libFAUDES

Sections

Index

Synthesis Plug-In
[PlugIns]

Functions

bool faudes::IsRelativelyMarked (const vGenerator &rGenPlant, const vGenerator &rGenCand)
 Test for relative marking.
bool faudes::IsRelativelyPrefixClosed (const vGenerator &rGenPlant, const vGenerator &rGenCand)
 Test for relative prefix-closedness.
bool faudes::IsRelativelyOmegaMarked (const vGenerator &rGenPlant, const vGenerator &rGenCand)
 Test for relative marking, omega langauges.
bool faudes::IsRelativelyOmegaClosed (const vGenerator &rGenPlant, const vGenerator &rGenCand)
 Test for relative closedness, omega languages.
bool faudes::IsControllable (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSupCandGen)
 Test controllability.
bool faudes::IsControllable (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSupCandGen, StateSet &rCriticalStates)
 Test controllability.
bool faudes::IsControllable (const cGenerator &rPlantGen, const vGenerator &rSupCandGen)
 Test controllability.
void faudes::SupConNB (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSpecGen, vGenerator &rResGen)
 Nonblocking Supremal Controllable Sublanguage.
void faudes::SupConNB (const cGenerator &rPlantGen, const vGenerator &rSpecGen, vGenerator &rResGen)
 Nonblocking Supremal Controllable Sublanguage.
void faudes::SupCon (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSpecGen, vGenerator &rResGen)
 Supremal Controllable Sublanguage.
void faudes::SupCon (const cGenerator &rPlantGen, const vGenerator &rSpecGen, vGenerator &rResGen)
 Supremal Controllable Sublanguage.
bool faudes::IsNormal (const Generator &rL, const EventSet &rOAlph, const Generator &rK)
 IsNormal: checks normality of a language K generated by rK wrt a language L generated by rL and the subset of observable events rOAlph.
bool faudes::SupNorm (Generator &rL, const EventSet &rOAlph, const Generator &rK, Generator &rResult)
 SupNorm: compute supremal normal sublanguage.
bool faudes::SupNormClosed (Generator &rL, const EventSet &rOAlph, const Generator &rK, Generator &rResult)
 SupNormClosed - compute supremal normal and closed sublanguage.
bool faudes::IsOmegaControllable (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSupCandGen)
 Test omega controllability.
bool faudes::IsOmegaControllable (const cGenerator &rPlantGen, const vGenerator &rSupCandGen)
 Test omega-controllability.
void faudes::SupConComplete (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSpecGen, vGenerator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConComplete (const cGenerator &rPlantGen, const vGenerator &rSpecGen, vGenerator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConCompleteNB (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSpecGen, vGenerator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConCompleteNB (const cGenerator &rPlantGen, const vGenerator &rSpecGen, vGenerator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::OmegaSupConNB (const vGenerator &rPlantGen, const EventSet &rCAlph, const vGenerator &rSpecGen, vGenerator &rResGen)
 Omega-synthesis (experimental).
void faudes::OmegaSupConNB (const cGenerator &rPlantGen, const vGenerator &rSpecGen, vGenerator &rResGen)
 Omega-synthesis (experimental).

Detailed Description

This plug-in implements functions that are related to controllability and normality, as originally proposed by W.M. Wonham et al in the 1980s. Examples are provided in the user reference, section Synthesis.

License

This plug-in is distributed with libFAUDES and under the terms of the LGPL.

Copyright (c) 2006, Bernd Opitz
Copyright (c) 2009, Thomas Moor, Sebastian Perk, Klaus Schmidt.


Function Documentation

bool faudes::IsControllable ( const cGenerator &  rPlantGen,
const vGenerator &  rSupCandGen 
)

Test controllability.

Tests whether the candidate supervisor h is controllable w.r.t. the plant g; this is a cGenerator wrapper for IsControllable

Parameters:
rPlantGen Plant g generator
rSupCandGen Supervisor candidate h generator
Exceptions:
Exception Alphabets of generators don't match (id 500) Plant generator nondeterministic (id 501) Specification generator nondeterministic (id 503) Plant & Spec generator nondeterministic (id 504)
Returns:
true / false
bool faudes::IsControllable ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSupCandGen,
StateSet &  rCriticalStates 
)

Test controllability.

Tests whether the candidate supervisor H is controllable w.r.t. the plant G. This implementation does not require the supervisor H to represent a sublanguage of the plant G.

If the candidate fails to be controllable, this version will return a set of "critical" states of the candidate supervisor. These states are characterised by (a) being reachable in the parallel composition of plant and supervisor (b) disabeling an uncontrollable transition of the plant

Parameter restrictions: both generators must be deterministic and have the same alphabet.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSupCandGen Supervisor candicate H
rCriticalStates Set of critical states
Exceptions:
Exception 
  • alphabets of generators don't match (id 200)
  • plant generator nondeterministic (id 201)
  • specification generator nondeterministic (id 203)
  • plant and Spec generator nondeterministic (id 204)
Returns:
true / false
bool faudes::IsControllable ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSupCandGen 
)

Test controllability.

RTI wrapper.

Tests whether the candidate supervisor H is controllable w.r.t. the plant G. This implementation does not require the supervisor H to represent a sublanguage of the plant G.

Parameter restrictions: both generators must be deterministic and have the same alphabet.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSupCandGen Supervisor candidate H
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant generator nondeterministic (id 201)
  • specification generator nondeterministic (id 203)
  • plant and Spec generator nondeterministic (id 204)
Returns:
true / false
bool faudes::IsNormal ( const Generator &  rL,
const EventSet &  rOAlph,
const Generator &  rK 
)

IsNormal: checks normality of a language K generated by rK wrt a language L generated by rL and the subset of observable events rOAlph.

This is done by checking if the following equality holds: pinv(p(K)) intersect L = K todo(?): check for efficient algorithm replacing above formula that returns false immediately after having found a non-normal string -> IsNormalFast() todo: implement test routines, verify correctness todo: compare speed with IsNormalAlt

Parameters:
rL generator of language L
rOAlph observable alphabet
rK generator of language K
Returns:
true if K is normal w.r.t. L and OAlph
Exceptions:
Exception 
bool faudes::IsOmegaControllable ( const cGenerator &  rPlantGen,
const vGenerator &  rSupCandGen 
)

Test omega-controllability.

Tests whether the candidate supervisor h is omega controllable w.r.t. the plant g; this is a cGenerator wrapper for IsOmegaControllable.

Parameters:
rPlantGen Plant g generator
rSupCandGen Supervisor candidate h generator
Exceptions:
Exception 
  • Alphabets of generators don't match (id 100)
  • Arguments are not omega trim (id 201, only if FAUDES_CHECKED is set)
  • Arguments are non-deterministic (id 202, only if FAUDES_CHECKED is set)
Returns:
true / false
bool faudes::IsOmegaControllable ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSupCandGen 
)

Test omega controllability.

Tests whether the candidate supervisor H is omega controllable w.r.t. the plant G. This implementation invokes IsControllable and IsRelativelyOmegaClosed. A future implementation may be more efficient.

Parameter restrictions: both generators must be deterministic, omega-trim and have the same alphabet.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSupCandGen Supervisor candidate H
Exceptions:
Exception 
  • Alphabets of generators don't match (id 100)
  • Arguments are not omega trim (id 201, only if FAUDES_CHECKED is set)
  • Arguments are non-deterministic (id 202, only if FAUDES_CHECKED is set)
Returns:
true / false
bool faudes::IsRelativelyMarked ( const vGenerator &  rGenPlant,
const vGenerator &  rGenCand 
)

Test for relative marking.

Tests whether the language Lm(GCand) is relatively marked w.r.t. the language Lm(GPlant). The formal definition of this property requires

closure(Lm(GCand)) ^ Lm(GPlant) <= Lm(GCand).

The implementation tests

L(GCand) ^ Lm(GPlant) <= Lm(GCand)

by first performing the product composition and then inspecting the marking to require

( forall accessible (qPlant,qCand) ) [ qPlant in QPlant_m implies qCand in QCand_m ].

In general, the test is only sufficient. Provided the arguments are trim and deterministic, the test is sufficient and necessary.

Parameters:
rGenPlant Generator GPlant
rGenCand Generator GCand
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • arguments are not trim (id 201, only if FAUDES_CHECKED is set)
  • arguments are non-deterministic (id 202, only if FAUDES_CHECKED is set)
Returns:
true / false
bool faudes::IsRelativelyOmegaClosed ( const vGenerator &  rGenPlant,
const vGenerator &  rGenCand 
)

Test for relative closedness, omega languages.

Tests whether the omega language Bm(GCand) is relatively closed w.r.t. the omega language Bm(GPlant). The formal definition of this property requires

closure(Bm(GCand)) ^ Bm(GPlant) = Bm(GCand).

The implementation first performs the product composition of the two generators with product state space QPlant x QCand and generated language L(GPlant x GCand) = L(GPlant) ^ L(GCand). It uses the composition to test the follwing three conditions:

  • L(GCand) subseteq L(GPlant);
  • no SCC of GPlant x GCand without GCand-marking contains a state with GPlant-marking; and
  • no SCC of GPlant x GCand without GPlant-marking contains a state with GCand-marking. If and only if all three tests are passed, the function returns true.

The arguments GCand and GPlant are required to be deterministic and omega trim.

Parameters:
rGenPlant Generator GPlant
rGenCand Generator GCand
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • arguments are not omega trim (id 201, only if FAUDES_CHECKED is set)
  • arguments are non-deterministic (id 202, only if FAUDES_CHECKED is set)
Returns:
true / false
bool faudes::IsRelativelyOmegaMarked ( const vGenerator &  rGenPlant,
const vGenerator &  rGenCand 
)

Test for relative marking, omega langauges.

Tests whether the omega language Bm(GCand) is relatively marked w.r.t. the omega language Bm(GPlant). The formal definition of this property requires

closure(Bm(GCand)) ^ Bm(GPlant) <= Bm(GCand).

The implementation first performs the product composition of the two generators with product state space QPlant x QCand and generated language L(GPlant x GCand) = L(Plant) ^ L(Cand). It then investigates all SCCs that do not contain a state that corresponds to GCand-marking. If and only if none of the considered SCCs has a GPlant marking, the function returns true.

The arguments GCand and GPlant are required to be deterministic and omega trim.

Parameters:
rGenPlant Generator GPlant
rGenCand Generator GCand
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • arguments are not omega-trim (id 201, only if FAUDES_CHECKED is set)
  • arguments are non-deterministic (id 202, only if FAUDES_CHECKED is set)
Returns:
true / false
bool faudes::IsRelativelyPrefixClosed ( const vGenerator &  rGenPlant,
const vGenerator &  rGenCand 
)

Test for relative prefix-closedness.

Tests whether the language Lm(GCand) is relatively closed w.r.t. the language Lm(GPant). The formal definition of this property requires

closure(Lm(GCand)) ^ Lm(GPlant) = Lm(GCand).

The implementation tests

L(GCand) ^ Lm(GPland) = Lm(GCand)

by performing the product composition and by testing

  • for L(GCand) subseteq L(GPlant), and
  • ( forall accessible (qPland,qCand) ) [ qPlant in QPlant_m if and only if qCand in QCand_m ].

In general, the test is only sufficient. Provided the arguments are trim and deterministic, the test is sufficient and necessary.

Parameters:
rGenPlant Generator GPlant
rGenCand Generator GCand
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • arguments are not trim (id 201, only if FAUDES_CHECKED is set)
  • arguments are non-deterministic (id 202, only if FAUDES_CHECKED is set)
Returns:
true / false
void faudes::OmegaSupConNB ( const cGenerator &  rPlantGen,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Omega-synthesis (experimental).

This function is experimental and perhaps not functional. In the long term it may synthesise supervisors for omega-languages.

This is the RTI wrapper for OmegaSupConNB(const vGenerator&, const EventSet&, const vGenerator&, vGenerator&). Controllability attributes are taken from the plant argument. If the result is specified as a cGenerator, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant cGenerator
rSpecGen Specification Generator
rResGen Reference to resulting Generator, the minimal restrictive nonblocking supervisor
Exceptions:
Exception Alphabets of generators don't match (id 100) plant nondeterministic (id 201) spec nondeterministic (id 203) plant and spec nondeterministic (id 204)
void faudes::OmegaSupConNB ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Omega-synthesis (experimental).

This function is experimental and perhaps not functional. In the long term it may synthesise supervisors for omega-languages.

Parameter restrictions: both generators must be deterministic and have the same alphabet.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator, the minimal restrictive nonblocking supervisor
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant nondeterministic (id 201)
  • spec nondeterministic (id 203)
  • plant and spec nondeterministic (id 204)
void faudes::SupCon ( const cGenerator &  rPlantGen,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Supremal Controllable Sublanguage.

This is the RTI wrapper for SupCon(const vGenerator&, const EventSet&, const vGenerator&, vGenerator&). Controllability attributes are taken from the plant argument. If the result is specified as a cGenerator, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant cGenerator
rSpecGen Specification Generator
rResGen Reference to resulting Generator, the minimal restrictive supervisor
Exceptions:
Exception Alphabets of generators don't match (id 100) plant nondeterministic (id 201) spec nondeterministic (id 203) plant and spec nondeterministic (id 204)
void faudes::SupCon ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Supremal Controllable Sublanguage.

Parameter restrictions: both generators must be deterministic and have the same alphabet.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSpecGen Specification E
rResGen Reference to resulting Generator, the minimal restrictive supervisor
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant nondeterministic (id 201)
  • spec nondeterministic (id 203)
  • plant and spec nondeterministic (id 204)
void faudes::SupConComplete ( const cGenerator &  rPlantGen,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Supremal controllable and complete sublanguage.

This is the RTI wrapper for SupConComplete(const vGenerator&, const EventSet&, const vGenerator&, vGenerator&). Controllability attributes are taken from the plant argument. If the result is specified as a cGenerator, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant cGenerator
rSpecGen Specification Generator
rResGen Reference to resulting Generator
Exceptions:
Exception Alphabets of generators don't match (id 100) plant nondeterministic (id 201) spec nondeterministic (id 203) plant and spec nondeterministic (id 204)
void faudes::SupConComplete ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Supremal controllable and complete sublanguage.

Given a plant and a specification, this function computes a realisation of the supremal controllable and complete sublange. This version consideres the generated languages (ignores the marking). In particular, this implies that the result is prefix closed. It is returned as generated language.

Starting with a product composition of plant and specification, the implementation iteratively remove states that either contradict controllability or completeness. Removal of states is continued until no contradicting states are left. Thus, the result is indeed controllable and complete. The algorithm was proposed in

R. Kumar, V. Garg, and S.I. Marcus. On supervisory control of sequential behaviors. IEEE Transactions on Automatic Control, Vol. 37: pp.1978-1985, 1992.

The paper proves supremality of the result. Provided that the corresponding omega language of the specification is closed, the result of the above algorithm also realises the least restrictive closed loop behaviour of the corresponding omega language control problem.

Parameter restrictions: both generators must be deterministic and have the same alphabet. The result will be accessible and deterministic.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant nondeterministic (id 201)
  • spec nondeterministic (id 203)
  • plant and spec nondeterministic (id 204)
void faudes::SupConCompleteNB ( const cGenerator &  rPlantGen,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Supremal controllable and complete sublanguage.

This is the RTI wrapper for SupConCompleteNB(const vGenerator&, const EventSet&, const vGenerator&, vGenerator&). Controllability attributes are taken from the plant argument. If the result is specified as a cGenerator, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant cGenerator
rSpecGen Specification Generator
rResGen Reference to resulting Generator
Exceptions:
Exception Alphabets of generators don't match (id 100) plant nondeterministic (id 201) spec nondeterministic (id 203) plant and spec nondeterministic (id 204)
void faudes::SupConCompleteNB ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Supremal controllable and complete sublanguage.

Given a plant and a specigfication, this function computes a realisation of the supremal controllable and complete sublange. This version consideres the marked languages.

Starting with a product composition of plant and specification, the implementation iteratively remove states that contradict controllability or completeness or that are not coaccessible. Removal of states is continued until no contradicting states are left. Thus, the result is indeed controllable, complete and coaccessible.

Considering the marked languages implies that only strings that simultanuosly reach a marking can survive the above procedure. From an omega-languages perspective, this is of limited use. However, in the special situation that the specification is relatively closed w.r.t. the plant, we can replace the specification by its prefix closure befor invoking SupConComlpleteNB. In this situation we claim that the procedure returns a realisation of the the least restrictive closed loop behaviour of the corresponding omega language control problem.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant nondeterministic (id 201)
  • spec nondeterministic (id 203)
  • plant and spec nondeterministic (id 204)
void faudes::SupConNB ( const cGenerator &  rPlantGen,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Nonblocking Supremal Controllable Sublanguage.

This is the RTI wrapper for SupConNB(const vGenerator&, const EventSet&, const vGenerator&, vGenerator&). Controllability attributes are taken from the plant argument. If the result is specified as a cGenerator, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant cGenerator
rSpecGen Specification Generator
rResGen Reference to resulting Generator, the minimal restrictive nonblocking supervisor
Exceptions:
Exception Alphabets of generators don't match (id 100) plant nondeterministic (id 201) spec nondeterministic (id 203) plant and spec nondeterministic (id 204)
void faudes::SupConNB ( const vGenerator &  rPlantGen,
const EventSet &  rCAlph,
const vGenerator &  rSpecGen,
vGenerator &  rResGen 
)

Nonblocking Supremal Controllable Sublanguage.

Computes the supremal nonblocking sublanguage of the specification E that is controllable w.r.t. the plant G. The result is given as a trim deterministic generator that may be used to supervise G in order to enforce H. This implementation does not require E to represent a sublanguage of G

See "C.G CASSANDRAS AND S. LAFORTUNE. Introduction to Discrete Event Systems. Kluwer, 1999." for base algorithm.

Parameter restrictions: both generators must be deterministic and have the same alphabet.

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator, the minimal restrictive nonblocking supervisor
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant nondeterministic (id 201)
  • spec nondeterministic (id 203)
  • plant and spec nondeterministic (id 204)
bool faudes::SupNorm ( Generator &  rL,
const EventSet &  rOAlph,
const Generator &  rK,
Generator &  rResult 
)

SupNorm: compute supremal normal sublanguage.

SupNorm calculates the supremal sublanguage of the closed language K (prefix closure of the language marked by rK) that is normal w.r.t. the closed language L (prefix closure of the language marked by rL) and the set of observable events.

Method: The supremal normal sublanguage is computed according to the Lin-Brandt-Formula: supnorm(K)wrt(L)=K-Pinv[P(L-K)]

SupNorm returns false on empty result.

Parameters have to be deterministic, result is deterministic.

Note: rL is not const, as the prefix closure is taken during computation. However, its original marked language is restored before return. See also SupNormClosed and supnorm_tutorial.cpp

Parameters:
rL generates the closed language L=L(rL)
rOAlph observable alphabet
rK generates the closed language K=L(rK)
rResult generates the supremal normal sublanguage, where Lm(rResult) is intersection of L(rResult) and Lm(rL) (marking consistent to rL)
Returns:
true for nonempty result
Exceptions:
Exception 
  • Alphabets of generators don't match (id 500)
  • rOAlph not subset of rL.Alphabet() (id 506)
  • K is not subset of L. (id 0)
bool faudes::SupNormClosed ( Generator &  rL,
const EventSet &  rOAlph,
const Generator &  rK,
Generator &  rResult 
)

SupNormClosed - compute supremal normal and closed sublanguage.

SupNormClosed calculates the supremal sublanguage of the closed language K (prefix closure of the language marked by rK) that is closed and normal w.r.t. the closed language L (prefix closure of the language marked by rL) and the set of observable events.

Method: The supremal normal sublanguage is computed according to the Lin-Brandt-Formula: supnormclosed(K)wrt(L)=K-Pinv[P(L-K)]Sigma* The difference to supnorm lies in the concatenation of Sigma*. SupNormClosed returns false on empty result.

Parameters have to be deterministic, result is deterministic.

Note: rL is not const, as the prefix closure is taken during computation. However, its original marked language is restored before return. See also supnorm_tutorial.cpp todo: check for efficient algorithm replacing above formula

Parameters:
rL generates the closed language L=L(rL)
rOAlph observable alphabet
rK generates the closed language K=L(rK)
rResult generates the supremal normal and closed sublanguage, where Lm(rResult) is intersection of L(rResult) and Lm(rL) (marking consistent to rL)
Returns:
true for nonempty result
Exceptions:
Exception 
  • Alphabets of generators don't match (id 500)
  • rOAlph not subset of rL.Alphabet() (id 506)
  • K is not subset of L. (id 0)

libFAUDES 2.16b --- 2010-9-8 --- c++ source docu by doxygen 1.6.3