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Detailed DescriptionThis plug-in implements functions that are related to controllability and normality, as originally proposed by W.M. Wonham et al in the 1980s and selected extensions thereof. Examples are provided in the user reference, section Synthesis. LicenseThis plug-in is distributed with libFAUDES and under the terms of the LGPL.
Function Documentation◆ CompositionalSynthesis()
Compositional synthesis This function implements controller synthesis for composed plants and composed specifications as discussed in "On Compostional Approaches for Discrete Event Systems Verification and Synthesis" Sahar Mohajerani, PhD, Sweden, 2015. The present implementation was developed by Hao Zhou in course of his Master Thesis "Abstraktion und Komposition fuer den Entwurf ereignisdiskreter Regler", Erlangen, 2015. This particular variant throughs an exception on invalid input data; see also CompositionalSynthesisUnchecked(const GeneratorVector&,const EventSet&,const GeneratorVector&,std::map<Idx,Idx>&,GeneratorVector&,GeneratorVector&);
Definition at line 1379 of file syn_compsyn.cpp. ◆ ComputeSynthObsEquiv()
Synthesis-observation equivalence Function to compute the coarsest synthesis-observation equivalence relation as proposed by Mohajerani, S., Malik, R. & Fabian, M. (2012). "Synthesis observation equivalence and weak synthesis observation equivalence", University of Waikato, Department of Computer Science. Compositional synthesis The present implementation was developed by Hao Zhou in course of his Master Thesis "Abstraktion und Komposition fuer den Entwurf ereignisdiskreter Regler", Erlangen, 2015. Technically, the implementation is based on a previous variant of the bisimulation algorithm from the core library.
Definition at line 916 of file syn_synthequiv.cpp. ◆ IsBuechiRelativelyClosed()
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:
The arguments GCand and GPlant are required to be deterministic and omega trim.
Definition at line 615 of file omg_buechifnct.cpp. ◆ IsBuechiRelativelyMarked()
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.
Definition at line 553 of file omg_buechifnct.cpp. ◆ IsControllable() [1/3]
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.
Definition at line 718 of file syn_supcon.cpp. ◆ IsControllable() [2/3]
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.
Definition at line 740 of file syn_supcon.cpp. ◆ IsControllable() [3/3]
Test controllability. Tests whether the candidate supervisor h is controllable w.r.t. the plant g; this is a System wrapper for IsControllable
Definition at line 885 of file syn_supcon.cpp. ◆ IsNormal()
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 \subseteq K Thus, we assume K \subseteq 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
Definition at line 104 of file syn_supnorm.cpp. ◆ IsRelativelyClosed()
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
In general, the test is only sufficient. Provided the arguments are trim and deterministic, the test is sufficient and necessary.
Definition at line 98 of file syn_functions.cpp. ◆ IsRelativelyMarked()
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.
Definition at line 44 of file syn_functions.cpp. ◆ IsStdSynthesisConsistent() [1/2]
Test consistency of an abstractions w.r.t. standard controller synthesis. Test whether abstraction-based supervisory controller design is guaranteed to lead to a non-blocking and controllable closed loop. This function implements the test proposed in "Moor, T.: Natural projections for the synthesis of non-conflicting supervisory controllers, Workshop on Discrete Event Systems (WODES), Paris, 2014". Parameter restrictions: the generator has to be deterministic and the alphabets must match (see below for exceptions).
Definition at line 388 of file syn_sscon.cpp. ◆ IsStdSynthesisConsistent() [2/2]Test consistency of an abstraction w.r.t standard synthesis. This is a convenience wrapprt for IsStdSynthesisConsistent(const Generator&, const EventSet&, const Generator&).
Definition at line 419 of file syn_sscon.cpp. ◆ SupCon() [1/2]
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.
Definition at line 757 of file syn_supcon.cpp. ◆ SupCon() [2/2]
Nonblocking Supremal Controllable Sublanguage This is the RTI wrapper for
Definition at line 895 of file syn_supcon.cpp. ◆ SupConClosed() [1/2]
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.
Definition at line 778 of file syn_supcon.cpp. ◆ SupConClosed() [2/2]
Supremal Controllable and Closed Sublanguage. This is the RTI wrapper for Controllability attributes are taken from the plant argument. If the result is specified as a System, attributes will be copied from the plant argument.
Definition at line 922 of file syn_supcon.cpp. ◆ SupConCmpl() [1/2]
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 SupConCompl. 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.
Definition at line 130 of file syn_supcmpl.cpp. ◆ SupConCmpl() [2/2]
Supremal controllable and complete sublanguage. This is the RTI wrapper for
Definition at line 190 of file syn_supcmpl.cpp. ◆ SupConCmplClosed() [1/2]
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.
Definition at line 45 of file syn_supcmpl.cpp. ◆ SupConCmplClosed() [2/2]
Supremal controllable and complete sublanguage. This is the RTI wrapper for
Definition at line 103 of file syn_supcmpl.cpp. ◆ SupConNorm()
SupConNorm: compute supremal controllable and normal sublanguage SupConNorm computes the supremal sublanguage of language K (marked by rK) that
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.
Definition at line 376 of file syn_supnorm.cpp. ◆ SupConNormClosed()
SupConNormClosed: compute supremal controllable, normal and closed sublanguage. SupConNormClosed computes the supremal sublanguage of language K (generated by rK) that is
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.
Definition at line 336 of file syn_supnorm.cpp. ◆ SupConNormCmpl() [1/2]
Supremal controllable, normal and complete sublanguage. SupConNormCmpl computes the supremal sublanguage of language K (marked by rSpecGen) that
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.
Definition at line 216 of file syn_supcmpl.cpp. ◆ SupConNormCmpl() [2/2]
rti wrapper Supremal controllable, normal and complete sublanguage. This is the RTI wrapper for
Definition at line 257 of file syn_supcmpl.cpp. ◆ SupNorm()
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.
Definition at line 234 of file syn_supnorm.cpp. ◆ SupNormClosed()
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.
Definition at line 287 of file syn_supnorm.cpp. ◆ SupReduce()
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!!!
Definition at line 210 of file syn_supreduce.cpp. ◆ SupRelativelyClosed()
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 SupCon. 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.
Definition at line 241 of file syn_functions.cpp. ◆ SupTcon() [1/2]
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 (!) Interface most likely to change — needs more testing/proper design (!)
Definition at line 274 of file syn_tsupcon.cpp. ◆ SupTcon() [2/2]
Nonblocking Supremal TDES-Controllable Sublanguage This is the RTI wrapper for (!) Interface most likely to change — needs more testing/ proper design (!)
Definition at line 297 of file syn_tsupcon.cpp. libFAUDES 2.33h --- 2025.06.18 --- c++ api documentaion by doxygen |
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