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.

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

rGen	input colored marking generator
rHighAlph	high-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

rGen	Reference to generator
redundantColor	Index 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

rGen	generator under investigation
rColors	colors that have to be contained in the SCCs
rColoredSCCs	SCCs 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

rGen	investigated generator
rSccSet	Set of strongly connected components (result).
rRoots	Set 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

rGen	Reference to generator
rResGen	Reference 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

rGen	Reference to generator
rProjectAlphabet	Alphabet 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

rGen1	First MtcSystem for parallel composition
rGen2	Second MtcSystem for parallel composition
rResGen	MtcSystem 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

rGen	Reference to generator
rProjectAlphabet	Projection alphabet
rResGen	Reference 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

rGen	Reference to generator
rProjectAlphabet	Projection alphabet
rResGen	Reference 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

rGen	Reference to generator
rProjectAlphabet	Projection 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

rPlantGen	Plant MtcSystem
rSpecGen	Specification MtcSystem
rResGen	Reference 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

rPlantGen	Plant MtcSystem
rSpecGen	Specification MtcSystem
rResGen	Reference 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

rGen	input colored marking generator
rOptimalColors	optimal color set to be removed
rHighAlph	hgh-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.

Detailed Description

License

Classes

Functions

Function Documentation

◆ calcNaturalObserver()

Example: Computation of an Lm-observer

◆ CheckRedundantColor()

◆ ColoredSCC()

◆ ComputeSCC()

◆ mtcDeterministic()

Example: Converting a nondeterministic MtcSystem to a deterministic one

◆ mtcInvProject()

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

◆ mtcParallel()

Example: Parallel composition of two colored marking generators

◆ mtcProject()

Example: Projection of an MtcSystem to a specified alphabet

◆ mtcProjectNonDet() [1/2]

◆ mtcProjectNonDet() [2/2]

◆ mtcSupConClosed()

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

◆ mtcSupConNB()

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

◆ OptimalColorSet()