CN109917658A - Nonlinear networked system filter and design method under a kind of multidiameter fading channel - Google Patents
Nonlinear networked system filter and design method under a kind of multidiameter fading channel Download PDFInfo
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Abstract
A kind of nonlinear networked system filter design method under multidiameter fading channel, comprising steps of establishing Discrete T-S fuzzy nonlinear model according to the analysis to nonlinear networked system；L rank Rice fading model is established to describe the multipath fading phenomenon of radio communication channel；Construct uncatalyzed coking H∞Filter.
Description
Technical field
The invention belongs to radio network technique field, in particular to nonlinear networked system under a kind of multidiameter fading channel
Filter and design method.
Background technique
Wireless network control system based on radio network technique building is applied to some special extreme or high-risk environments,
Such as in military field, extensive attacking and defending system based on network control system passes through the cooperation control to weapon platform
System, so that attack and defense is more efficient.In this type of application, the fading channel phenomenon of wireless communication is generally existing.It is logical
Normal open believes that the radio beam of earth station's transmitting is wider, due to factors such as atural object, landforms and sea situations in its transmission process
Influence, the signal that receiver receives be reflected, reflect and the mulitpaths such as direct projection reach electromagnetic wave.Due to each path
Intensity, the difference of propagation time and transmitted signal bandwidth, the reception signal of multipath electromagnetic wave synthesis amplitude, phase even
Be likely on waveform can great changes will take place, this phenomenon that causes to distort is known as multipath effect.This multipath channel decaying nothing
The q&r that can reduce signal is doubted, the performance indicator of system is influenced, even results in the deterioration of systematic entirety energy.Cause
This, fully considers that communication channel decays this objective factor, and searching can guarantee that system reaches required properties index and is easy to real
Existing filtering algorithm has great theoretical and practical significance.
In practical applications, when filter is realized, there is always some inevitable disturbances or drifts, such as word
Long limited, component aging and rounding error etc., this set designed filter parameter can not accurately.Once
Filter parameter is perturbed, even the variation of amplitude very little, is likely to will lead to the degradation of system performance very
To thorough failure.Traditional robust filtering is filtered device just for the Parameter uncertainties or structural uncertainty of system model
Design, but have ignored the probabilistic influence of gain of filter itself, that is to say, that traditional filter has height
Fragility.The deviation of this filter parameter is inevitable in practical reality, so the design of uncatalyzed coking filter is asked
Topic causes the extensive concern of researcher.
Summary of the invention
The present invention provides a kind of uncatalyzed coking H of network control system∞Filter design method, filtering method and filtering
Device.Consider that network control system there are multipath channel decline measurement and filter parameter perturbation situation, devises uncatalyzed coking
H∞Filter so that network control system is still able to maintain mean square stability in these cases, and has specified Disturbance Rejection
Ability.
One of embodiment of the present invention, a kind of nonlinear networked system filter design method under multidiameter fading channel, packet
Include following steps:
According to the analysis to nonlinear networked system, Discrete T-S fuzzy nonlinear model is established；
L rank Rice fading model is established to describe the multipath fading phenomenon of radio communication channel；
Construct uncatalyzed coking H∞Filter.
Compared with prior art, the present invention has the following advantages that and remarkable result:
1) present invention realizes the uncatalyzed coking H of nonlinear networked system under multidiameter fading channel∞Filtering information processing side
The design of method, and this method algorithm is simpler, computational efficiency is high, is easily programmed realization.
2) accidental channel decline measurement, filter parameter perturbation and external disturbance have been comprehensively considered to the shadow of filtering performance
It rings, and incorporates it under unified model frame, establish networking filtering error system model, for complex networkization control system
The modeling of system provides new approaches.
3) Lyaponov functional based method, stochastic analysis technology and linear matrix inequality approach are merged, can guarantee
Filtering error system index Asymptotic Stability and meets linear matrix inequality existing for the filter of AF panel performance requirement and fill
Slitting part, while giving the analytical expression of filter parameter.But also it can be asked by solving a convex optimization
The performance indicator for inscribing optimization system makes networked system have better interference free performance.
4) present invention has fully considered the outside that statistical property is unknown in practice in the design of filtering information processing method
The influence of disturbance, multipath channel decline and Parameter Perturbation to system, so gained design result more meets actual use situation.
Detailed description of the invention
The following detailed description is read with reference to the accompanying drawings, above-mentioned and other mesh of exemplary embodiment of the invention
, feature and advantage will become prone to understand.In the accompanying drawings, if showing by way of example rather than limitation of the invention
Dry embodiment, in which:
Fig. 1 is the filter structure figure according to system nonlinear networked under the multidiameter fading channel of the embodiment of the present invention；
Fig. 2 is the filter design method flow chart according to the embodiment of the present invention；
Fig. 3 is the fading channel situation schematic diagram slave sensor to filter according to the embodiment of the present invention；
Fig. 4 is white Gaussian noise n (k) schematic diagram according to the embodiment of the present invention；
Fig. 5 is the sensor measurement output signal y (k) and the practical reception signal y of filter according to the embodiment of the present inventionf
(k) schematic diagram, wherein dotted line indicates ideal measurement output signal y (k), and solid line indicates the practical reception signal y of filterf(k)；
Fig. 6 is the signal z (k) to be estimated and its estimation signal z according to the embodiment of the present inventionf(k) schematic diagram, wherein dotted line
Indicate signal z (k) to be estimated, solid line indicates that it estimates signal zf(k)。
Specific embodiment
According to one or more embodiment, as illustrated in fig. 1 and 2, nonlinear networked system under a kind of multidiameter fading channel
The uncatalyzed coking H of system∞Filtering method, comprising the following steps:
Step 1: nonlinear networked system is analyzed in foundation, establishes following Discrete T-S fuzzy nonlinear model
Wherein θ (k) is the former piece variable of fuzzy rule, and r is fuzzy rule sum, gi(θ (k)) is the mould of the i-th rule
Subordinating degree function is pasted, g is meti(θ (k)) >=0 (i=1,2 ..., r), It is the state vector of system respectively, measurement exports and be estimated signal.System square
Battle array Ai, Ei,Bi,Fi,Ci,DiAnd LiFor the constant matrices of appropriate dimension；φ (s) is original state.It is l2[0, ∞)
On external input disturbance；It is l2[0, ∞) on output measure disturbance；For zero-mean gaussian white noise
Sound sequence meets δksIt is Kronecer function and w (k) and n (k) is mutual
It is independent.
Step 2: establishing following L rank Rice fading model to describe the multipath fading phenomenon of radio communication channel
Wherein l (k)=min { L, k }, L are model orders；yf(k) filter receives under a multipath fading channel
Measurement output；Channel coefficientsIt is mutually independent random variables on [0,1], reflects wireless
The random amplitude of communication fade channel signal is decayed, it is expected that being respectively with varianceWith
EdIt is the known constant matrix of appropriate dimension；It is the external disturbance in communication channel.
Step 3: uncatalyzed coking H∞The building of filtering information processing method
Step 3.1: in view of being inevitably present filter parameter perturbation in reality, according to network control system
Model foundation contains the filter model of undetermined parameter
WhereinWithRespectively filter status, filter input and z's (k)
Estimation；Afi, BfiAnd LfiIt is filter parameter to be designed.ΔAfi(k) and Δ BfiIt (k) is the Perturbation and table of filter parameter
Show as follows
Wherein Mai,Nai, Mbi, NbiIt is known constant matrices；Δai(k) and ΔbiIt (k) is to meet Unknown matrix.In order to indicate convenient, by gi (θ (k)) and gi (θ (k+1))
Respectively brief note make gi and
Step 3.2: convolution (1), (2) and (3) establishes filtering error system model
Wherein:
ξ (k)=[ηT(k-1)ηT(k-2) ... ηT(k-L)]T,
Filter evaluated error ze(k)=z (k)-zf(k),
And it requires filtering error system (5) while meeting following two requirement:
(R1) filtering error system (5) exponential mean square stability；
(R2) under zero initial condition, meet following H∞Performance indicator
Wherein γ > 0 is a given scalar, reflects Disturbance Rejection level.
Step 3.3: construction Lyapunov function
V (k)=V1(k)+V2(k),
WhereinPi0 (i=of >
1,2 ... r) and Rm> 0 (m=1,2 ..., L) is positive definite matrix undetermined.
Step 3.4: stability and H are carried out to filtering error system (5)∞Performance evaluation, the uncatalyzed coking met the requirements
H∞Linear matrix inequality adequate condition existing for filter (3):
Given scalar γ > 0, if there is matrix Pi> 0, Rm> 0, G1, G2, G3,Positive scalar ε1>
0,ε2> 0, ε3> 0 and ε4> 0 makes linear matrix inequality (7) to all i, j, s=1,2 ..., r, m=1,2 ..., L
It is set up with l (k) ∈ { 1,2 ..., L }, then filtering error system (5) mean square stability and there is specified H∞Performance γ, uncatalyzed coking
H∞Filter parameter matrix is
Wherein:
The step 3.4 includes following several sub-steps:
Step 3.4.1: stability and H are carried out to filtering error system (5)∞Performance evaluation, what is met the requirements is non-crisp
Weak H∞Inequality adequate condition existing for filter (3):
For giving scalar γ > 0, if there is positive definite matrix Pi> 0 (i=1,2 ..., r) and Rm> 0 (m=1,
2 ..., L) make following MATRIX INEQUALITIES
Wherein
All j, s=1,2 ..., r and l (k) ∈ { 1,2 ..., L } are set up, that
Filtering error system (5) is mean square stability and has the given horizontal γ of Disturbance Rejection.
The stability of system is analyzed first.According to filtering error system trajectory (5), calculating Lyapunov function
Difference can obtain
Wherein
When w (k)=0,When with d (k)=0, definitionConvolution (9) and
(10), it can obtain
Wherein
Lemma is mended according to Schur, formula (8) establishment meansSo to allHaveCan thus be concluded that filtering error system (5) in w (k)=0,It is that side is steady when with d (k)=0
Fixed.
The H of following analysis system∞Performance.Under zero initial condition, following target function is introduced
Wherein n is nonnegative integer.Convolution (9), (10) and (12), has
Wherein
From formula (13) if can be seen that MATRIX INEQUALITIES
Ωijs (14)
It sets up, then has J (n)≤0.In fact, mending lemma according to Schur, inequality (8) and (14) are of equal value.So
Formula (8) establishment means J (n)≤0.As n → ∞, can be obtained by formula (12)
This shows that system meets design performance and requires (6).
Step 3.4.2: in above-mentioned adequate condition, inequality (8) contains simultaneouslyWithIt is not linear matrix
Inequality.This means that its feasible solution is sought in the presence of very big difficulty, that is to say, that we are difficult to acquire the gain ginseng of filter
Number.In order to solve this problem, we introduce a special relaxation matrix variable and are retouched with obtaining a linear matrix inequality
The adequate condition stated, it is specific as follows.
On the both sides of MATRIX INEQUALITIES (8), premultiplication and the right side multiply matrix simultaneouslyAnd its transposition, it can obtain
ByWithIt is found that if following formula is set up, formula
(15) certain to set up.
Define new variablesBy the determination item and indeterminate of formula
Separation, can obtain formula (16) and be equivalent to
Wherein
Lemma is mended according to Schur and following lemma 1, formula (17) are equivalent to formula (7).Formula (7) is the uncatalyzed coking met the requirements
H∞Linear matrix inequality adequate condition existing for filter.
Lemma 1: matrix L=L of appropriate dimension is givenT, H and E, to meeting FFTThe matrix F of≤I will make L+HFE+ETFTHT
< 0 is set up, and if only if there are scalar ε > 0 to make L+ ε-1HHT+εETE < 0, or of equal value
Step 3.5: calculating optimal uncatalyzed coking H∞Filter parameter matrix
Optimization problem is solved using the tool box Matlab LMI:
S.t. formula (7) and ρ=γ2；I, j=1,2 ..., r；M=1,2 ..., L.
When formula (6) has solution, optimal H∞Performance indicator isCorresponding to optimal filter parameter is
When formula (6) is without solution, then optimal filter cannot be obtained, is terminated；
Step 3.6: realizing that uncatalyzed coking filter parameter matrix substitutes into formula (3), obtain a kind of nonlinear networked system
Uncatalyzed coking H∞Filter.
Effectiveness of the invention and superiority are verified below according to example.
Consider discrete-time fuzzy model (1) and attenuation measurement (2), model parameter are
It is assumed that the order of attenuation model is L=2.The mathematic expectaion of attenuation coefficientRespectively 0.9,0.75,
0.5 and corresponding variance be
The uncertain gain matrix of uncatalyzed coking filter is
Ma1=Mb1=[1 0.7 0.9]T, Na1=[0.03 0.01 0.01], Nb1=[0.03 0.01],
Ma2=Mb2=[0.8 0.6 0.7]T, Na2=[0.01 0.03 0.01], Nb2=[0.01 0.03],
Δa1(k)=Δb2(k)=sin (k), Δa2(k)=Δb1(k)=cos (k)
Fuzzy membership function isg2(k)=1-g1(k).
The convex optimization problem in formula (18) is solved by Matlab, filter parameter can be acquired are as follows:
Lf1=[1.7983-1.6669-0.9080], Lf2=[1.7648-1.6338 0.9002],
And the smallest H∞Performance
If system and the original state of filter are x (0)=xf(0)=[0 0 0]T,
External disturbance w1(k)=exp (- 0.2k) sin (0.5k), w2(k)=exp (- 0.4k) sin (0.3k),
D (k)=m (k)/(1+5k), wherein m (k) is [0,1] equally distributed stochastic variable.Simulation result such as Fig. 3 to figure
Shown in 6.Wherein Fig. 3 features the fading channel situation from sensor to filter.Fig. 4 depicts white Gaussian noise n (k).Fig. 5
Illustrate sensor measurement signal y (k) and the practical received signal y of filterf(k).It can be seen that channel fading can be led
The distortion and fluctuation for the number of writing, this just demonstrates the necessity of influence of the research channel fading to system filter.Fig. 6 is depicted
Output signal z (k) to be estimated and its estimation zf(k), designed fuzzy uncatalyzed coking H therefrom can be confirmed∞Filter can mention
For satisfied tracking performance.So the fuzzy uncatalyzed coking H that the present invention designs∞Filter is effective.
It is worth noting that although foregoing teachings are by reference to several essences that detailed description of the preferred embodimentsthe present invention has been described creates
Mind and principle, it should be appreciated that, the invention is not limited to the specific embodiments disclosed, the division also unawareness to various aspects
Taste these aspect in feature cannot combine, it is this divide merely to statement convenience.The present invention is directed to cover appended power
Included various modifications and equivalent arrangements in the spirit and scope that benefit requires.
Claims (5)
1. a kind of nonlinear networked system filter design method under multidiameter fading channel, which is characterized in that including following step
It is rapid:
According to the analysis to nonlinear networked system, Discrete T-S fuzzy nonlinear model is established；
L rank Rice fading model is established to describe the multipath fading phenomenon of radio communication channel；
Construct uncatalyzed coking H∞Filter.
2. nonlinear networked system filter design method, feature under multidiameter fading channel according to claim 1
It is, Discrete T-S fuzzy nonlinear model is
Wherein, θ (k) is the former piece variable of fuzzy rule, and r is fuzzy rule sum, gi(θ (k)) is the fuzzy person in servitude of the i-th rule
Category degree function, meets gi(θ (k) >=0 (i=1,2 ..., r),
It is the state vector of system respectively, measurement exports and is estimated signal,
Sytem matrix Ai, Ei,Bi,Fi,Ci,DiAnd LiFor the constant matrices of appropriate dimension；φ (s) is original state,
It is l2[0, ∞) on external input disturbance；It is l2[0, ∞) on output measure disturbance；
For zero mean Gaussian white noise sequence, meetδksIt is
Kronecer function and w (k) and n (k) are independent from each other.
3. nonlinear networked system filter design method, feature under multidiameter fading channel according to claim 2
It is,
L rank Rice fading model is
Wherein, l (k)=min { L, k }, L are model orders；
yf(k) it is exported for the measurement that filter receives under a multipath fading channel；
Channel coefficientsIt is mutually independent random variables on [0,1], it is expected that and variance difference
ForWithEdIt is the known constant matrix of appropriate dimension；
It is the external disturbance in communication channel.
4. nonlinear networked system filter design method, feature under multidiameter fading channel according to claim 3
It is, uncatalyzed coking H∞Filter building process includes:
S301, it is contemplated that be inevitably present filter parameter perturbation in reality, given according to the mathematical model that step 1) is established
Out containing the filter model of undetermined parameter
WhereinWithRespectively filter status, filter input and z's (k) estimates
Meter；Afi, BfiAnd LfiIt is filter parameter to be designed.ΔAfi(k) and Δ BfiIt (k) is the Perturbation of filter parameter and expression
It is as follows:
Wherein, Mai,Nai, Mai, NbiIt is known constant matrices；Δai(k) and Δbi(κ) is to meet Unknown matrix, by gi(θ (k)) and gi(θ (k+1)) brief note makees g respectivelyiWith
S302 establishes filtering error system model according to model (1), (2) and (3)
Wherein:ξ (k)=[ηT(k-1) ηT(k-2)...ηT(k-L)]T,
Filter evaluated error
And it requires filtering error system (5) while meeting following two requirement:
(R1) filtering error system (5) mean square stability；
(R2) under zero initial condition, meet following H ∞ performance indicator
Wherein γ > 0 is a given scalar, reflects Disturbance Rejection level；
S303 constructs Lyapunov function
V (k)=V1(k)+V2(k),
Wherein
(i=1,2 ..., r) and Rm> 0 (m=1,2 ..., L) is positive definite matrix undetermined；
S304 carries out stability and H to filtering error system (5)∞Performance evaluation, the uncatalyzed coking H met the requirements∞Filter
Linear matrix inequality adequate condition existing for model (3):
Given scalar γ > 0, if there is matrix Pi> 0, Rm> 0, G1, G2, G3,Positive scalar ε1> 0, ε2
> 0, ε3> 0 and ε4> 0 makes linear matrix inequality (7) to all i, j, s=1,2 ..., r, m=1,2 ..., L and l
(k) ∈ { 1,2 ..., L } is set up, then filtering error system (5) mean square stability and has specified H∞Performance γ, uncatalyzed coking H∞Filter
Wave device parameter matrix is
Wherein:
S305 calculates optimal uncatalyzed coking H∞Filter parameter matrix solves optimization problem:
S.t. formula (7) and ρ=γ2；I, j=1,2 ..., r；M=1,2 ..., L.
When formula (18) has solution, optimal H∞Performance indicator isCorresponding to optimal filter parameter is
When formula (18) is without solution, then optimal filter cannot be obtained,
S306 realizes that uncatalyzed coking filter parameter matrix substitutes into formula (3), obtains the uncatalyzed coking H of nonlinear networked system∞Filtering
Device.
5. nonlinear networked system filter under a kind of multidiameter fading channel, which is characterized in that the filter is by according to right
It is required that design method described in 1 designs.
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| CN112947063A (en) * | 2021-01-18 | 2021-06-11 | 山东科技大学 | Non-fragile fuzzy proportional integral control method of attenuation channel networking system |
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