CN103235514A - Linear hybrid system-oriented equivalent migration system construction method - Google Patents

Abstract

The invention provides a linear hybrid system-oriented equivalent migration system construction method, which comprises an input side and an output side, wherein the input side is a linear hybrid system model; the output side is a migration system model; a linear hybrid automata is used as the linear hybrid system which is expressed as H=(X, Sigma, V, E, V0, Alpha, Beta, Gamma); X is a finite set of real value system variables and the number of variables in X is the dimensionality of the hybrid automata; Sigma is a finite set of event names; V is a finite set of position nodes; a time variable t is introduced in a conversion system to represent a time interval of any time length; and meanwhile, state migration T of each node v is added on the node to form a self-cycle to simulate the continuous change in the position node v. The value relationship between the current state of the node and the new state after migration is calculated according to the change rate of the node and t. The conversion system of the method can equivalently convert the linear hybrid system into the migration system model, so that the conventional analysis and verification tool for the migration system can be used for verification of the linear hybrid system.

Description

Blend together the migratory system building method of equal value of system towards linearity

Technical field

The present invention relates to the Computer Applied Technology field, in particular to a kind of converting system, be suitable for that linearity is blended together system equivalence and be converted to migratory system.

Background technology

Blending together system (Hybrid System) is that a class had both comprised the Discrete Dynamic behavior, comprises the complication system of continuous dynamic behaviour again.Flourish along with relevant built-in fields such as space flight, automobile, machinery controls, numerous aspects that the system that blendes together has spread all over our life, worked.Therefore, embody very important practical sense to blending together systematic research, the quality assurance of the system of blending together is also become an important topic.At present, the correlative study work that blendes together the mass of system guarantee mainly concentrates on the formalization checking field of system, comprises security (safety property) checking and active (liveness property) checking of system.Security verification will guarantee that the bad behavior of system can not take place, so the security verification problem usually also is converted into the accessibility decision problem; Active checking will guarantee that then the good behavior of system is bound to take place.Wherein, the security verification work that blendes together system is current main research focus.

The main flow model that blendes together system modelling now is to blend together automat (Hybrid Automata).Blend together automat in operational process, both comprised the Discrete Change of state, comprise the continuous variation of state again, its relevant checking work is very difficult.Even linearity blendes together automat (Linear Hybrid Automata)---blend together a simple relatively subclass of automat, it is undecidable that its Reachability question also is proved to be.Existing linearity blendes together the automaton model inspection technology and instrument mainly contains following two classes:

Classical model inspection technology: by methods such as polyhedron calculating, be specific mathematical field and calculate its complete accessible state spatial aggregation with the accessible state collection of system is abstract, but polyhedron Calculation Method complexity only is applicable to minisystem.Exemplary tool such as HyTech, PHAVer etc.

Bounded model testing technology (Bounded Model Checking, be called for short BMC): adopt boolean to retrain coding the behavior of the k of system within the step, utilize SAT methods such as (boolean SATisfiability) to seek the feasible solution of boolean's constraint set then, thereby judge whether the system action of k within the step has the situation that does not satisfy stipulations.The BMC technology has been dwindled problem scale, but it need carry out binary encoding with behavior in the k of system step and once find the solution, but therefore the verification system scale is rather limited.Exemplary tool such as MathSAT, HySAT etc.

Now, association area has existed a large amount of proven technique and instrument to can be applicable to the analysis verification of migratory system.For example: ARMC (Abstraction Refinement Model Checking) can carry out model testing and can stop judgement migratory system; InvGen (In-variant Generator) can the computation migration system loop invariant etc.So will play great role to blending together systematic research if the linearity system of blending together is converted into migratory system.

Summary of the invention

The object of the invention is to provide a kind of converting system, linearity can be blended together the system model equivalence and convert the migratory system model to, makes existing analysis verification instrument for migratory system can be used in the checking that linearity blendes together system.

For reaching above-mentioned purpose, the present invention proposes a kind ofly to blend together the migratory system building method of equal value of system towards linearity, comprises input side and outgoing side, and this input side is that linearity blendes together system model, and this outgoing side is the migratory system model, wherein:

Blending together automat with linearity blendes together system model as linearity and is expressed as H=(X, Σ, V, E, V ⁰α, β, γ), wherein: X is that the number of variable among the finite aggregate of real number value system variable and the X is the dimension that blendes together automat, Σ is the finite aggregate of event name, and V is the finite aggregate of nodes of locations, E be between the nodes of locations element e among redirect set of relationship and the E represent redirect relation (e shape as

Wherein, v, v' ∈ V, σ ∈ Σ,

Be that shape is

Conversion defend formula set, ψ is that shape is the replacement set of actions of x:=c.Above x, x _i(the ∈ X of 0≤i≤l), a, b, c _i(the ∈ R of 0≤i≤l), a can value to-∞, b can value to ∞), V ⁰Be the initial position node set, α is the first mark function, and it is mapped to a node invariant with each position among the V, β is the second mark function, it is mapped to the set of a rate of change with each position among the V, and γ is the 3rd mark function, and it gathers V with start node ⁰In each position be mapped to one group of starting condition;

The migratory system model representation is P=(X _T, L, T, L ₀, θ), wherein: X _TBe system variable, L is the node name set, L ⁰Be the start node set, θ is the starting condition set, and T is the transition relationship set;

The linearity that described converting system will be imported with following rule blendes together the migratory system model that system model is converted to output:

System variable X _T, it comprises linearity and blendes together system variable X all in the system model and introduce time variable t, and X is arranged _T=X ∪ { t};

Node name set L, it is decided by that directly linearity blendes together the nodes of locations set of system model, has L=V;

Start node set L ⁰, it is decided by that directly linearity blendes together the initial position set of system model, has L ⁰=V ⁰

Starting condition set θ, its initial position satisfies θ (l)=γ to the mapping function θ of starting condition, and (v), l is initial position, and v is nodes of locations;

Transition relationship set T comprises by linearity blending together the transition relationship τ that the continuous variation of system model constructs and the Discrete Change that is blended together system model by linearity

The transition relationship δ that constructs, wherein:

Transition relationship τ be expressed as (l, l ', ρ), l, l ' represent source node and the destination node v of transition relationship τ respectively, and ρ is the constrain set on the transition relationship τ, the node invariant α that constrain set ρ derives from nodes of locations v correspondence (v) (v), has with node rate of change β

ρ＝α(v)| _X∪α(v)| _X′∪β(v)| _X,X′,t∪{t＞0,t′＞0}

V ∈ V, X represents current variate-value, the variate-value of X ' expression migration back new state, α (v) | _XExpression variable currency will satisfy the node invariant, α (v) | _{X '}Variate-value after the expression state transition will satisfy the present node invariant, β (v) | _{X, X ', t}Variate-value after expression variable currency and the migration will satisfy the variable rate relation in the time variable t;

Transition relationship δ is expressed as that (ρ), v and v ' are respectively source node and the destination node of transition relationship δ for v, v', and ρ is the constrain set on the transition relationship δ, has herein

V ∈ V, X represents current variate-value, the variate-value of X ' expression migration back new state,

Expression variable currency will satisfy the conversion that blendes together discrete redirect e on the automat and defend formula, ψ | _{X '}Variate-value after the expression state transition will satisfy the replacement action that blendes together discrete redirect e on the automat, α (v) | _XExpression variable currency will satisfy the node invariant, α (v ') | _{X '}Variate-value after the expression state transition will satisfy the present node invariant.

By above technical scheme of the present invention as can be known, beneficial effect of the present invention is to introduce the time period that time variable t represents a random time length in converting system, adds the state transition τ that points to oneself at each node v simultaneously and forms the continuous variation that self-loopa comes analog position node v inside.That is: the inside of v in t chronomere changes the migration of pointing to v with v continuously and represents that t then represents the residence time on v in the migration this time.Calculate according to node rate of change and t that value concerns between the new state that can get after node current state and the migration.Simultaneously finishing the back in transition be t assignment t '＞0 again, represents that with its assignment be the residence time of any nonnegative real number when being described in next transition.In the case, this migratory system can be expressed the given concrete meaning that blendes together automat.Stop and in this migratory system, to express in the random time on each discrete nodes.

Description of drawings

Fig. 1 is the synoptic diagram of converting system of the present invention.

Fig. 2 blendes together the illustraton of model of system for cistern water level monitor (WLM).

Fig. 3 is the illustraton of model of cistern water level monitor migratory system.

Embodiment

In order more to understand technology contents of the present invention, especially exemplified by specific embodiment and cooperate appended graphic being described as follows.

As shown in Figure 1, according to preferred embodiment of the present invention, converting system comprises input side and outgoing side, and this input side is that linearity blendes together system model, and this outgoing side is the migratory system model, wherein:

Blend together automat with linearity and blend together the modeler model of system as linearity, linearity blendes together automat can be expressed as H=(X, Σ, V, E, V ⁰, α, beta, gamma), wherein:

1) X is the finite aggregate of real number value system variable, and the number of variable is also referred to as the dimension (dimension) that blendes together automat among the X;

2) Σ is the finite aggregate of event name;

3) V is the finite aggregate of nodes of locations;

4) E is redirect set of relationship between the nodes of locations, and the element e among the E represents redirect relation, shape as V wherein, v ' ∈ V, σ ∈ Σ,

It is behavior

Conversion defend formula set, ψ is the replacement set of actions of behavior x:=c.Above x, x _i(the ∈ X of 0≤i≤l), a, b, c _i(the ∈ R of 0≤i≤l), a can value-∞, and b can value ∞;

5) V ⁰It is the initial position node set;

6) α is a mark function, and it is mapped to a node invariant, invariant behavior with each position among the V

The set of variable bound, above x, x _i(the ∈ X of 0≤i≤l), a, b, c _i(the ∈ R of 0≤i≤l), a can value-∞, and b can value ∞;

7) β is a mark function, and it is mapped to the set of a rate of change with each position among the V, rate of change be shape as

Formula, for optional position v ∈ V, arbitrarily x ∈ X has and only has one $\stackrel{\·}{x}=[a,b]\∈\mathrm{\β}\left(v\right);$

8) γ is a mark function, and it is with start node V ⁰In each position be mapped to one group of starting condition, starting condition has the formula of shape such as x:=a (x ∈ X, a ∈ R), for any x ∈ X, has and only have an x:=a ∈ γ (v).

The migratory system model representation is P=(X _T, L, T, L ₀, θ), wherein:

1) X _TBe the finite aggregate of real number value system variable, X _TThe number n of middle variable is called as the dimension of migratory system;

2) L is the finite aggregate of nodes of locations name;

3) L ⁰Be the initial position node set,

4) θ is a mark function, and it is with start node L ⁰In each position be mapped to one group of starting condition, starting condition has shape such as x:=a (x ∈ X _T, a ∈ R) formula;

5) T is transition relationship set, the transition relationship set of its structure, and migration set T derives from following two parts: the transition relationship τ that is constructed by the continuous variation of H and the transition relationship δ that is constructed by the Discrete Change of H.

Because the linear continuous behavior that blendes together automat is present in each nodes of locations inside, shows as node rate of change, node invariant etc.; The linear discrete behavior that blendes together automat then is present between the nodes of locations, shows as internodal redirect.And in migratory system, do not have a concept that time on the node stops, therefore in the present embodiment, introducing time variable t represents the time period of a random time length, adds the state transition τ that points to oneself at each node v simultaneously and forms the continuous variation that self-loopa comes analog position node v inside.That is: the inside of v in t chronomere changes the migration of pointing to v with v continuously and represents that t then represents the residence time on v in the migration this time.Calculate according to node rate of change and t that value concerns between the new state that can get after node current state and the migration.Simultaneously finishing the back in transition be t assignment t '＞0 again, represents that with its assignment be the residence time of any nonnegative real number when being described in next transition.In the case, this migratory system can be expressed the given concrete meaning that blendes together automat.Stop and in this migratory system, to express in the random time on each discrete nodes.

Based on this, in the present embodiment, the linearity that converting system will be imported with following rule blendes together the migratory system model that system model is converted to output:

System variable X _T, it comprises linearity and blendes together system variable X all in the system model and introduce time variable t, and X is arranged _T=X ∪ { t};

Node name set L, it is decided by that directly linearity blendes together the nodes of locations set of system model, has L=V;

Start node set L ⁰, it is decided by that directly linearity blendes together the initial position set of system model, has L ⁰=V ⁰

Starting condition set θ is because L ⁰=V ⁰, any one initial position l ∈ L among the P ⁰, all have v ∈ V ⁰, making then has l=v, and initial position satisfies θ (l)=γ to the mapping function θ of starting condition, and (v), l is initial position, and v is nodes of locations;

Transition relationship set T, the transition relationship set of structure P, migration set T derives from following two parts: by the continuous varied configurations transition relationship of H with by the Discrete Change tectonic transport relation of H, wherein:

1) continually varying transition relationship structure among the H: the state transition τ that points to oneself with nodes of locations v forms the continuous variation that self-loopa comes analog position node v inside, and the τ here just refers to the new transition relationship by the continuous varied configurations of H.Transition relationship τ be shape as (l, l ', tlv triple ρ), l, l ' represent source node and the destination node of transition relationship τ respectively, ρ is the constrain set that represents transition relationship τ.Yi Zhi, the source node of Gou Zao transition relationship τ and destination node all are nodes of locations v here; The node invariant α that the constraint set ρ of τ derives from nodes of locations v correspondence (v) (v), has with node rate of change β

ρ＝α(v)| _X∪α(v)| _X′∪β(v)| _X,X′,t∪{t＞0,t′＞0}

V ∈ V, X represents current variate-value, the variate-value of X ' expression migration back new state, α (v) | _XExpression variable currency will satisfy the node invariant, α (v) | _{X '}Variate-value after the expression state transition will satisfy the present node invariant, β (v) | _{X, X ', t}Variate-value after expression variable currency and the migration will satisfy the variable rate relation in the time variable t; Simultaneously, the origin node v that migration is this time simulated goes up t residence time＞0, and need peel off and this relation the residence time of migration simulation next time, therefore resets to any nonnegative number t '＞0.

2) transition relationship of Discrete Change structure among the H: the Discrete Change of H is reflected on the redirect set of relationship E of H, and the element e of set of relationship E represent a redirect and concerns that e is five-tuple, shape as

Each redirect concerns that e is with a new transition relationship δ of tectonic transport system, shape is as (v, v', ρ), v and v ' are respectively source node and the destination node of new transition relationship δ, and ρ is the constrain set on the transition relationship δ herein, its should reflect that redirect concerns that formula is defended in redirect on the e and the operation of resetting outside, also want to reflect the invariant on the source and target node of redirect relation, have

V ∈ V, X represents current variate-value, the variate-value of X ' expression migration back new state,

Expression variable currency will satisfy the conversion that blendes together discrete redirect e on the automat and defend formula, ψ | _{X '}Variate-value after the expression state transition will satisfy the replacement action that blendes together discrete redirect e on the automat, α (v) | _XExpression variable currency will satisfy the node invariant, α (v ') | _{X '}Variate-value after the expression state transition will satisfy the present node invariant.

As shown in Figures 2 and 3, be example with cistern water level monitor (WLM) system of blending together below, this converting system is described.

Figure 1 shows that the linearity that a linearity that comprises 6 nodes of locations, two system variables blendes together automat blendes together system model, this automat has been described the workflow of a level monitoring device.Monitor monitors the water level in the water tank, and correspondingly opens or closes valve.v ₀Be the start node of automat, other 5 nodes of locations v ₁, v ₂, v ₃, v ₄, v ₅Corresponding 5 kinds of states of system respectively.At position v ₁, v ₂Place's valve open; At position v ₃, v ₄The place, valve closing; At position v ₅The place, systematic water level reduces to 0, and system quits work.System variable y describes current water level, the time-delay of system variable x reflection current demand signal.

According to the transfer principle of above-mentioned converting system, structure water tank level monitoring device migratory system Water=(X _T, L, T, L ₀, θ)

1）X _T＝{x,y,t}；

2）L＝{v ₁,v ₂,v ₃,v ₄,v ₅}；

3）L ⁰＝{v ⁰}；

4）θ(v ₀)＝{y:＝1,x:＝0}

5) with v ₁Node and e ₁The limit is example, the structure of two class transition relationships below illustrating:

1. linearity blendes together continually varying transition relationship structure in the automat: with v ₁Be example: τ=(v ₁, v ₂, ρ), wherein

ρ＝α(v ₁)| _X∪α(v ₁)| _X′∪β(v ₁)| _X,X′,t∪{t＞0,t′＞0}

α(v ₁)| _X＝{y≤10}，α(v ₁)| _X′＝{y′≤10}，β(v ₁)| _X，X′,t＝{x′＝x+t,y′＝y+t}

Therefore,

ρ＝{y≤10,y′≤10,x′＝x+t,y′＝y+t,t＞0,t′＞0}

τ＝(v ₁,v ₁,{y≤10,y′≤10,x′＝x+t,y′＝y+t,t＞0,t′＞0}).

2. the linear transition relationship that blendes together Discrete Change in the automat is constructed: with v ₁Be example: δ=(v ₁, v ₂, ρ), wherein

Therefore,

ρ＝{y＝1,x′＝0,y≤10,x′≤2}

δ＝(v ₁,v ₂,{y＝1,x′＝0,y≤10,x′≤2})

Finally, be converted to as shown in Figure 3 migratory system model of equal value.

Though the present invention discloses as above with preferred embodiment, so it is not in order to limit the present invention.The persond having ordinary knowledge in the technical field of the present invention, without departing from the spirit and scope of the present invention, when being used for a variety of modifications and variations.Therefore, protection scope of the present invention is as the criterion when looking claims person of defining.

Claims (1)

1. one kind blendes together the migratory system building method of equal value of system towards linearity, comprises input side and outgoing side, it is characterized in that input side is that linearity blendes together system model, and outgoing side is the migratory system model, wherein:

Blending together automat with linearity blendes together system model as linearity and is expressed as H=(X, Σ, V, E, V ⁰α, β, γ), wherein: X is that the number of variable among the finite aggregate of real number value system variable and the X is the dimension that blendes together automat, Σ is the finite aggregate of event name, and V is the finite aggregate of nodes of locations, E be between the nodes of locations element e among redirect set of relationship and the E represent redirect relation (e shape as

Wherein, v, v' ∈ V, σ ∈ Σ,

Be that shape is

Conversion defend formula set, ψ is that shape is the replacement set of actions of x:=c.Above x, x _i(the ∈ X of 0≤i≤l), a, b, c _i(the ∈ R of 0≤i≤l), a value is to-∞, the b value is to ∞), V ⁰Be the initial position node set, α is the first mark function, and it is mapped to a node invariant with each position among the V, β is the second mark function, it is mapped to the set of a rate of change with each position among the V, and γ is the 3rd mark function, and it gathers V with start node ⁰In each position be mapped to one group of starting condition;

The migratory system model representation is P=(X _T, L, T, L ₀, θ), wherein: X _TBe system variable, L is the node name set, L ⁰Be the start node set, θ is the starting condition set, and T is the transition relationship set;

The linearity that described converting system will be imported with following rule blendes together the migratory system model that system model is converted to output:

System variable X _T, it comprises linearity and blendes together system variable X all in the system model and introduce time variable t, and X is arranged _T=X ∪ { t};

Node name set L, it is decided by that directly linearity blendes together the nodes of locations set of system model, has L=V;

Start node set L ⁰, it is decided by that directly linearity blendes together the initial position set of system model, has L ⁰=V ⁰

Starting condition set θ, its initial position satisfies θ (l)=γ to the mapping function θ of starting condition, and (v), l is initial position, and v is nodes of locations;

Transition relationship set T comprises by linearity blending together the transition relationship τ that the continuous variation of system model constructs and the Discrete Change that is blended together system model by linearity

The transition relationship δ that constructs, wherein:

Transition relationship τ be expressed as (l, l ', ρ), l, l ' represent source node and the destination node v of transition relationship τ respectively, and ρ is the constrain set on the transition relationship τ, the node invariant α that constrain set ρ derives from nodes of locations v correspondence (v) (v), has with node rate of change β

ρ＝α(v)| _X∪α(v)| _X′∪β(v)| _X,X′,t∪{t＞0,t′＞0}

V ∈ V, X represents current variate-value, the variate-value of X ' expression migration back new state, α (v) | _XExpression variable currency will satisfy the node invariant, α (v) | _{X '}Variate-value after the expression state transition will satisfy the present node invariant, β (v) | _{X, X ', t}Variate-value after expression variable currency and the migration will satisfy the variable rate relation in the time variable t;

Transition relationship δ is expressed as that (ρ), v and v ' are respectively source node and the destination node of transition relationship δ for v, v', and ρ is the constrain set on the transition relationship δ, has herein

V ∈ V, X represents current variate-value, the variate-value of X ' expression migration back new state,

Expression variable currency will satisfy the conversion that blendes together discrete redirect e on the automat and defend formula, ψ | _{X '}Variate-value after the expression state transition will satisfy the replacement action that blendes together discrete redirect e on the automat, α (v) | _XExpression variable currency will satisfy the node invariant, α (v ') | _{X '}Variate-value after the expression state transition will satisfy the present node invariant.

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