CN107168281B - Multi-agent system method for diagnosing faults based on finite time observer - Google Patents
Multi-agent system method for diagnosing faults based on finite time observer Download PDFInfo
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- CN107168281B CN107168281B CN201710333127.9A CN201710333127A CN107168281B CN 107168281 B CN107168281 B CN 107168281B CN 201710333127 A CN201710333127 A CN 201710333127A CN 107168281 B CN107168281 B CN 107168281B
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0259—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterized by the response to fault detection
- G05B23/0283—Predictive maintenance, e.g. involving the monitoring of a system and, based on the monitoring results, taking decisions on the maintenance schedule of the monitored system; Estimating remaining useful life [RUL]
Abstract
The present invention relates to a kind of multi-agent system method for diagnosing faults based on finite time observer, belongs to applied to multi-agent system technical field.The method that the present invention observes the failure of intelligent body adjacent thereto by establishing finite time Unknown Input Observer in some specific intelligent body, realizes the distributed diagnostics to multi-agent system.Designed distributed diagnostics design method in the present invention, extraneous time-varying can be theoretically inhibited to interfere the influence to fault diagnosis, and can be in preset finite time, the failure or multiple intelligent bodies occur to any one intelligent body in each adjacent intelligent body carries out effectively accurate finite time inline diagnosis and Fault Estimation when breaking down simultaneously.
Description
Technical field
The present invention relates to a kind of multi-agent system method for diagnosing faults based on finite time observer, belongs to and is applied to
Multi-agent system technical field.
Background technique
In recent years, the tool of complication system can be effectively treated as one kind, multi-agent Technology has been caused extensively
General concern is simultaneously applied to multiple key areas.But it the distinctive network linking of multi-agent system itself, is freely distributed, believes
The advantages that breath is shared also allows it to be easier the influence by failure.When event occurs in some intelligent body in multi-agent system
When barrier, failure can go to influence other intelligent bodies by the distinctive network linking of multi-agent system, to make entire more intelligence
Energy system system is by acid test.Therefore, in order to promote the stability and safety of multi-agent system, for its failure
Diagnostic techniques should also give the attention of height.Fault diagnosis can be divided into fault detection, fault reconstruction and Fault Estimation.Failure is examined
It is open close system operation situation to be monitored excessively to determine whether faulty generation, while determining the specifying information that failure occurs,
Such as time, position and size etc..
The existing fault diagnosis based on observer relies primarily on the steady-state performance in observer, whether is fixed against observer
Stablize, i.e., when the time approaching infinity, can the error that observer estimated value and system mode are formed infinite approach equalization point.
But due to multi-agent system, all flight control systems if you need to formation flight are the one high technologies for expending high investment, for
Its fault diagnosis must have accuracy and rapidity.This is just all made that the transient performance of fault diagnosis and constringency performance
It is required that.Therefore, finite time technology can be introduced, a limited time interval of finite time, that is, previously given.At this
In time, the state of control system will be in this Finite-time convergence to stable equilibrium point.
Chinese patent application 2016108243782 proposes " leader-follower type multi-agent system finite time robust
Fault diagnosis design method " communicates topological structure based on digraph, obtains Laplacian Matrix；It is established again for each node
State equation and output equation, and be new vector by state vector and fault vectors augmentation；According to the digraph of building, construction
Distributed error equation and global error equation based on digraph；It is finally based on finite time robust control, is obtained mostly intelligent
The gain matrix of the fault diagnosis observer of system system.But there is also following deficiencies for this method: first is that this method although it is contemplated that
The presence of external interference, but it is only reduced to a certain extent to failure by the design philosophy of robust control in the design process
The adverse effect of diagnostic result, and cannot thoroughly eliminate, this more or less causes diagnostic accuracy in design level
It reduces；Second is that the method for the multi-agent system fault diagnosis that this method uses is to need to establish phase in each intelligent body
Corresponding observer, higher cost；Third is that although this method can carry out fault diagnosis in finite time, when this is limited
Between not can be carried out and preset, the rapidity of online real-time fault diagnosis also needs to further increase.
Summary of the invention
The invention proposes a kind of multi-agent system method for diagnosing faults based on finite time observer, by certain
Finite time Unknown Input Observer is established in one specific intelligent body to observe the side of the failure of intelligent body adjacent thereto
Method realizes the distributed diagnostics to multi-agent system.Designed distributed diagnostics design side in the present invention
Method can theoretically inhibit extraneous time-varying to interfere the influence to fault diagnosis, and can be in preset finite time, to each
The failure or multiple intelligent bodies that any one intelligent body occurs in adjacent intelligent body are carried out effectively accurate when breaking down simultaneously
Finite time inline diagnosis and Fault Estimation.
The present invention is to solve its technical problem to adopt the following technical scheme that
A kind of multi-agent system method for diagnosing faults based on finite time observer, comprises the following specific steps that:
Step 1: constructing multi-agent system connection figure and by the communication link between multi-agent system with non-directed graph
It indicates, to obtain weighted adjacent matrix Λ；
Step 2: being directed to each intelligent body, the method by carrying out local linearization in operating point obtains the multiple agent
The local dynamic station equation of system, and establish according to obtained non-directed graph the global dynamical equation of multi-agent system；
Step 3: arbitrarily choosing an intelligent body in multi-agent system, the global dynamic of multi-agent system is reconstructed
Equation, system output at this time are made of local dynamic station information relevant to the intelligent body；
Step 4: system dynamical equation obtained in third step is resolved into three subsystems by two coordinate transforms,
And obtain depression of order subsystem not comprising Unknown worm；
Step 5: by designing two independent observers in the intelligent body of selection, construction theoretical based on finite time
A convergent finite time Unknown Input Observer within a preset time out；The state obtained according to the finite time observer
Estimated value and a fault diagnosis rule complete on-line fault diagnosis and Fault Estimation to adjacent intelligent body in finite time.
The concrete mode of weighted adjacent matrix Λ is obtained in the first step are as follows:
If being made of the non-directed graph of a complete multi-agent system one group of vertex and side, wherein V={ v1,v2,...,
vNIt is defined as the set on vertex, v1For the 1st intelligent body, v2For the 2nd intelligent body, vNIndicate n-th intelligent body；ε={ (vi,
vj):vi,vj∈ V } it is defined as the set on side；Vertex νiWith vjRespectively indicate i-th of intelligent body and j-th of intelligent body, i, j ∈ 1,
2 ..., N } and i ≠ j；Side (νi,νj) be used to indicate that intelligent body j can receive the information of intelligent body i；Definition and vertex νpIt is adjacent
The collection on vertex is combined into Np={ vj∈V:(vp,vj)∈ε,p≠j}；
Define Λ=[aij]∈RN×NIndicate the weighted adjacent matrix of the non-directed graph, wherein aijIndicate the weight of each edge；
If (νi,νj) ∈ ε, then aij=1, otherwise aij=0；And aii=0.
The local dynamic station equation of multi-agent system described in second step:
In above-mentioned equation, xi(t) and yi(t) be respectively each intelligent body state vector and output vector,Indicate every
The differential term of a intelligent body state vector, ui(t) be each intelligent body control input vector, fiIt (t) is the system failure, di(t)
For extraneous time-varying perturbation vector；A, B, C are respectively the state matrix, input matrix, output matrix of the multi-agent system, square
Battle array E is failure distribution matrix, and matrix D is disturbance distribution matrix.
In the third step, an intelligent body p is arbitrarily chosen, wherein p ∈ (1~N), be based on non-directed graph, according to intelligent body
P, the global dynamical equation reconstruct of the multi-agent system are as follows:
Wherein: fr(t) it indicates to occur in r (r ∈ Np) failure in a intelligent body, and f-r(t) it indicates from global fault f
(t) f is removed inr(t) matrix after,It is corresponding to fr(t) distribution matrix, and beA sub- square
Battle array, andIndicate fromMiddle removalRemaining submatrix afterwards,Indicate intelligence
The local dynamic station information of body p,Indicate setRadix, whereinIndicate intelligent body p adjacent vertex
The intersection of set and intelligent body p composition；It indicates local message matrix and is sequency spectrum matrix, wherein InIndicate one
The unit matrix of n × n dimension,A submatrix for being a row non-singular matrix and being weighted adjacent matrix Λ.
DefinitionThe global dynamic of the multi-agent system
Equation:
(3) it indicates are as follows:
Obtained system dynamical equation is resolved into three subsystems described in 4th step method particularly includes:
Assuming that matrixIt is all sequency spectrum matrix with matrix M, in view ofIt is also sequency spectrum matrix, definitionRank (M)=l,(l+q≤p)；Wherein, rank (X) indicates a square
The order of battle array X；
Assuming that In such case
Under, matrixThere will be left pseudoinverse:
Wherein,Indicate the left pseudoinverse of a matrix X；
The state equation of system is coordinately transformed first, defines a nonsingular matrix:
Wherein: W=P1W0, W ∈ RNn×(Nn-l-q), W0It is any one order matrixNon- surprise
Different matrix, square matrixAnd
Meet P1 2=P1, i.e. P1It is an idempotent matrix, wherein INnFor the unit matrix of Nn × Nn dimension；
By nonsingular matrix T, system (4) is broken down into:
Wherein:State vector after being defined as system decomposition,For the state vector after system decomposition
Differential term,State matrix, input matrix, output matrix after the respectively described multi-agent system decomposition, square
Battle arrayIt is the failure distribution matrix after decomposing, matrixIt is specific as follows for the disturbance distribution matrix after decomposition:
And haveWithIndicate the state vector after decomposing； It is the state matrix after decomposing；Similarly,WithTable
Show that the input matrix after decomposing, T are above-mentioned obtained nonsingular matrix, T-1For the inverse matrix of matrix T；IlWith IqIt respectively indicates
The unit matrix of unit matrix and q × q dimension that one l × l is tieed up；
WithDifferential term all respectively directly by fr(t) it is influenced, is removed with two Unknown worms of ω (t)
WithDifferential term after, system (5) is writeable are as follows:
Wherein: INn-l-qFor one (Nn-l-q) × (Nn-l-q) dimension unit matrix,
Next the output equation of system is coordinately transformed, defines a nonsingular matrix:
Wherein: Q=P2Q0, Q ∈ Rp×(p-l-q), Q0It is chosen for any one order matrix
Nonsingular matrix；Square matrix
And meet P2 2=P2, i.e. P2It is an idempotent matrix；
DefinitionU1(t)∈Rl×p, U2(t)∈Rq×p, U3(t)∈R(p-l-q)×p, define Ip-l-qIndicate one
(p-l-q) × (p-l-q) unit matrix tieed up, then have:
Obviously, haveWithWherein, 0l×(Nn-l-q)With
0q×(Nn-l-q)Respectively indicate l × (Nn-l-q) peacekeeping q × (Nn-l-q) dimension null matrix；Again to the output equation equation in (6)
Both sides while premultiplication U-1It obtains:
By these equatioies, required depression of order subsystem is obtained:
Wherein:Distribution matrix is exported for depression of order,
For depression of order output vector.
By designing two independent observers in the intelligent body of selection in 5th step, managed based on finite time
By the method for constructing a convergent finite time Unknown Input Observer within a preset time is:
First, it is assumed thatIt is that can see, then two independent Design of Observer are as follows:
Wherein: z1(t) and z2(t) state vector of two observers respectively constructed,WithRespectively z1(t)
With z2(t) differential term,And L1With L2It is the observer gain matrix for needing to design；
Secondly, passing through definition:
Wherein:
Above-mentioned two independent observer constitutes an observer, adds a time lag τ for estimated stateThen
Establish the finite time Design of unknown input observer in the intelligent body p of selection are as follows:
Wherein:Indicate state vectorEstimated value, t0Indicate initial time, z (t- τ) is i.e. to observer state
In addition time lag τ, K=[an INn-l-q 0Nn-l-q][S eFτS]-1,And INn-l-qExpression one (Nn-l-q) ×
(Nn-l-q) unit matrix tieed up；For z (t), t ∈ [t0-τ,t0], it is assumed that Wherein,AndIt is set as the constant value of any one bounded.
Fault diagnosis rule in 5th stepConcrete form are as follows:
Wherein:Indicate state vectorEstimated value.
Beneficial effects of the present invention are as follows:
First is that the distributed type fault diagnosis method that the present invention designs, takes and establish observer in some intelligent body and go to monitor
The mode of its periphery intelligent body does not need to establish observer for each intelligent body, greatly reduces required observer
Quantity, to reduce the cost of system diagnostics.
Fault diagnosis is carried out to multi-agent system second is that the present invention is based on Unknown Input Observers, in design observer
In the process, system disturbance etc. is considered as Unknown worm and carries out system decomposition, additional interference can be effectively reduced in this way to system
The influence of diagnosis, to keep fault diagnosis result more reliable.
Third is that the present invention not only allows for the steady-state performance of observer, the steady-state performance of observer estimation procedure is more considered
And constringency performance, it may finally accomplish to carry out inline diagnosis and Fault Estimation in preset finite time, improve event
Hinder the accuracy and rapidity of diagnosis.
Detailed description of the invention
Fig. 1 for the present invention implements the tool established of example of verifying, and there are four the multi-agent system of intelligent body node is undirected
Figure, in which: icon 1-4 respectively indicates intelligent body 1, intelligent body 2, intelligent body 3 and intelligent body 4 in the multi-agent system.
Fig. 2 is by Ι of the embodiment of the present invention intelligent body 1,2,4 surveyed while when breaking down, designed through the invention
The result schematic diagram that distributed type fault diagnosis method obtains；Wherein Fig. 2 (a) is true for the Fault Estimation value and failure of intelligent body 1
The correlation curve schematic diagram of value；Fig. 2 (b) is the schematic diagram of the failure true value occurred in intelligent body 2；Fig. 2 (c) is intelligent body 3
Fault Estimation value and failure true value correlation curve schematic diagram；Fig. 2 (d) is true for the Fault Estimation value and failure of intelligent body 4
The correlation curve schematic diagram of real value.
Fig. 3 is by Ι of the embodiment of the present invention Ι intelligent body 2,3,4 surveyed while when breaking down, designed through the invention
The result schematic diagram that distributed type fault diagnosis method obtains.Wherein Fig. 3 (a) is true for the Fault Estimation value and failure of intelligent body 1
The correlation curve schematic diagram of value；Fig. 3 (b) is the schematic diagram of the failure true value occurred in intelligent body 2；Fig. 3 (c) is intelligent body 3
Fault Estimation value and failure true value correlation curve schematic diagram；Fig. 3 (d) is true for the Fault Estimation value and failure of intelligent body 4
The correlation curve schematic diagram of real value.
Specific embodiment
The invention is described in further details with reference to the accompanying drawing.
The present invention goes out using certain following VTOL aircraft longitudinal movement equation as objective for implementation in its formation flight
Existing actuator failures propose a kind of multi-agent system distributed diagnostics based on finite time Unknown Input Observer
Design method, the method for diagnosing faults can be improved the transient performance and constringency performance of fault diagnosis, presetting system
Finite time in complete inline diagnosis and Fault Estimation；
Consider certain following VTOL aircraft longitudinal movement equation:
Wherein, xi(t) and yi(t) be respectively each intelligent body state vector and output vector,Indicate each intelligence
The differential term of body state vector, ui(t) be each intelligent body control input vector, fiIt (t) is the system failure, diIt (t) is the external world
Time-varying perturbation vector.A, B, C are respectively the state matrix, input matrix, output matrix of the multi-agent system, and matrix E is
Failure distribution matrix, matrix D are disturbance distribution matrix.The each matrix of system is expressed as follows:
Assuming that actuator failures occur for the system: it is the part occurred controlling input in view of actuator failures, therefore this
Invent faulty distribution matrix E=B；It is assumed that the distribution matrix of the input disturbance of system is [0 01 0] D=T。
Firstly, constructing multi-agent system connection figure and indicating with non-directed graph, weighted adjacent matrix Λ is obtained:
If being made of the non-directed graph of a complete multi-agent system several vertex and several sides, wherein V=
{v1,v2,...,vNIt is defined as the set on vertex, v1For the 1st intelligent body, v2For the 2nd intelligent body, vNIndicate n-th intelligence
Body；ε={ (vi,vj):vi,vj∈ V } it is defined as the set on side；Vertex νiWith vjRespectively indicate i-th of intelligent body and j-th of intelligence
Body, i, j ∈ { 1,2 ..., N } and i ≠ j；Side (νi,νj) be used to indicate that intelligent body j can receive the information of intelligent body i；Definition with
Vertex νpThe collection of adjacent vertex is combined into Np={ vj∈V:(vp,vj)∈ε,p≠j}。
Define Λ=[aij]∈RN×NIndicate the weighted adjacent matrix of the non-directed graph, wherein aijIndicate the weight of each edge；
If (νi,νj) ∈ ε, then aij=1, otherwise aij=0；And aii=0.
According to the non-directed graph of building, the global dynamical equation of the multi-agent system can be constructed:
Wherein: x (t) ∈ RNnIt is defined as the global state vector of the multi-agent system,Indicate global state vector
Differential term, y (t) are the global output vector of the multi-agent system, u (t) ∈ RNmIt is global control input vector,For global fault's vector,For global perturbation vector,For global state distribution matrix,
Input distribution matrix is controlled for the overall situation,Distribution matrix is disturbed for the overall situation,Distribution matrix is exported for the overall situation,For global fault's distribution matrix.In addition, INIndicate N × N-dimensional unit matrix,Represent Kronecker product.Specifically
It is as follows:
Wherein:For the transposition of the state vector of first intelligent body,For the state vector of second intelligent body
Transposition,For the transposition of the state vector of n-th intelligent body；For the control input vector of first intelligent body
Transposition,For the transposition of the control input vector of second intelligent body,For the control input vector of n-th intelligent body
Transposition；For the transposition of the output vector of first intelligent body,For turn of the output vector of second intelligent body
It sets,For the transposition of the output vector of n-th intelligent body；f1 TIt (t) is the transposition of the fault vectors of first intelligent body,For the transposition of the fault vectors of second intelligent body,For the transposition of the fault vectors of n-th intelligent body；For
The transposition of the perturbation vector of first intelligent body,For the transposition of the perturbation vector of second intelligent body,For n-th
The transposition of the perturbation vector of intelligent body.
Further, the system dynamical equation of each intelligent body is directed to described in second step, its implementation is to each
Obtained by nonlinear system is linearized in operating point.
Further, in the third step, an intelligent body p (p ∈ (1~N)) is arbitrarily chosen, is based on non-directed graph, foundation
The global dynamical equation of intelligent body p, the multi-agent system may be expressed as:
Wherein: fr(t) it indicates to occur in r (r ∈ Np) failure in a intelligent body, and f-r(t) it indicates from global fault f
(t) f is removed inr(t) matrix after.It is corresponding to fr(t) distribution matrix, and beA sub- square
Battle array, andIndicate fromMiddle removalRemaining submatrix afterwards.Indicate intelligence
The available local dynamic station information of body p.Indicate setRadix, whereinIndicate intelligent body p adjacent top
The intersection of set and intelligent body the p composition of point.It indicates local message matrix and is sequency spectrum matrix, wherein InIt indicates
The unit matrix of one n × n dimension,A submatrix for being a row non-singular matrix and being weighted adjacent matrix Λ.
Known Λ=[aij]∈RN×N, wherein aijThe weight for indicating each edge, if (νi,νj) ∈ ε, then aij=1, otherwise aij=0.Together
Reason, ΛpIn the above-mentioned set of element representationIncluded in the mutual phase composition of node each edge weight.
DefinitionThen (3) can indicate are as follows:
Further, system decomposition in the 4th step method particularly includes:
Matrix is assumed in the present inventionIt is all sequency spectrum matrix with matrix M, in view ofIt is also sequency spectrum
Matrix can defineRank (M)=l,(l+q≤p).Wherein, rank
(X) order of a matrix X is indicated.
Then assume in the present invention In this case, matrixThere will be left pseudoinverse:
Wherein,Indicate the left pseudoinverse of a matrix X.
The state equation of system is coordinately transformed first, defines a nonsingular matrix:
Wherein: W=P1W0, W ∈ RNn×(Nn-l-q), W0It is that any one can be with order matrix
Nonsingular matrix.Square matrixAnd
Meet P1 2=P1, i.e. P1It is an idempotent matrix, wherein INnFor the unit matrix of Nn × Nn dimension.
By nonsingular matrix T, system (4) can be broken down into:
Wherein:State vector after being defined as system decomposition,For the state vector after system decomposition
Differential term,State matrix, input matrix, output matrix after the respectively described multi-agent system decomposition, square
Battle arrayIt is the failure distribution matrix after decomposing, matrixIt is specific as follows for the disturbance distribution matrix after decomposition:
And haveWithIndicate the state vector after decomposing； It is the state matrix after decomposing；Similarly,WithTable
Show that the input matrix after decomposing, T are above-mentioned obtained nonsingular matrix, T-1For the inverse matrix of matrix T.In addition, IlWith IqPoint
It Biao Shi not the unit matrix of l × l dimension and the unit matrix of q × q dimension.
Obviously,WithDifferential term all respectively directly by fr(t) it is influenced, is removed with two Unknown worms of ω (t)WithDifferential term after, system (5) is writeable are as follows:
Wherein: INn-l-qFor one (Nn-l-q) × (Nn-l-q) dimension unit matrix,
Next the output equation of system is coordinately transformed, defines a nonsingular matrix:
Wherein: Q=P2Q0, Q ∈ Rp×(p-l-q), Q0It can be chosen for any one order matrixNonsingular matrix.Square matrixAnd meet P2 2=P2, i.e. P2
It is an idempotent matrix.
DefinitionU1(t)∈Rl×p, U2(t)∈Rq×p, U3(t)∈R(p-l-q)×p, define Ip-l-qIndicate one
(p-l-q) × (p-l-q) unit matrix tieed up, then have:
Obviously, haveWithWherein, 0l×(Nn-l-q)With
0q×(Nn-l-q)Respectively indicate l × (Nn-l-q) peacekeeping q × (Nn-l-q) dimension null matrix.Again to the output equation equation in (6)
Both sides while premultiplication U-1It is available:
By these equatioies, available required reduced order system:
Wherein:Distribution matrix is exported for depression of order,
For depression of order output vector.
Further, the method that finite time Unknown Input Observer is designed in the 5th step is:
Firstly, assuming in the present inventionIt is considerable, then the observer of two separation may be designed as:
Wherein: z1(t) and z2(t) state vector of two observers respectively constructed,WithRespectively z1(t)
With z2(t) differential term,And L1With L2It is the observer gain matrix for needing to design.
Secondly, passing through definition:
Wherein:
Above-mentioned two independent observer may be constructed an observer, add a time lag τ for estimated stateThe finite time Unknown Input Observer then established in the intelligent body p of selection can be designed as:
Wherein:Indicate state vectorEstimated value, t0Indicate initial time, z (t- τ) is i.e. to observer state
In addition time lag τ, K=[an INn-l-q 0Nn-l-q][S eFτS]-1,And INn-l-qExpression one (Nn-l-q) ×
(Nn-l-q) unit matrix tieed up.It include time lag during due to design, then observer must have a primary condition.It is right
In z (t), t ∈ [t0-τ,t0], without loss of generality, assume in the present inventionWherein,AndIt can be set as the constant value of any one bounded.
Inline diagnosis and Fault Estimation, the present invention are carried out to the failure of multi-agent system in finite time in order to realize
Finite time Unknown Input Observer described in 5th step must satisfy:
1) boundedness: the evaluated error of the observerIn time interval [t0,t0+ τ] in must keep
Bounded；
2) convergence: the observer can restrain in finite time τ, it may be assumed that
When the observer meets following two constraint condition:
1) F is stable；
2)det[S,eFτS]≠0；
Finite time Unknown Input Observer described in 5th step of the invention exists and can guarantee having in estimation procedure
Criticality simultaneously is estimated to do well in finite time τWherein, second constraint condition det [S, eFτS] ≠ 0 can be by right
Observer gain L1With L2Selection reach.Any one scalar σ < 0 is given, as the L of selection1With L2It can make
Re(λi(F2)) < σ < Re (λj(F1)) < 0, i, j=1 ..., Nn-l-q
Then to substantially any one τ ∈ R+, det [S, eFτS] ≠ 0 can meet, in which: λi(F2) representing matrix F2
Any one characteristic value, λj(F1) representing matrix F1Any one characteristic value.
Fault diagnosis rule in 5th stepConcrete form are as follows:
Wherein:Indicate state vectorEstimated value,
In order to preventIt cannot obtain in some systems, Ke YiyongTo replace:
Wherein: α is the scalar greater than zero, ypfIt (t) is replacement output yp(t) the new output vector constructed,For ypf
(t) differential term.
In this way, fault diagnosis rule becomes:Root
The state estimation obtained according to the finite time observer established in intelligent body p and fault diagnosis rule can be in finite times
The interior on-line fault diagnosis and Fault Estimation for completing to abut it intelligent body r.
As shown in Figure 1, intelligent body 1, intelligent body 2, intelligent body 3 and intelligent body 4 represent the non-directed graph with 4 sections in Fig. 1
Point.Weighted adjacent matrix as can be drawn from Figure 1In the present embodiment, intelligent body 2 is chosen to build
Vertical finite time Unknown Input Observer is used to carry out fault diagnosis to its periphery intelligent body.As seen from Figure 1, intelligent body 2
It is connected with other three intelligent bodies, therefore in the present embodimentThen Λp=Λ.Available public affairs in specific implementation process
Two important parameters in formula (3) are as follows:
Two seat transformation matrixs for needing to use are as follows:
Using Matlab software, preset finite time is chosen for τ=1s, α=0.001 is chosen, pole is matched
It sets in [- 2-1-2-2] and [- 7-6-7-7], available:
For the effect for verifying distributed type fault diagnosis method of the present invention, tested using following two emulation embodiment
Card joined noise as disturbance in two embodiments in system model.
Embodiment Ι
Assuming that there is failure simultaneously in intelligent body 1,2,4:
The failure that 1st intelligent body occurs
The failure that 2nd intelligent body occurs
The failure that 4th intelligent body occurs
Fig. 2 is by Ι of the embodiment of the present invention intelligent body 1,2,4 surveyed while when breaking down, designed through the invention
The result schematic diagram that distributed type fault diagnosis method obtains.Wherein Fig. 2 (a) is true for the Fault Estimation value and failure of intelligent body 1
The correlation curve schematic diagram of value；Fig. 2 (b) is the schematic diagram of the failure true value occurred in intelligent body 2；Fig. 2 (c) is intelligent body 3
Fault Estimation value and failure true value correlation curve schematic diagram；Fig. 2 (d) is true for the Fault Estimation value and failure of intelligent body 4
The correlation curve schematic diagram of real value.And wherein intelligent body 2 is to be selected as establishing finite time Unknown Input Observer in the present embodiment
Intelligent body, so theoretically the fault diagnosis to its periphery intelligent body should not be influenced in the failure wherein occurred.
Embodiment Ι Ι
Assuming that intelligent body 2,3,4 breaks down simultaneously, the failure wherein occurred in intelligent body 2 be set as in embodiment Ι
Size is constant:
The failure that 3rd intelligent body occurs
The failure that 4th intelligent body occurs
Fig. 3 is by Ι of the embodiment of the present invention Ι intelligent body 2,3,4 surveyed while when breaking down, designed through the invention
The result schematic diagram that distributed type fault diagnosis method obtains.Wherein Fig. 3 (a) is true for the Fault Estimation value and failure of intelligent body 1
The correlation curve schematic diagram of value；Fig. 3 (b) is the schematic diagram of the failure true value occurred in intelligent body 2；Fig. 3 (c) is intelligent body 3
Fault Estimation value and failure true value correlation curve schematic diagram；Fig. 3 (d) is true for the Fault Estimation value and failure of intelligent body 4
The correlation curve schematic diagram of real value.And wherein intelligent body 2 is to be selected as establishing finite time Unknown Input Observer in the present embodiment
Intelligent body, so theoretically the fault diagnosis to its periphery intelligent body should not be influenced in the failure wherein occurred.
As shown in the picture, it when failure occurs in the intelligent body on 2 periphery of intelligent body, establishes limited in intelligent body 2
Time Unknown Input Observer can complete inline diagnosis and Fault Estimation in pre-set finite time τ=1s.And
And the failure in other intelligent bodies occurs, the result of fault diagnosis will not all be produced including the failure in intelligent body 2 occurs
It is raw to influence.And the method for the Unknown Input Observer used in the present invention it can be seen from curve in figure, it greatly inhibits additional
The influence of noise.
From simulation result it can be concluded that, when intelligent bodies one or more in multi-agent system break down, it is only necessary to
Design a small amount of observer, the present invention design based on finite time Unknown Input Observer distributed type fault diagnosis method
To carry out inline diagnosis and Fault Estimation in preset finite time, and additional time-varying interference can be inhibited well
It influences.The present invention has important practical reference with accurate measurements for fault diagnosis of the multi-agent system in finite time
Value.
All explanations not related to belong to techniques known in a specific embodiment of the invention, can refer to known skill
Art is implemented.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (8)
1. a kind of multi-agent system method for diagnosing faults based on finite time observer, which is characterized in that including having as follows
Body step:
Step 1: construct multi-agent system connection figure by the communication link between multi-agent system and indicated with non-directed graph,
To obtain weighted adjacent matrix Λ；
Step 2: being directed to each intelligent body, the method by carrying out local linearization in operating point obtains the multi-agent system
Local dynamic station equation, and establish according to obtained non-directed graph the global dynamical equation of multi-agent system；
Step 3: arbitrarily choosing an intelligent body in multi-agent system, the global dynamical equation of multi-agent system is reconstructed,
System output at this time is made of local dynamic station information relevant to the intelligent body；
Step 4: system dynamical equation obtained in third step is resolved into three subsystems, and obtain by two coordinate transforms
To the depression of order subsystem not comprising Unknown worm；
Step 5: by designing two independent observers in the intelligent body of selection, it is theoretical based on finite time, construct one
A finite time Unknown Input Observer convergent within a preset time；The state estimation obtained according to the finite time observer
Value and a fault diagnosis rule complete on-line fault diagnosis and Fault Estimation to adjacent intelligent body in finite time.
2. the multi-agent system method for diagnosing faults according to claim 1 based on finite time observer, feature
Be, the concrete mode of weighted adjacent matrix Λ obtained in the first step are as follows: set be made of one group of vertex and side one it is complete more
The non-directed graph of multiagent system, wherein V={ v1,v2,...,vNIt is defined as the set on vertex, v1For the 1st intelligent body, v2It is
2 intelligent bodies, vNIndicate n-th intelligent body；ε={ (vi,vj):vi,vj∈ V } it is defined as the set on side；Vertex νiWith vjRespectively
Indicate i-th of intelligent body and j-th of intelligent body, i, j ∈ { 1,2 ..., N } and i ≠ j；Side (νi,νj) be used to indicate that intelligent body j connects
Receive the information of intelligent body i；Definition and vertex νpThe collection of adjacent vertex is combined into Np={ vj∈V:(vp,vj)∈ε,p≠j}；
Define Λ=[aij]∈RN×NIndicate the weighted adjacent matrix of the non-directed graph, wherein aijIndicate the weight of each edge；If (νi,
νj) ∈ ε, then aij=1, otherwise aij=0；And aii=0.
3. the multi-agent system method for diagnosing faults according to claim 1 based on finite time observer, feature
It is, the local dynamic station equation of multi-agent system described in second step:
In above-mentioned equation, xi(t) and yi(t) be respectively each intelligent body state vector and output vector,Indicate each intelligence
The differential term of energy body state vector, ui(t) be each intelligent body control input vector, fiIt (t) is the system failure, diIt (t) is outer
Boundary's time-varying perturbation vector；A, B, C are respectively the state matrix, input matrix, output matrix of the multi-agent system, matrix E
It is failure distribution matrix, matrix D is disturbance distribution matrix.
4. the multi-agent system method for diagnosing faults according to claim 3 based on finite time observer, feature
It is, in the third step, arbitrarily chooses an intelligent body p, wherein p ∈ (1~N), be based on non-directed graph, it, should according to intelligent body p
The global dynamical equation of multi-agent system reconstructs are as follows:
Wherein: fr(t) it indicates to occur in r (r ∈ Np) failure in a intelligent body, and f-r(t) it indicates from global fault f (t)
Remove fr(t) matrix after,It is corresponding to fr(t) distribution matrix, and beA submatrix, andIndicate fromMiddle removalRemaining submatrix afterwards,Indicate intelligent body p
Local dynamic station information,Indicate setRadix, whereinIndicate the set of intelligent body p adjacent vertex
With the intersection of intelligent body p composition；It indicates local message matrix and is sequency spectrum matrix, wherein InIndicate a n × n
The unit matrix of dimension,A submatrix for being a row non-singular matrix and being weighted adjacent matrix Λ.
5. the multi-agent system method for diagnosing faults according to claim 4 based on finite time observer, feature
It is, definesThe global dynamic side of the multi-agent system
Journey:
(3) it indicates are as follows:
6. the multi-agent system method for diagnosing faults according to claim 5 based on finite time observer, feature
It is, obtained system dynamical equation is resolved into three subsystems described in the 4th step method particularly includes:
Assuming that matrixIt is all sequency spectrum matrix with matrix M, in view ofIt is also sequency spectrum matrix, definition(l+q≤p)；Wherein, rank (X) indicates one
The order of a matrix X；
Assuming that At this
In the case of kind, matrixThere will be left pseudoinverse:Wherein,Indicate the left pseudoinverse of a matrix X；
The state equation of system is coordinately transformed first, defines a nonsingular matrix:
Wherein: W=P1W0, W ∈ RNn×(Nn-l-q), W0It is any one order matrixNonsingular square
Battle array, square matrixAnd meet P1 2
=P1, i.e. P1It is an idempotent matrix, wherein INnFor the unit matrix of Nn × Nn dimension；
By nonsingular matrix T, formula (4) is broken down into:
Wherein:State vector after being defined as system decomposition,For the differential of the state vector after system decomposition
,State matrix, input matrix, output matrix after the respectively described multi-agent system decomposition, matrix
It is the failure distribution matrix after decomposing, matrixIt is specific as follows for the disturbance distribution matrix after decomposition:
And haveWithIndicate the state vector after decomposing； It is the state matrix after decomposing；Similarly,WithTable
Show that the input matrix after decomposing, T are above-mentioned obtained nonsingular matrix, T-1For the inverse matrix of matrix T；IlWith IqIt respectively indicates
The unit matrix of unit matrix and q × q dimension that one l × l is tieed up；
WithDifferential term all respectively directly by fr(t) it is influenced, is removed with two Unknown worms of ω (t)WithDifferential term after, formula (5) is written as:
Wherein: INn-l-qFor one (Nn-l-q) × (Nn-l-q) dimension unit matrix,
Next the output equation of system is coordinately transformed, defines a nonsingular matrix:
Wherein: Q=P2Q0, Q ∈ Rp×(p-l-q), Q0It is chosen for any one order matrix
Nonsingular matrix；Square matrix
And meet P2 2=P2, i.e. P2It is an idempotent matrix；
DefinitionU1(t)∈Rl×p, U2(t)∈Rq×p, U3(t)∈R(p-l-q)×p, define Ip-l-qIndicate (a p-l-
Q) unit matrix × (p-l-q) tieed up, then have:
Obviously, haveWithWherein, 0l×(Nn-l-q)With
0q×(Nn-l-q)Respectively indicate l × (Nn-l-q) peacekeeping q × (Nn-l-q) dimension null matrix；Again to the output equation equation in (6)
Both sides while premultiplication U-1It obtains:
By these equatioies, required depression of order subsystem is obtained:
Wherein:Distribution matrix is exported for depression of order,For
Depression of order output vector.
7. the multi-agent system method for diagnosing faults according to claim 6 based on finite time observer, feature
It is, theoretical based on finite time by designing two independent observers in the intelligent body of selection in the 5th step, structure
The method for producing a convergent finite time Unknown Input Observer within a preset time is:
First, it is assumed thatIt is that can see, then two independent Design of Observer are as follows:
Wherein: z1(t) and z2(t) state vector of two observers respectively constructed,WithRespectively z1(t) and z2
(t) differential term,And L1With L2It is the observer gain matrix for needing to design；
Secondly, passing through definition:
Wherein:
Above-mentioned two independent observer constitutes an observer, adds a time lag τ for estimated stateThen establish
Finite time Design of unknown input observer in the intelligent body p of selection are as follows:
Wherein:Indicate state vectorEstimated value, t0Indicate that initial time, z (t- τ) add observer state
One time lag τ, K=[INn-l-q 0Nn-l-q][S eFτS]-1,And INn-l-qIndicate (Nn-l-q) × (Nn-
L-q) the unit matrix tieed up；For z (t), t ∈ [t0-τ,t0], it is assumed thatWherein,AndIt is set as the constant value of any one bounded.
8. the multi-agent system method for diagnosing faults according to claim 7 based on finite time observer, feature
It is, the fault diagnosis rule in the 5th stepConcrete form are as follows:
Wherein:Indicate state vectorEstimated value.
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| CN108803317B (en) * | 2018-05-08 | 2021-08-03 | 天津大学 | Self-adaptive multivariable four-rotor unmanned aerial vehicle finite time fault-tolerant control method |
| CN108681320A (en) * | 2018-05-11 | 2018-10-19 | 北京理工大学 | A kind of distributed multi agent real-time fault detection method based on regional cooperative |
| CN110058519B (en) * | 2019-04-02 | 2020-07-07 | 南京航空航天大学 | Active formation fault-tolerant control method based on rapid self-adaptive technology |
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| CN112347640B (en) * | 2020-11-05 | 2024-02-13 | 西北工业大学 | Fault diagnosis method based on fixed time fault observer |
| CN113156812B (en) * | 2021-01-28 | 2021-11-23 | 淮阴工学院 | Fault detection method for secondary chemical reactor based on unknown input observer |
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