CN109039725A - It is a kind of with the complex network optimal estimating method that couples at random - Google Patents
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Abstract
It is a kind of with the complex network optimal estimating method that couples at random, the present invention relates to Random Coupling complex network optimal estimating method.The present invention solves standing state estimation method cannot handle the time lag complex network coupled at random with measurement Loss and inaccurate probability of happening simultaneously, cause to estimate that performance accuracy rate is low, and there are loss of transmitted data, transmission failure, switching nodes can not receive in the simultaneous situation of other nodal informations, leads to the problem for estimating that performance accuracy rate is low.Process are as follows: one, the random generation coupling time lag complex network dynamic model of foundation；Two, state estimation is carried out to dynamic model under event-triggered protocols；Three, ∑ is calculatedi,k+1|k；Four, K is calculatedi,k+1；Five, it obtainsJudge whether k+1 reaches M, if k+1 < M, executes six, otherwise terminate；Six, ∑ is calculatedi,k+1|k+1；Another k=k+1 executes two, until meeting k+1=M.The present invention is used for complex network optimal estimating field.
Description
Technical Field
The invention relates to a random coupling complex network optimization estimation method.
Background
State estimation of a complex network is an important research problem in a control system, and is widely applied to signal estimation tasks in the fields of engineering, power grids, social networks and the like.
When the network is congested, the measurement loss phenomenon often occurs, and in practical application, the coupling between nodes occurs randomly due to network switching. Therefore, it is necessary to design a state estimation method suitable for these network-induced phenomena, especially when the probability of random coupling is uncertain;
the existing state estimation method can not process the randomly coupled time-lag complex network with measurement loss and inaccurate occurrence probability at the same time, so that the estimation performance accuracy is low;
the existing state estimation method has the problems of low estimation performance accuracy rate caused by the loss of transmission data, transmission failure and incapability of receiving information of other nodes by a coupling node.
Disclosure of Invention
The invention solves the problems that the existing state estimation method can not simultaneously process the time-lag complex network with random coupling and measurement loss and inaccurate occurrence probability, which causes low estimation performance accuracy, and the estimation performance accuracy is low under the condition that transmission data is lost, transmission fails, and coupling nodes can not receive other node information simultaneously, and provides the complex network optimization estimation method with random coupling.
A complex network optimization estimation method with random coupling comprises the following specific processes:
the complex network can be a network formed by satellites, a network formed by robots, a network formed by spacecrafts or a network formed by radars;
establishing a random coupling time-lag complex network dynamic model with measurement loss and inaccurate occurrence probability;
secondly, performing state estimation on the random coupling time-lag complex network dynamic model with the measurement loss phenomenon and the inaccurate occurrence probability established in the first step under an event trigger protocol;
step three, calculating the upper bound sigma of the one-step prediction error covariance matrix of the state estimation of each node of the complex networki,k+1|k；
Step four, according to the one-step prediction error covariance matrix upper bound sigma obtained in step threei,k+1|kCalculating an estimated gain moment for each node of the complex networkMatrix Ki,k+1；
Step five, obtaining the estimated gain matrix K of each node in the step fouri,k+1Substituting the state estimation formula 8 in the step two to obtain the state estimation of the ith node at the (k + 1) th momentThe state estimation of the randomly generated coupling time-lag complex network with the measurement loss phenomenon and the inaccurate generation probability is realized.
Judging whether k +1 reaches the total time length M of the complex network, if k +1 is less than M, executing a sixth step, and if k +1 is equal to M, ending the operation;
step six, according to the estimated gain matrix K of each node of the complex network calculated in the step fouri,k+1Calculating the upper bound sigma of the covariance matrix of the estimation error of each node of the complex networki,k+1|k+1；
And k is k +1, and the step two is executed until k +1 is M.
The invention has the following effects:
the invention provides a time-lag complex network state estimation method with random coupling of measurement loss phenomenon and inaccurate occurrence probability, which considers the influence of the random coupling of the measurement loss phenomenon and the inaccurate occurrence probability on state estimation performance, and utilizes an extended Kalman filtering method to comprehensively consider effective information of an estimation error covariance matrix; the method solves the problems that the existing state estimation method can not simultaneously process the randomly coupled time-lag complex network with the measurement loss phenomenon and the inaccurate occurrence probability, so that the estimation performance accuracy is low, and the estimation performance accuracy is improved.
The method utilizes an extended Kalman filtering method, obtains an estimated error covariance matrix by considering effective information of the estimated error covariance matrix, and then ensures that the trace of the estimated error covariance matrix can obtain the minimum value in each step by designing a gain matrix. A minimization of the estimation error is guaranteed. The performance estimation is not affected under the condition that the transmission data is lost, the transmission fails and the condition that the existing coupling node cannot receive other node information (coupling occurs randomly) occurs simultaneously, and the estimation accuracy is improved.
Solves the problem of low accuracy of estimation performance caused by the existing method under the condition that the transmission data is lost, the transmission fails and the coupling node can not receive the information of other nodes at the same time,
the relative error at all times of all nodes in case one is 24.82%, and the relative error at all times of all nodes in case two is 38.48% with reference to the figure. It can be seen that as the trigger threshold increases, the state estimation performance of the network gradually decreases.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2a is a diagram of the actual state trace of the first node of the complex networkState estimation trajectory at two different trigger thresholdsIn the comparison of the figures of (a),a first component of a state variable at a kth time for a 1 st node of the complex network; whereinIs the trajectory of the state of the system,is the state estimation trajectory for the case that,is the state estimation trajectory in case two;
FIG. 2b is a diagram of the actual state trace of the first node of the complex networkState estimation trajectory at two different trigger thresholdsIn the comparison of the figures of (a),a second component of the state variable at the kth time for the 1 st node of the complex network;
FIG. 3a is a diagram of the actual state trace of a second node of a complex networkState estimation trajectory at two different trigger thresholdsIn the comparison of the figures of (a),a first component of a state variable of a 2 nd node of the complex network at a kth time;
FIG. 3b is a diagram of the actual state trace of a second node of a complex networkState estimation trajectory at two different trigger thresholdsIn the comparison of the figures of (a),a second component of the state variable at the kth time of the 2 nd node of the complex network;
FIG. 4a is a diagram of the actual state trace of the third node of the complex networkState estimation trajectory at two different trigger thresholdsIn the comparison of the figures of (a),a first component of a state variable of a 3 rd node of the complex network at a kth time;
FIG. 4b is the track of the actual state of the third node of the complex networkState estimation trajectory at two different trigger thresholdsIn the comparison of the figures of (a),a second component of the state variable at the kth time of the 3 rd node of the complex network;
FIG. 5a is a trace plot of the upper bound trace of the state estimation error covariance matrix of the first node at different measurement loss probabilities1,k|kUpper bound of covariance matrix of estimation error of 1 st node at k-th time2,k|kUpper bound of covariance matrix of estimation error of 2 nd node at k-th time, sigma3,k|kUpper bound, tra, of the covariance matrix of the estimation error of the 3 rd node at the k-th time instantce(Σ1,k|k) Is sigma1,k|kTrace of (d, trace (sigma)2,k|k) Is sigma2,k|kTrace of (d, trace (sigma)3,k|k) Is sigma3,k|kStep is iteration times, and k is time; whereinIs thatA trace map of the trace that is under,is thatA trace map of the trace that is under,is thatA trace map of the trace that is under,is thatA trace map of the traces;
FIG. 5b is a trace plot of the upper bound trace of the state estimation error covariance matrix of the second node at different measurement loss probabilities;
FIG. 5c is a trace plot of the upper bound of the state estimation error covariance matrix of the third node at different measurement loss probabilities.
Detailed Description
The first embodiment is as follows: the embodiment is described with reference to fig. 1, and a specific process of the complex network optimization estimation method with random occurrence coupling of the embodiment is as follows:
the complex network can be a network formed by satellites, a network formed by robots, a network formed by spacecrafts or a network formed by radars;
establishing a random coupling time-lag complex network dynamic model with measurement loss and inaccurate occurrence probability;
secondly, performing state estimation on the random coupling time-lag complex network dynamic model with the measurement loss phenomenon and the inaccurate occurrence probability established in the first step under an event trigger protocol;
step three, calculating the upper bound sigma of the one-step prediction error covariance matrix of the state estimation of each node of the complex networki,k+1|k；
Step four, according to the one-step prediction error covariance matrix upper bound sigma obtained in step threei,k+1|kCalculating an estimated gain matrix K for each node of the complex networki,k+1；
Step five, obtaining the estimated gain matrix K of each node in the step fouri,k+1Substituting the state estimation formula (8) in the step two to obtain the state estimation of the ith node at the (k + 1) th momentThe state estimation of the randomly generated coupling time-lag complex network with the measurement loss phenomenon and the inaccurate generation probability is realized.
Judging whether k +1 reaches the total time length M of the complex network, if k +1 is less than M, executing a sixth step, and if k +1 is equal to M, ending the operation;
step six, according to the estimated gain matrix K of each node of the complex network calculated in the step fouri,k+1Calculating the upper bound sigma of the covariance matrix of the estimation error of each node of the complex networki,k+1|k+1；
And k is k +1, and the step two is executed until k +1 is M.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: establishing the measurement loss phenomenon (lambda) in the step onei,k) And probability of occurrence of inaccuracy (gamma)i,k) The random coupling time lag complex network dynamic model;
the state space form of the random coupling time-lag complex network dynamic model with the measurement loss phenomenon and the inaccurate occurrence probability is as follows:
yi,k＝λi,kCi,kxi,k+νi,k,i＝1,2,…,N, (2)
in the formula,
respectively representing the state variables of the ith node of the complex network at the k, k +1 and k-d moments; d is a fixed network time lag;is a real number domain of the state of the complex network dynamic model, and n is a dimension; x is the number ofj,kThe state variable of the jth node of the complex network at the kth moment;the measurement output of the ith node at the kth moment;a real number domain is output by a complex network dynamic model, and p is a dimension;is the initial value of the ith node at time k, k-d, -d +1, …, 0; Γ is a known connection matrix; w ═ Wij]N×NIs a known coupling matrix, wijCoupling weights for the ith node and the jth node;is a mean of zero and a variance of Qi,kThe process noise of (a) is generated,a real number domain of the process noise of the complex network dynamic model is formed, and q is a dimension;is a mean of zero and a variance of Ri,kThe measurement noise of (2); n is the number of nodes of the complex network; a. thei,kIs a system matrix of known time k, Bi,kIs a known noise distribution matrix at time k, Ci,kFor a known measurement matrix at time k,a system matrix of known dimensions and associated with a time lag k-d; gamma rayi,kAnd λi,kRandom variables obeying Bernoulli distribution respectively depict random coupling phenomenon and measurement loss phenomenon, and satisfy the following conditions:
wherein,
γi,k+1、λi,k+1random variables obeying Bernoulli distribution respectively depict random coupling phenomenon and measurement loss phenomenon,is a known constant, which is the expected probability of random coupling of the ith node at the time k + 1;the constant is a known constant and is the measurement loss probability of the ith node at the moment k + 1;andhas a value range of (0,1), Δ γi,k＝1Inaccuracy of characterization probability; prob { } is a probability,as desired;
the above-mentionedThe inaccuracy of the characterization probability is such that,is an upper bound of probability inaccuracy, is a known constant, and satisfies
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: performing state estimation on the random coupling time-lag complex network dynamic model with the measurement loss phenomenon and the inaccurate occurrence probability established in the step one under the event triggering protocol in the step two; the specific process is as follows:
firstly, aiming at the ith node, selecting the following event trigger formula:
whereinFor the measurement output of the ith node at the last trigger time,for the corresponding last value of the triggering time, δi0 is a known adjustment threshold, T is transposed; the next event trigger sequence for the ith nodeIteratively generated by:
whereinIs a positive integer set, inf { } is a lower limit taking function;
after the event triggering mechanism, the true measurement value delivered to the filter is
When the next event trigger sequence does not arrive, the real measurement value is always the value of the previous trigger time;
and aiming at the ith node of the complex network, constructing a state estimator:
in the formula,
is xi,kOne-step prediction at the time k (the specific process of one-step prediction is formula 7),for the state estimate of the ith node at time k +1,for the state estimation of the ith node at the K-d time, Ki,k+1For the estimated gain matrix at time k +1 for the ith node,for the state estimate of the ith node at the kth time,for the state estimate of the jth node at the kth instant,for the measurement output of the ith node at time k +1, Ci,k+1A measurement matrix at a known time k + 1;the expected probability of random coupling at time k for the ith node,is a known constant.
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: computing a one-step prediction error covariance matrix upper bound sigma of a state estimate for each node of the complex network in step threei,k+1|k(ii) a The specific process is as follows:
calculating the upper bound sigma of the one-step prediction error covariance matrix of the state estimation of each node of the complex network according to the following formulai,k+1|k：
In the formula, τ1、τ2、τ4、τ5Is the intermediate variable(s) of the variable,
in the formula, τ1＝1+ε1+ε2+ε3，
εsFor weighting factors greater than zero, s is 1,2, …,7 (for ∑ isi,k+1|kTrace of (d) is minimal);is epsilons1,2, …, 7;
wiis the intermediate variable(s) of the variable,Σi,k+1|kone-step prediction error covariance matrix upper bound, Σ, for the ith node at time ki,k|kThe covariance matrix of the estimation error at the kth time for the ith node is bounded,are respectively Ai,k,Γ,Bi,k,Transposing; sigmai,k-d|k-dUpper bound of covariance matrix of estimation error of ith node at k-dj,k|kAnd (4) the estimation error covariance matrix of the jth node at the kth moment is bounded.
Other steps and parameters are the same as those in one of the first to third embodiments.
The fifth concrete implementation mode: the difference between this embodiment and one of the first to fourth embodiments is: the fourth step is to obtain the upper bound sigma of the one-step prediction error covariance matrix according to the third stepi,k+1|kCalculating an estimated gain matrix K for each node of the complex networki,k+1(ii) a The specific process is as follows:
calculating an estimated gain matrix K of each node of the complex network according to the formula (9) as followsi,k+1：
In the formula,
is the intermediate variable(s) of the variable,ηlis a constant greater than zero (in order to make Σ in step six)i,k+1|k+1Trace of (d) is minimal), l ═ 1,2,3, 4;is etalThe inverse of (a) is,is λi,k+1The variance of (a) is determined,Ki,k+1for the estimated gain matrix of the ith node at time k +1,is Ci,k+1I is an identity matrix, Ri,k+1V isi,k+1The variance of (c) is.
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode: the difference between this embodiment and one of the first to fifth embodiments is: in the sixth step, the estimated gain matrix K of each node of the complex network calculated in the fourth stepi,k+1Calculating the upper bound sigma of the covariance matrix of the estimation error of each node of the complex networki,k+1|k+1(ii) a The specific process is as follows:
the formula is as follows:
wherein,
Σi,k+1|k+1estimate for the ith node at time k +1The upper bound of the covariance matrix of the error is counted,andare respectively asAnd Ki,k+1The transposing of (1).
Furthermore, it can be shown that with probability, other conditions are not changedIncrease of (1), estimation error covariance matrix upper bound ∑i,k+1|k+1The trace of (a) is not increased. Sigmai,k+1|k+1Carry over to step three (replace Σ in equation 9)i,k|k)。
The theory in the third step, the fourth step and the fifth step is as follows:
the minimum upper bound of the estimation error covariance matrix of each node is calculated. Find sigmai,k+1|k+1So that P isi,k+1|k+1≤∑i,k+1|k+1WhereinThe covariance matrix of the estimated error at the time k +1 for the ith node,is the estimation error at the time instant k +1,to the expectation of the element { · },is composed ofThe transposing of (1).
Because the estimation error covariance matrix has uncertain items, the true value of the estimation error covariance matrix cannot be obtained. Optimization estimation error covariance matrix upper bound sigmai,k+1|k+1The estimated gain matrix K of the ith node at the moment K +1 can be obtainedi,k+1。
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the method of the invention is adopted for simulation:
system parameters:
B1,k＝[0.8 0.7]T，B2,k＝[7.5+0.1sin(2k) 0.55]T，B3,k＝[0.65 0.85]T，
C1,k＝[1.6 1.8]，C2,k＝[1.6 1.3]，C3,k＝[1.65 1.8]，
Γ＝diag{0.8,0.8}，
d＝3。
other simulation initial values are selected as follows:
x1,0＝[0.5 1]T，x2,0＝[-1 0.25]T，x3,0＝[-0.5 -0.75]T，xi,j＝[0.2 0.2]T，(i＝1,2,3,j＝-1,-2)，Q1,k＝0.2，Q2,k＝0.15，Q3,k＝0.1，R1,k＝0.2，R2,k＝0.1，R3,k＝0.1，ε1＝0.3，εi＝0.1(i＝2,3,4)，εi＝1(i＝5,6,7)，η1＝0.2，η2＝5，η3＝1，η4＝0.5，Σ1,0|0＝2I2，Σ2,0|0＝2.5I2，Σ3,0|0＝3I2，Σi,j|j＝10I2(i＝1,2,3,j＝-1,-2,-3)。
case one (Case I):
δ1＝0.1，δ2＝0.5，δ3＝0.5；
case two (Case II):
δ1＝5，δ2＝5，δ3＝5。
the state estimator effect:
as can be seen from fig. 2a, 2b, 3a, 3b, 4a, and 4b, the state estimator design method of the present invention can effectively estimate the target state for a randomly-coupled time-lapse complex network with measurement loss and inaccurate occurrence probability under an event trigger mechanism.
As can be seen from fig. 5a, 5b, 5c, for each node, the probability is followedIncrease of (1), estimation error covariance matrix upper bound ∑i,k+1|k+1Is decremented.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (6)
1. A complex network optimization estimation method with random coupling is characterized in that: the method comprises the following specific processes:
step one, establishing a complex network dynamic model with randomly generated coupling time lag;
secondly, performing state estimation on the randomly-generated coupling time-lag complex network dynamic model established in the first step under an event trigger protocol;
step three, calculating the upper bound sigma of the one-step prediction error covariance matrix of the state estimation of each node i of the complex networki,k+1|k；
Step four, according to the one-step prediction error covariance matrix upper bound sigma obtained in step threei,k+1|kCalculating an estimated gain matrix K for each node of the complex networki,k+1；
Step five, obtaining the estimated gain matrix K of each node in the step fouri,k+1Substituting the step two to obtain the state estimation of the ith node at the k +1 th moment
Judging whether k +1 reaches the total time length M of the complex network, if k +1 is less than M, executing a sixth step, and if k +1 is equal to M, ending the operation;
step six, according to the estimated gain matrix K of each node of the complex network calculated in the step fouri,k+1Calculating an estimation error covariance matrix upper bound sigma of each node of the complex networki,k+1|k+1；
And k is k +1, and the step two is executed until k +1 is M.
2. The method of claim 1, wherein the method comprises: establishing a random coupling time lag complex network dynamic model in the first step;
the state space form of the complex network dynamic model with the randomly generated coupling time lag is as follows:
yi,k＝λi,kCi,kxi,k+νi,k,i＝1,2,…,N, (2)
in the formula,
respectively representing the state variables of the ith node of the complex network at the k, k +1 and k-d moments; d is the network skew;is a real number domain of the state of the complex network dynamic model, and n is a dimension; x is the number ofj,kThe state variable of the jth node of the complex network at the kth moment;the measurement output of the ith node at the kth moment;a real number domain is output by a complex network dynamic model, and p is a dimension;is the initial value of the ith node at time k, k-d, -d +1, …, 0; Γ is the connection matrix; w is aijCoupling weights for the ith node and the jth node;is a mean of zero and a variance of Qi,kThe process noise of (a) is generated,a real number domain of the process noise of the complex network dynamic model is formed, and q is a dimension;is a mean of zero and a variance of Ri,kThe measurement noise of (2); n is the number of nodes of the complex network; a. thei,kIs a system matrix, Bi,kAs a noise distribution matrix, Ci,kIs the measurement matrix for the time instant k,of known dimensions and with a time lag k-d a related system matrix; gamma rayi,kAnd λi,kRandom variables obeying Bernoulli distribution respectively depict random coupling phenomenon and measurement loss phenomenon, and satisfy the following conditions:
wherein,
γi,k+1、λi,k+1random variables obeying Bernoulli distribution respectively depict random coupling phenomenon and measurement loss phenomenon,the expected probability of random coupling of the ith node at the moment k + 1;the measurement loss probability of the ith node at the moment k +1 is obtained;andhas a value range of (0,1), Δ γi,k＝1Inaccuracy of characterization probability; prob { } is a probability,as desired.
3. The method of claim 2, wherein the method comprises: performing state estimation on the randomly generated coupling time-lag complex network dynamic model established in the step one under the event triggering protocol in the step two; the specific process is as follows:
firstly, aiming at the ith node, selecting the following event trigger formula:
whereinFor the measurement output of the ith node at the last trigger time,for the corresponding last value of the triggering time, δiIf > 0, the adjusting threshold is set, and T is transposition; the next event trigger sequence for the ith nodeIteratively generated by:
whereinIs a positive integer set, inf { } is a lower limit taking function;
after the event triggering mechanism, the true measurement value delivered to the filter is
And aiming at the ith node of the complex network, constructing a state estimator:
in the formula,
is xi,kA one-step prediction at the time instant k,for the state estimate of the ith node at time k +1,for the state estimation of the ith node at the K-d time, Ki,k+1For the estimated gain matrix at time k +1 for the ith node,for the state estimate of the ith node at the kth time,for the state estimate of the jth node at the kth instant,for the measurement output of the ith node at time k +1, Ci,k+1The measurement matrix is the measurement matrix at the moment k + 1;the expected probability of random coupling at time k for the ith node.
4. The method of claim 3, wherein the method comprises: calculating the one-step prediction error covariance matrix upper bound sigma of the state estimation of each node i of the complex network in the step threei,k+1|k(ii) a The specific process is as follows:
calculating each node of the complex network according to the following formulaUpper bound sigma of the covariance matrix of the one-step prediction error of the state estimationi,k+1|k：
In the formula,
τ1、τ2、τ4、τ5is an intermediate variable, wiIs the intermediate variable(s) of the variable,Σi,k+1|kone-step prediction error covariance matrix upper bound, Σ, for the ith node at time ki,k|kThe covariance matrix of the estimation error at the kth time for the ith node is bounded,ΓT,are respectively Ai,k,Γ,Bi,k,Transposing; sigmai,k-d|k-dUpper bound of covariance matrix of estimation error of ith node at k-dj,k|kAnd (4) the estimation error covariance matrix of the jth node at the kth moment is bounded.
5. The method of claim 4, wherein the method comprises: the fourth step is to obtain the upper bound sigma of the one-step prediction error covariance matrix according to the third stepi,k+1|kCalculating an estimated gain matrix K for each node of the complex networki,k+1(ii) a The specific process is as follows:
according to (A)9) Formula an estimated gain matrix K for each node of a complex network is calculated as followsi,k+1：
In the formula,
is the intermediate variable(s) of the variable,ηlis a constant greater than zero, 1,2,3, 4;is etalThe inverse of (a) is,is λi,k+1The variance of (a) is determined,Ki,k+1for the estimated gain matrix of the ith node at time k +1,is Ci,k+1I is an identity matrix, Ri,k+1V isi,k+1The variance of (c) is.
6. The method of claim 5, wherein the method comprises: in the sixth step, the estimated gain matrix K of each node of the complex network calculated in the fourth stepi,k+1Calculating the upper bound sigma of the covariance matrix of the estimation error of each node of the complex networki,k+1|k+1(ii) a The specific process is as follows:
the formula is as follows:
wherein, sigmai,k+1|k+1The covariance matrix of the estimation error at the (k + 1) th node is bounded,andare respectively asAnd Ki,k+1The transposing of (1).
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