes::mtcDeterministic (const MtcSystem &rGen, MtcSystem &rResGen)
 Make generator deterministic. More...
 
void faudes::mtcProjectNonDet (MtcSystem &rGen, const EventSet &rProjectAlphabet)
 Project generator to alphabet rProjectAlphabet. More...
 
void faudes::mtcProjectNonDet (const MtcSystem &rGen, const EventSet &rProjectAlphabet, MtcSystem &rResGen)
 Project generator to alphabet rProjectAlphabet. More...
 
void faudes::mtcProject (const MtcSystem &rGen, const EventSet &rProjectAlphabet, MtcSystem &rResGen)
 Minimized Deterministic projection. More...
 
void faudes::mtcInvProject (MtcSystem &rGen, const EventSet &rProjectAlphabet)
 Inverse projection. More...
 
bool faudes::ComputeSCC (const Generator &rGen, std::set< StateSet > &rSccSet, StateSet &rRoots)
 Computes the strongly connected components (SCCs) of an automaton. More...
 
void faudes::ColoredSCC (MtcSystem &rGen, ColorSet &rColors, std::set< StateSet > &rColoredSCCs)
 Compute all strongly connected components (SCCs) in a colored marking generator (CMG) that are marked with a given set of colors. More...
 
bool faudes::CheckRedundantColor (MtcSystem rGen, Idx redundantColor)
 Check if a color in a colored marking generator is redundant for the supervisor synthesis. More...
 
void faudes::OptimalColorSet (const MtcSystem &rGen, ColorSet &rOptimalColors, EventSet &rHighAlph)
 Compute an optimal subset of the colors that should be removed. More...
 
void faudes::mtcSupConNB (const MtcSystem &rPlantGen, const MtcSystem &rSpecGen, MtcSystem &rResGen)
 Nonblocking Supremal Controllable Sublanguage (wrapper function) More...
 
void faudes::mtcSupConClosed (const MtcSystem &rPlantGen, const MtcSystem &rSpecGen, MtcSystem &rResGen)
 Supremal Controllable Sublanguage (wrapper function) More...
 

Function Documentation

◆ calcNaturalObserver()

FAUDES_API Idx faudes::calcNaturalObserver ( const MtcSystem rGen,
EventSet rHighAlph 
)

Calculate a colored natural observer by extending a given high-level alphabet.

This function extends a given high-level alphabet such that the corresponding natural projection becomes a colored observer for a given colored marking generator. The function calls the function ExtendHighAlphabet in the Observer plugin.

Parameters
rGeninput colored marking generator
rHighAlphhigh-level alphabet that is extended towards a colored observer
Returns
number of states of the high-level colored marking generator

Example: Computation of an Lm-observer

Original generator
Original high-level alphabet (rHighAlph): cb4-cb12, cb12-cb4, cb11-cb4, cb4-cb11
Result of calcNaturalObserver(rGenObs, rHighAlph);
New high-level alphabet (rNewHighAlph): cb4-cb12, cb12-cb4, cb11-cb4, cb4-cb11, mh1end

Definition at line 41 of file mtc_observercomputation.cpp.

◆ CheckRedundantColor()

FAUDES_API bool faudes::CheckRedundantColor ( MtcSystem  rGen,
Idx  redundantColor 
)

Check if a color in a colored marking generator is redundant for the supervisor synthesis.

This function determines if a color can be removed from a CMG if it is redundant for the supervisor synthesis. The algorithm implements the work in K. Schmidt and J.E.R. Cury, "Redundant Colors in the Multitasking Supervisory Control for Discrete Event Systems", Workshop on Dependable Control of Discrete Event Systems, 2009.

Parameters
rGenReference to generator
redundantColorIndex of the color to be removed
Returns
true if the color can be removed, false otherwise

Definition at line 172 of file mtc_redundantcolors.cpp.

◆ ColoredSCC()

FAUDES_API void faudes::ColoredSCC ( MtcSystem rGen,
ColorSet rColors,
std::set< StateSet > &  rColoredSCCs 
)

Compute all strongly connected components (SCCs) in a colored marking generator (CMG) that are marked with a given set of colors.

This function finds all SCCs in a CMG that contain states with all colors in a given color set. To find all SCCs, first the function ComputeSCC is called.

Parameters
rGengenerator under investigation
rColorscolors that have to be contained in the SCCs
rColoredSCCsSCCs marked with all colors in rColors

Definition at line 140 of file mtc_redundantcolors.cpp.

◆ ComputeSCC()

FAUDES_API bool faudes::ComputeSCC ( const Generator rGen,
std::set< StateSet > &  rSccSet,
StateSet rRoots 
)

Computes the strongly connected components (SCCs) of an automaton.

This function is the wrapper function for Trajan's algorithm that is implemented in the function SearchSCC.

Parameters
rGeninvestigated generator
rSccSetSet of strongly connected components (result).
rRootsSet of states that each are root of some SCC (result).
Returns
true if SCCs have been found, false if not.

Definition at line 121 of file mtc_redundantcolors.cpp.

◆ mtcDeterministic()

FAUDES_API void faudes::mtcDeterministic ( const MtcSystem rGen,
MtcSystem rResGen 
)

Make generator deterministic.

(function wrapper)

Parameters
rGenReference to generator
rResGenReference to resulting deterministic generator

Example: Converting a nondeterministic MtcSystem to a deterministic one

Original MtcSystem gen
The MtcSystem contains two initial states and, leaving from state 2, it has two transitions containing the same event b which are leading to two separate states.
Result of the deterministic operation
Both initial states are combined to a single one. All color labels appearing in all original states are adapted to the new initial state. Furthermore, states are merged in that way that the generator's language stays the same, but the generator gets deterministic.

Definition at line 73 of file mtc_project.cpp.

◆ mtcInvProject()

FAUDES_API void faudes::mtcInvProject ( MtcSystem rGen,
const EventSet rProjectAlphabet 
)

Inverse projection.

This adds selfloop transition at every state for all missing events.

Parameters
rGenReference to generator
rProjectAlphabetAlphabet for inverse projection

Example: Inverse projection of an MtcSystem for a specified alphabet which is larger than the MtcSystem's one.

Original MtcSystem
The projection alphabet contains the events {a, b, c}.
Result of the projection
Events, that are not part of the MtcSystem's alphabet are inserted as self-loops into every state.

Definition at line 498 of file mtc_project.cpp.

◆ mtcParallel()

FAUDES_API void faudes::mtcParallel ( const MtcSystem rGen1,
const MtcSystem rGen2,
MtcSystem rResGen 
)

Parallel composition of two colored marking generators, controllability status is observed.

Parameters
rGen1First MtcSystem for parallel composition
rGen2Second MtcSystem for parallel composition
rResGenMtcSystem in which the result of the parallel composition is saved

Example: Parallel composition of two colored marking generators

MtcSystems for composition
The left MtcSystem contains only one colored state, state 2, whereas the right one possesses two color labels - one for each state.
Result of the parallel composition
The composed MtcSystem contains all colors that appear in both single MtcSystems.
The single states are labeled with a color when both states to combine are labeled with it. A color label is also added when it occurs in one of the two currently regarded states to compose and, at the same time, it does not appear in the second single MtcSystem.

Definition at line 32 of file mtc_parallel.cpp.

◆ mtcProject()

FAUDES_API void faudes::mtcProject ( const MtcSystem rGen,
const EventSet rProjectAlphabet,
MtcSystem rResGen 
)

Minimized Deterministic projection.

This function does not modify the MtcSystem. It calls project, determine and statemin.

Parameters
rGenReference to generator
rProjectAlphabetProjection alphabet
rResGenReference to resulting deterministic generator

Example: Projection of an MtcSystem to a specified alphabet

Original MtcSystem gen
The projection alphabet contains the events {a, b, d}.
Result of the projection
The resulting MtcSystem contains all events that appear in the oringinal MtcSystem and in the specified alphabet. Moreover, the resulting MtcSystem is deterministic.

Definition at line 421 of file mtc_project.cpp.

◆ mtcProjectNonDet() [1/2]

FAUDES_API void faudes::mtcProjectNonDet ( const MtcSystem rGen,
const EventSet rProjectAlphabet,
MtcSystem rResGen 
)

Project generator to alphabet rProjectAlphabet.

Parameters
rGenReference to generator
rProjectAlphabetProjection alphabet
rResGenReference to result

Definition at line 415 of file mtc_project.cpp.

◆ mtcProjectNonDet() [2/2]

FAUDES_API void faudes::mtcProjectNonDet ( MtcSystem rGen,
const EventSet rProjectAlphabet 
)

Project generator to alphabet rProjectAlphabet.

Parameters
rGenReference to generator
rProjectAlphabetProjection alphabet

Definition at line 328 of file mtc_project.cpp.

◆ mtcSupConClosed()

FAUDES_API void faudes::mtcSupConClosed ( const MtcSystem rPlantGen,
const MtcSystem rSpecGen,
MtcSystem rResGen 
)

Supremal Controllable Sublanguage (wrapper function)

Parameters
rPlantGenPlant MtcSystem
rSpecGenSpecification MtcSystem
rResGenReference to resulting MtcSystem, the minimal restrictive supervisor
Exceptions
Exception
  • Alphabets of generators don't match (id 500)
  • plant nondeterministic (id 501)
  • spec nondeterministic (id 503)
  • plant and spec nondeterministic (id 504)

Example: Synthesis of a multitasking supervisor for a model and a corresponding specification. Supervisor does not take care of nonblocking behavior.

Model MtcSystem
The model contains one state that results in a blocking behavior.
Specification MtcSystem
The specification expresses, that after an event b an event c has to occur before b can happen again. Furthermore, it forbids that event c occurs before event b has taken place.
Before being able to compute a supervisor, an inverse projection step has to be applied on the specification. It inserts self-loops for event a in both states, as the alphabets of model and specification must be identical.
Strongly nonblocking supervisor
The supervisor synthesized by this function is strongly nonblocking. Of course, it ensures that the specification condition is fulfilled.

Definition at line 130 of file mtc_supcon.cpp.

◆ mtcSupConNB()

FAUDES_API void faudes::mtcSupConNB ( const MtcSystem rPlantGen,
const MtcSystem rSpecGen,
MtcSystem rResGen 
)

Nonblocking Supremal Controllable Sublanguage (wrapper function)

Computes symbolic state names in resulting supervisor automaton if symbolic state names are enabled in rPlantGen and rSpecGen

Parameters
rPlantGenPlant MtcSystem
rSpecGenSpecification MtcSystem
rResGenReference to resulting MtcSystem, the minimal restrictive nonblocking supervisor
Exceptions
Exception
  • Alphabets of generators don't match (id 500)
  • plant nondeterministic (id 501)
  • spec nondeterministic (id 503)
  • plant and spec nondeterministic (id 504)

Example: Synthesis of a strongly nonblocking supervisor for a model and a corresponding specification

Model MtcSystem
The model contains one state that results in a blocking behavior.
Specification MtcSystem
The specification expresses, that after an event b an event c has to occur before b can happen again. Furthermore, it forbids that event c occurs before event b has taken place.
Before being able to compute a supervisor, an inverse projection step has to be applied on the specification. It inserts self-loops for event a in both states, as the alphabets of model and specification must be identical.
Strongly nonblocking supervisor
The synthesized supervisor ensures that the specification condition is fulfilled. That is why state 5 of the model and the corresponding transitions are erased. Observe that the operation does not make a generator nonblocking, as is shown in the example where state 3 is still existing.

Definition at line 41 of file mtc_supcon.cpp.

◆ OptimalColorSet()

FAUDES_API void faudes::OptimalColorSet ( const MtcSystem rGen,
ColorSet rOptimalColors,
EventSet rHighAlph 
)

Compute an optimal subset of the colors that should be removed.

This function tries to find an optimal subset of colors that can be removed from the given colored marking generator without affecting supervisor synthesis. Here, optimality is defined w.r.t. the smallest number of states of a high-level generator after removing the colors.

Parameters
rGeninput colored marking generator
rOptimalColorsoptimal color set to be removed
rHighAlphhgh-level alphabet for hierarchical abstraction after color removal. Initially, the alphabet should contain all events that must be present in the high-level alphabet

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Definition at line 242 of file mtc_redundantcolors.cpp.

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