Synthesis Plug-In
[PlugIns]

Functions

bool faudes::IsRelativelyMarked (const Generator &rGenPlant, const Generator &rGenCand)
 Test for relative marking.
bool faudes::IsRelativelyPrefixClosed (const Generator &rGenPlant, const Generator &rGenCand)
 Test for relative prefix-closedness.
void faudes::SupRelativelyPrefixClosed (const Generator &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Supremal Relatively Closed Sublanguage.
bool faudes::IsRelativelyOmegaMarked (const Generator &rGenPlant, const Generator &rGenCand)
 Test for relative marking, omega langauges.
bool faudes::IsRelativelyOmegaClosed (const Generator &rGenPlant, const Generator &rGenCand)
 Test for relative closedness, omega languages.
bool faudes::IsControllable (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSupCandGen)
 Test controllability.
bool faudes::IsControllable (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSupCandGen, StateSet &rCriticalStates)
 Test controllability.
bool faudes::IsControllable (const System &rPlantGen, const Generator &rSupCandGen)
 Test controllability.
void faudes::SupConNB (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Nonblocking Supremal Controllable Sublanguage.
void faudes::SupConNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Nonblocking Supremal Controllable Sublanguage.
void faudes::SupConClosed (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Supremal Controllable and Closed Sublanguage.
void faudes::SupConClosed (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Supremal Controllable and Closed 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 (const Generator &rL, const EventSet &rOAlph, const Generator &rK, Generator &rResult)
 SupNorm: compute supremal normal sublanguage.
bool faudes::SupNormClosed (const Generator &rL, const EventSet &rOAlph, const Generator &rK, Generator &rResult)
 SupNormClosed - compute supremal normal and closed sublanguage.
void faudes::SupConNormClosed (const Generator &rL, const EventSet &rCAlph, const EventSet &rOAlph, const Generator &rK, Generator &rResult)
 SupConNormClosed: compute supremal controllable, normal and closed sublanguage.
void faudes::SupConNormNB (const Generator &rL, const EventSet &rCAlph, const EventSet &rOAlph, const Generator &rK, Generator &rResult)
 SupConNormNB: compute supremal controllable and normal sublanguage.
bool faudes::SupReduce (const System &rPlantGen, const System &rSupGen, System &rReducedSup)
 Supervisor Reduction algorithm.
void faudes::SupTconNB (const Generator &rPlantGen, const EventSet &rCAlph, const EventSet &rFAlph, const EventSet &rPAlph, const Generator &rSpecGen, Generator &rResGen)
 Nonblocking Supremal TDES-Controllable Sublanguage.
void faudes::SupTconNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Nonblocking Supremal TDES-Controllable Sublanguage.
bool faudes::IsOmegaControllable (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSupCandGen)
 Test omega controllability.
bool faudes::IsOmegaControllable (const System &rPlantGen, const Generator &rSupCandGen)
 Test omega-controllability.
void faudes::SupConCmplClosed (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConCmplClosed (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConCmplNB (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConCmplNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Supremal controllable and complete sublanguage.
void faudes::SupConNormCmplNB (const Generator &rPlantGen, const EventSet &rCAlph, const EventSet &rOAlph, const Generator &rSpecGen, Generator &rResGen)
 Supremal controllable, normal and complete sublanguage.
void faudes::SupConNormCmplNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 rti wrapper
void faudes::OmegaSupConNB (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis.
void faudes::OmegaSupConNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis.
void faudes::OmegaConNB (const Generator &rPlantGen, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis.
void faudes::OmegaConNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis.
void faudes::OmegaSupConNormNB (const Generator &rPlantGen, const EventSet &rOAlph, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis for partial observation (experimental!).
void faudes::OmegaSupConNormNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis for partial observation.
void faudes::OmegaConNormNB (const Generator &rPlantGen, const EventSet &rOAlph, const EventSet &rCAlph, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis for partial observation (experimental!).
void faudes::OmegaConNormNB (const System &rPlantGen, const Generator &rSpecGen, Generator &rResGen)
 Omega-synthesis for partial observation (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.
Copyright (c) 2010, 2011, Thomas Moor.


Function Documentation

bool faudes::IsControllable ( const System &  rPlantGen,
const Generator &  rSupCandGen 
)

Test controllability.

Tests whether the candidate supervisor h is controllable w.r.t. the plant g; this is a System 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 Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  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 Note: this was reimplemented in libFAUDES 2.20b.

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 Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSupCandGen 
)

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.

Parameter restrictions: both generators must be deterministic and share 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

Thus, we assume K L for a sufficient and necessary test.

Todos: check for efficient algorithm replacing above formula that returns false immediately after having found a non-normal string -> IsNormalFast(); implement test routines, verify correctness; compare performance 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 System &  rPlantGen,
const Generator &  rSupCandGen 
)

Test omega-controllability.

Tests whether the candidate supervisor h is omega controllable w.r.t. the plant g; this is a System 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 Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  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 Generator &  rGenPlant,
const Generator &  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 Generator &  rGenPlant,
const Generator &  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 Generator &  rGenPlant,
const Generator &  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 Generator &  rGenPlant,
const Generator &  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::OmegaConNB ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis.

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

Parameters:
rPlantGen Plant System
rSpecGen Specification Generator
rResGen Reference to resulting Generator to realize the closed-loop behaviour.
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::OmegaConNB ( const Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis.

This procedure first computes the supremal omega-controllable sublanguage as proposed by J. Thistle, 1992, applied to the specific case of deterministoc Buechi automata. It then applies a control pattern to obtain a relatively topologically-closed result, i.e., the topological closure of the result can be used as a supervisor.

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 to realize the closed-loop behaviour.
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::OmegaConNormNB ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis for partial observation (experimental!).

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

Parameters:
rPlantGen Plant System
rSpecGen Specification Generator
rResGen Reference to resulting Generator to realize the closed-loop behaviour.
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::OmegaConNormNB ( const Generator &  rPlantGen,
const EventSet &  rOAlph,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis for partial observation (experimental!).

Variation of supremal controllable prefix under partial observation. This variation applies a control pattern to obtain a relatively closed and omega-normal result. The latter properties are validated and an exception is thrown on an error. Thus, this function should not produce "false-positives". However, since it is derived from OmegaSupConNormNB(), is may return the empty languages even if a non-empty controller exists.

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

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rOAlph Observable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator to realize the supremal closed-loop behaviour.
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 System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis.

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

Parameters:
rPlantGen Plant System
rSpecGen Specification Generator
rResGen Reference to resulting Generator to realize the supremal closed-loop behaviour.
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 Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis.

Computation of the supremal oemga-controllable sublanguage as proposed by Thistle/Wonham in "Control of w-Automata, Church's Problem, and the Emptiness Problem for Tree w-Automata", 1992, and, here, applied to the specific case of deterministic Buechi automata. In the given setting, the result matches the limit of the controllable prefix intersected with the plant and specification omega-languages.

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

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator to realize the supremal closed-loop behaviour.
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::OmegaSupConNormNB ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis for partial observation.

This is the RTI wrapper for OmegaSupConNormNB(const Generator&, const EventSet&, const Generator&, Generator&). Controllability attributes and observability attributes are taken from the plant argument. If the result is specified as a System, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant System
rSpecGen Specification Generator
rResGen Reference to resulting Generator to realize the supremal closed-loop behaviour.
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::OmegaSupConNormNB ( const Generator &  rPlantGen,
const EventSet &  rOAlph,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Omega-synthesis for partial observation (experimental!).

Variation of supremal omega-controllable sublanguage to address normality requirements in the context of partial observation. The test used in this implementation is sufficient but not known to be necessary. Thus, the function may return only a subset of the relevant controllable prefix.

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

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rOAlph Observable events
rSpecGen Specification Generator E
rResGen Reference to resulting Generator to realize the supremal closed-loop behaviour.
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::SupConClosed ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Supremal Controllable and Closed Sublanguage.

This is the RTI wrapper for SupCon(const Generator&, const EventSet&, const Generator&, Generator&).

Controllability attributes are taken from the plant argument. If the result is specified as a System, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant System
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::SupConClosed ( const Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Supremal Controllable and Closed Sublanguage.

Given a closed plant language L and a closed specification E, this function computes a realisation of the supremal controllable and closed sublanguage of L^E. Arguments and result generate the respective language (i.e. marked languages are not considered.)

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

Parameters:
rPlantGen Plant L generated by rPlantGen
rCAlph Controllable events
rSpecGen Specification E generated rSpecGen
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::SupConCmplClosed ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Supremal controllable and complete sublanguage.

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

Parameters:
rPlantGen Plant System
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::SupConCmplClosed ( const Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  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::SupConCmplNB ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Supremal controllable and complete sublanguage.

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

Parameters:
rPlantGen Plant System
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::SupConCmplNB ( const Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  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 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 SupConComplNB. 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 System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Nonblocking Supremal Controllable Sublanguage.

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

Parameters:
rPlantGen Plant System
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 Generator &  rPlantGen,
const EventSet &  rCAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Nonblocking Supremal Controllable Sublanguage.

Given a generator G (argument rPlantGen) and a specification language E (marked by argument rSpecGen), this procedures computes an automaton S such that Lm(S) is the supremal controllable sublanguage of Lm(G) ^ Lm(E) w.r.t. L(G). The result is given as a trim deterministic generator that may be used to supervise G in order to enforce E.

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 to mark 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::SupConNormClosed ( const Generator &  rL,
const EventSet &  rCAlph,
const EventSet &  rOAlph,
const Generator &  rK,
Generator &  rResult 
)

SupConNormClosed: compute supremal controllable, normal and closed sublanguage.

SupConNormClosed computes the supremal sublanguage of language K (generated by rK) that is

  • controllable w.r.t. the language L (generated by rL);
  • normal w.r.t. the language L; and
  • prefix closed.

The implementation is based on results by Brandt et al "Formulas for calculation supremal and normal sublanguages", Thm 4, System and Control Letters, 1990.

Parameters have to be deterministic, result is deterministic.

Parameters:
rL generates the closed language L=L(rL)
rCAlph controllable alphabet
rOAlph observable alphabet
rK generates the closed language K=L(rK)
rResult marks and generates the supremal contr, normal and closed sublanguage
Exceptions:
Exception 
  • Alphabets of generators don't match (id 500)
  • rCAlph not subset of rL.Alphabet() (id 506)
  • rOAlph not subset of rL.Alphabet() (id 506)
  • K is not subset of L. (id 0)
void faudes::SupConNormCmplNB ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

rti wrapper

Supremal controllable, normal and complete sublanguage.

This is the RTI wrapper for SupConNormCmplNB(const Generator&, const EventSet&, const EventSet&, const Generator&, Generator&). Event attributes are taken from the plant argument. If the result is specified as a System, attributes will be copied from the plant argument.

Parameters:
rPlantGen Plant System
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::SupConNormCmplNB ( const Generator &  rPlantGen,
const EventSet &  rCAlph,
const EventSet &  rOAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Supremal controllable, normal and complete sublanguage.

SupConNormCmplNB computes the supremal sublanguage of language K (marked by rSpecGen) that

  • is controllable w.r.t. the language L (marked by rPlantGen);
  • has a prefix closure that is normal w.r.t. the closure of L
  • is complete

The implementation is based on an iteration by Yoo, Lafortune and Lin "A uniform approach for computing supremal sublanguages arising in supervisory control theory", 2002, further developped in Moor, Baier, Yoo, Lin, and Lafortune "On the computation of supremal sublanguages relevant to supervisory control, WODES 2012. The relationship to the supervision of omega languages under partial observation is discussed as an example in the WODES 2012 paper.

Parameters have to be deterministic, result is deterministic.

Parameters:
rPlantGen Plant L
rCAlph Controllable events
rCAlph Observable 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::SupConNormNB ( const Generator &  rL,
const EventSet &  rCAlph,
const EventSet &  rOAlph,
const Generator &  rK,
Generator &  rResult 
)

SupConNormNB: compute supremal controllable and normal sublanguage.

SupConNormNB computes the supremal sublanguage of language K (marked by rK) that

  • is controllable w.r.t. the language L (marked by rL);
  • has a prefix closure that is normal w.r.t. the closure of L

The implementation is based on results by Yoo, Lafortune and Lin "A uniform approach for computing supremal sublanguages arising in supervisory control theory", 2002.

Parameters have to be deterministic, result is deterministic.

Parameters:
rL generates the closed language L=L(rL)
rCAlph controllable alphabet
rOAlph observable alphabet
rK generates the closed language K=L(rK)
rResult marks the supremal normal and controllable sublanguage
Exceptions:
Exception 
  • Alphabets of generators don't match (id 500)
  • rCAlph not subset of rL.Alphabet() (id 506)
  • rOAlph not subset of rL.Alphabet() (id 506)
  • K is not subset of L. (id 0)
bool faudes::SupNorm ( const 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 (generated by rK) that is normal w.r.t. the closed language L (generated 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.

Parameters:
rL generates the closed language L=L(rL)
rOAlph observable alphabet
rK generates the closed language K=L(rK)
rResult marks the supremal normal sublanguage (not necessaryly prefix closed)
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 ( const 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 (generated by rK) that is closed and normal w.r.t. the closed language L (generated 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*

Parameters have to be deterministic, result is deterministic.

Parameters:
rL generates the closed language L=L(rL)
rOAlph observable alphabet
rK generates the closed language K=L(rK)
rResult marks and generates the supremal normal and closed sublanguage
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::SupReduce ( const System &  rPlantGen,
const System &  rSupGen,
System &  rReducedSup 
)

Supervisor Reduction algorithm.

Computes a reduced supervisor from a given potentially non-reduced supervisor and the plant. This algorithm implements the results obtained in

R. Su and W. M. Wonham. Supervisor Reduction for Discrete-Event Systems. Discrete Event Dynamic Systems vol. 14, no. 1, January 2004.

Both, plant and supervisor MUST be deterministic and share the same alphabet!!!

Parameters:
rPlantGen Plant generator
rSupGen Supervisor generator
rReducedSup Reduced supervisor generator
Returns:
True if a reduction was achieved
Exceptions:
Exception 
  • alphabets of generators don't match (id 100)
  • plant nondeterministic (id 201)
  • supervisor nondeterministic (id 203)
  • plant and supervisor nondeterministic (id 204)
void faudes::SupRelativelyPrefixClosed ( const Generator &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Supremal Relatively Closed Sublanguage.

Computes the supremal sublanguage of the specification E that is relatively closed w.r.t. the plant G. The result is given as a trim deterministic generator that may be used as a specification for a subsequent controller design via SupConNB.

The implementation removes states from the product GxE that conflict with relative closedness. From the known formula supR(E)= (L^E) - (L-E)Sigma*, we know that the supremal sublanguage can be realized as a subautomaton of GxE. Thus, we conclude that our implementation indeed returns the supremum.

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

Parameters:
rPlantGen Plant G
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::SupTconNB ( const System &  rPlantGen,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Nonblocking Supremal TDES-Controllable Sublanguage.

This is the RTI wrapper for SupTconNB(const Generator&, const EventSet&, const Generator&, Generator&). Controllability attributes are taken from the plant argument and tick is the only preemptable event. If the result is specified as a System, attributes will be copied from the plant argument.

(!) Interface most likely to change --- needs more testing/ proper design (!)

Parameters:
rPlantGen Plant System
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::SupTconNB ( const Generator &  rPlantGen,
const EventSet &  rCAlph,
const EventSet &  rFAlph,
const EventSet &  rPAlph,
const Generator &  rSpecGen,
Generator &  rResGen 
)

Nonblocking Supremal TDES-Controllable Sublanguage.

Controllable sublanguage w.r.t. specified forcible and preemptable events. When the set of preemptable events consist exclusively of the tick event, this corresponds to TDES-controllability.

(!) Interface most likely to change --- needs more testing/proper design (!)

Parameters:
rPlantGen Plant G
rCAlph Controllable events
rFAlph Forcible events
rPAlph Premptable 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)

libFAUDES 2.23h --- 2014.04.03 --- c++ api documentaion by doxygen