CN108388133A - A kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism - Google Patents
A kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism Download PDFInfo
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Abstract
The present invention relates to a kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism；First, for the LINEAR CONTINUOUS positive system containing external disturbance a positivity augmented system is obtained with system mode and interference for augmented state；Secondly, the positive full micr oprocessorism that can ensure that State Viewpoint measured value is always positive is designed for positivity augmented system；Again, it based on the estimator obtained by full micr oprocessorism, designs the positive system Dynamic Output Feedback antidisturbance control with Interference Cancellation effect and restrains；Finally, using the linear combination of former positive system state, state estimation error and Interference Estimation error as state variable, obtain a closed-loop system, based on linearly together with positive Lyapunov functions provide closed-loop system be Asymptotic Stability positive system condition, and controller and observer parameter are resolved by linear programming algorithm, the method can be used for positive system, and there are under complex jamming and be unable to measure to obtain the stable control under system mode situation.
Description
Technical field
The present invention relates to a kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism, this side
Method can be used for positive system there are complex jamming, be unable to measure to obtain under system mode situation and there is certain require to system pole
Stable control.
Background technology
Positive system is that one kind requires system variable and system output to remain non-negative system, this kind of system is very much
There is important application in field.In the object including fields such as economics, social science, biologic pharmacological sciences, analyzed and studied
State usually has non-negative property, such as the probability in economics, the size of population in social science, the concentration in biologic pharmacological science
The concepts such as dosage are especially suitable for being described using positive system related notion.It is positive to be in practical positive system control task
The complexity of object of uniting and the diversity of environment can be that controlled system brings complicated external disturbance, be produced to the performance of control system
Life seriously affects, therefore, the problem of positive system antidisturbance control in the case of complex jamming becomes urgent need to resolve.Meanwhile
In many cases, due to the shortage of measurement means or the complexity of measuring environment, the state of system can not be obtained or be surveyed by measuring
There are critical noisies for the system mode measured, so that it cannot application system quantity of state carries out the controller design of positive system,
At this point, can measure the output feedback ontrol of obtained output information progress positive system using system becomes necessary means.It is defeated
It is to carry out feedback control using the efficient combination of Partial State Information to go out feedback control essentially, and this incompleteness causes
System has certain limitation in POLE PLACEMENT USING, thus can carry out positive system by using the mode of Dynamic Output Feedback
Control.Dynamic output feedback control utilizes system output amount design point observer, and is constituted finally based on state estimation
Feedback Control Laws, it is seen then that the design of observer is most important for Dynamic output feedback controllers.However, positive system is defined on
In cone rather than in European linear space, the nonnegativity limitation of alignment system system mode, output variable so that General System
Many conclusions be no longer desirable for positive system, wherein including just the design and system stability criterion etc. of observer, thus need
The positive observer for positive system is designed, to ensure the positivity of positive system state estimation, and is proposed a kind of based on just full dimension
The positive system Dynamic Output Feedback anti-interference control method of observer makes the final Asymptotic Stability of positive system.It is this to be tieed up based on just complete
The positive system Dynamic Output Feedback anti-interference control method of observer has great potential on engineer application, has anti-interference, work
The features such as journey practicability is high.
Currently, for the control problem of positive system, there is scholar to carry out technique study and patent application.Chinese patent application
Number to propose a kind of output feedback ontrol of the time lag positive system based on linear Lyapunov methods in 201610432088.3
Device design method, for noisy time lag positive system, design output feedback controller so that system is stable and meets L1
Can, but that there are problems is as follows：(1) what the control method that this patent proposes took interference is the mode inhibited, and AF panel is logical
It often needs to be inhibited and controlled using the interference upper bound, thus simple inhibition interference can bring larger conservative；(2) application is quiet
State output feedback is so that closed loop positive system has limitation in terms of assigned pole, and is not directed to the design phase of positive observer
Hold inside the Pass.Certainly, many for the achievement in research of General System output feedback ontrol.Chinese Patent Application No. is
A kind of LPV systems by output feedback controller is proposed in 201710775956.2, but this patent has three：(1) system
Object is conventional system, different from the research object of the present invention without system mode and the positive system feature that output is positivity；
(2) output ultramagnifier uses Static Output Feedback, has limitation in terms of assigned pole, and is not related to Design of Observer aspect
Content；(3) for being interfered present in system, using H∞Control carries out AF panel, but simple AF panel can be brought
Larger conservative；China Patent No. proposes a kind of without the defeated of towing satellite relative displacement channel in being 201610196301.5
Go out to feed back anti-interference control method, but there are the following problems：(1) this patent using without towing satellite as research object, actually
Controller design is carried out to a General System, it is different from the positive system in the present invention；(2) this patent builds quadratic form
Lyapunov functions prove closed-loop system stability, and the method is complex when carrying out the verification of positive system stability, with this hair
The method that positive system stability is carried out together with positive Lyapunov functions of bright middle application is different；(3) State Viewpoint designed in this patent
Survey device can not ensure to the State Viewpoint measured value of system be just, it is nonsensical for positive system Obj State.It is mentioned above to solve
The problem of, there is an urgent need for design a kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism.
Invention content
The technical problem to be solved by the present invention is to：Consider positive system object, state can not be surveyed and be deposited in practice for engineering
In the situation of complex jamming, a kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism is proposed,
Reduce the influence that interference brings system performance.
The present invention solve the technical solution that uses of above-mentioned technical problem for：A kind of positive system based on positive full micr oprocessorism is dynamic
State output feedback anti-interference control method, the positive full micr oprocessorism about system mode and interference, and base are designed for positive system
Output feedback anti-interference controller is designed in positive full micr oprocessorism so that in the positive system dynamical output based on positive full micr oprocessorism
It feeds back under anti-interference controller effect, closed-loop system is asymptotically stable positive system.Compared with existing the relevant technologies, tool is more adapted to
Have in the actual environment of complex jamming, and in view of measuring condition limitation in engineering, engineer application is high, for positive system object
For, prior art is relatively deficient, and the method is important technique complementary.
Specifically include following steps：First, it for the LINEAR CONTINUOUS positive system model containing external disturbance, provides with system
State and the positivity augmented system that interference is augmented state；Secondly, positive full micr oprocessorism is designed for positivity augmented system；Again
It is secondary, it is measured based on the State Viewpoint in full micr oprocessorism and disturbance-observer amount, system output of the design with Interference Cancellation effect is anti-
Present antidisturbance control rule；Finally, according to the positive system Dynamic Output Feedback antidisturbance control based on positive full micr oprocessorism of design
Device obtains augmentation closed-loop system, resolves controller and observer parameter by linear programming algorithm so that closed loop augmented system exists
Lower positive system Dynamic Output Feedback anti-interference controller effect based on positive full micr oprocessorism is asymptotically stable positive system.This side
Method can be used for positive system under complex jamming and be unable to measure to obtain the stable control under system mode situation；Specific steps
It is as follows：
1, for the LINEAR CONTINUOUS positive system containing external disturbance：
Wherein,WithRespectively the state of system,
Control input, the external disturbance of control input channel, control export and measure output, WithTo fit dimension parameter matrix known to system, and A is Metzler matrixes, B, C, D and CmFor non-negative square
Battle array, wherein if there is a matrixThere is Mij>=0, i, j=1 ..., n, then matrix M is referred to as Metzler matrixes, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j=1 ..., n, then matrix N is referred to as non-negative square
Battle array, be expressed as N >=>=0.Meanwhile positivity external disturbance d (t) can be described by an external system, it is specific as follows：
Wherein,For external system state,For known systematic parameter matrix, and W is
Metzler matrixes, V are nonnegative matrix.
WithIt is an augmentation by original system and external disturbance system combination for augmented system state
Positive system：
Wherein, It is system known matrix.
2, the positive full micr oprocessorism that can ensure that State Viewpoint measured value is always positive is designed for positivity augmented system：
Wherein,It is augmented system stateEstimated value,It is
The estimated value of original system state x (t),It is the estimated value of interference system state w (t),
For observer gain matrix to be solved.
For positive system, the state of system and interference are in t>0 be always just, thus design State Observer need
Ensure that state estimation is always just just meaningful, according to the Rule of judgment of positive system, that is, it is Metzler matrixes, L to need G
For nonnegative matrix, ifWhereinIfWhereinIt is observer system output matrix.Wherein, positive system
Rule of judgment is systemIt is a positive system, is Metzler matrixes and if only if A, B, C are non-negative
Matrix.Wherein A and B is systematic parameter matrix, and C is system output matrix, if there is a matrixThere is Mij>=0, i, j=
1 ..., n, MijFor the element of matrix M the i-th row jth row, then matrix M is referred to as Metzler matrixes, is expressed asIf having one
MatrixThere is form Nij>0, i=1 ..., m j=1 ..., n, NijFor the element of matrix N the i-th row jth row, then claim square
Battle array N be nonnegative matrix, be expressed as N >=>=0.
If augmented state evaluated errorWherein,
For original system state estimation error,For disturbance state evaluated error.Obtain the evaluated error of augmented state
System：
If G12=0, G22=W makes augmented state be decoupled with interference external system state w (t), then has the estimation of augmented state
Error system：
Third walks, and is measured based on the State Viewpoint in full micr oprocessorism and disturbance-observer amount, design have Interference Cancellation effect
Systems by output feedback antidisturbance control rule：
Wherein K is controller parameter to be designed,It is the estimated value of external disturbance d (t),It is original systemEstimated value,It is augmented system stateEstimated value,It is the estimated value of original system state x (t),It is interference system state w (t)
Estimated value, InDiagonal matrix is tieed up for n.Control law can be expressed as：
Therefore closed-loop system can be obtained：
Wherein,WithRespectively the state of system,
Control input, the external disturbance of control input channel, control export and measure output, To fit dimension parameter matrix known to system.
4th step is obtained according to the positive system Dynamic Output Feedback anti-interference controller based on positive full micr oprocessorism of design
Using the linear combination of former positive system state, state estimation error and Interference Estimation error as the augmentation closed-loop system of augmented state.
First withFor augmented state, closed loop augmented system is obtained：
To ensure the positivity feasibility of closed-loop system, with the linear combination of existing system mode
For system mode, closed-loop system can be obtained：
Wherein, H=BVWVTBT(BVVTBT)-1For known matrix, WithFor known suitable dimension parameter matrix, IqUnit matrix, I are tieed up for qnUnit matrix is tieed up for n.
Based on linearly the condition that closed-loop system is Asymptotic Stability positive system is provided together with positive Lyapunov functions, parameter square is solved
Battle array K, L and non-negative vectorSo that its satisfaction：
L≥≥0
-BK≥≥0
In+A-L1Cm+BK-G11≥≥0
H-BVL2Cm-BVG21≥≥0
BVG21≥≥0
C+DK≥≥0
-DK≥≥0
(In+A+BK)υ1-BKυ2+Iqυ3≤≤0
(In+A-L1Cm+BK-G11)υ1+(-BK+G11)υ2+Iqυ3≤≤0
(H-BVL2Cm-BVG21-(I+A+BK))υ1+(BVG21+BK)υ2+(H-In)υ3≤≤0
And by linear programming algorithm resolve controller and observer parameter matrix K,
So that closed loop augmented system is gradually under the positive system Dynamic Output Feedback anti-interference controller effect based on positive full micr oprocessorism
Closely stable positive system.Wherein,It is controller parameter matrix to be solved,
For observer gain matrix to be solved, ifWherein IfWhereinAc、Bc、A、B、C、D、Cm、Cmc, W and V be known system
Parameter matrix.If there is a matrixThere is Mij>=0, i, j=1 ..., n, MijFor matrix M the i-th row jth row element, then
Matrix M is referred to as Metzler matrixes, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j
=1 ..., n, NijFor matrix N the i-th row jth row element, then matrix N is referred to as nonnegative matrix, be expressed as N >=>=0.Wherein, base
Refer in linearly providing the condition that closed-loop system is Asymptotic Stability positive system together with positive Lyapunov functions：For a positive systemWherein AvfIt is systematic parameter matrix, CvfIt is system output matrix, design one is linearly together with just
Lyapunov function V (t)=pTxvf(t), wherein p is a positive vector to be solved, it is known that positive system state is just, then to have V
(t)=pTxvf(t)>0, positive system be it is asymptotically stable, and if only ifThat is pTAvf<0 or
Avf Tp<0。
The advantages of the present invention over the prior art are that：It is corresponding just dry for complex jamming design existing for positive system
Observer is disturbed, and output feedback controller is designed for existing the problem of being unable to get system mode in practice, more adapts to tool
There is the actual environment of complex jamming, and in view of measuring condition limitation in engineering, there is higher engineer application；And it uses
Interference compensation strategy makes full use of known interference characteristic, carries out fine antidisturbance control so that system performance control is guarded
Lower, the control accuracy higher of property；For positive system object, prior art is relatively deficient, and the method is important technology benefit
It fills.
Description of the drawings
Fig. 1 is a kind of positive system Dynamic Output Feedback anti-interference control method flow based on positive full micr oprocessorism of the present invention
Figure.
Specific implementation mode
Below in conjunction with the accompanying drawings and specific implementation mode further illustrates the present invention.
A kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism of the present invention, specifically includes
Following steps：
The first step, for the LINEAR CONTINUOUS positive system containing external disturbance,
Wherein,WithRespectively the state of system,
Control input, the external disturbance of control input channel, control export and measure output, WithTo fit dimension parameter matrix known to system, and A is Metzler matrixes, B, C, D and CmFor non-negative square
Battle array, wherein if there is a matrixThere is Mij>=0, i, j=1 ..., n, then matrix M is referred to as Metzler matrixes, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j=1 ..., n, then matrix N is referred to as non-negative square
Battle array, be expressed as N >=>=0.If n=2, m=1, r=1, s=1,C=[1 1], D=1, Cm=[1
1].Meanwhile positivity external disturbance d (t) can be described by an external system, it is specific as follows：
Wherein,For external system state,For known systematic parameter matrix, and W is
Metzler matrixes, V are nonnegative matrix.If q=2,V=[1 1].
WithIt is an augmentation by original system and external disturbance system combination for augmented system state
Positive system：
Wherein, It is system known matrix.Matrix value substitution can be obtainedCc=[1 11 1], Dc=1, Cmc=[1 10 0].
Second step can ensure the positive full micr oprocessorism that State Viewpoint measured value is always positive for the design of positivity augmented system：
Wherein,It is augmented system stateEstimated value,It is
The estimated value of original system state x (t),It is the estimated value of interference system state w (t),
For observer gain matrix to be solved.
For positive system, the state of system and interference are in t>0 be always just, thus design State Observer need
Ensure that state estimation is always just just meaningful, according to the Rule of judgment of positive system, that is, it is Metzler matrixes, L to need G
For nonnegative matrix, ifWhereinIfWhereinIt is observer system output matrix.Wherein, positive system
Rule of judgment is systemIt is a positive system, is Metzler matrixes and if only if A, B, C are non-negative
Matrix.Wherein A and B is systematic parameter matrix, and C is system output matrix, if there is a matrixThere is Mij>=0, i, j=
1 ..., n, MijFor the element of matrix M the i-th row jth row, then matrix M is referred to as Metzler matrixes, is expressed asIf having one
MatrixThere is form Nij>0, i=1 ..., m j=1 ..., n, NijFor the element of matrix N the i-th row jth row, then claim square
Battle array N be nonnegative matrix, be expressed as N >=>=0.
If augmented state evaluated errorWherein,
For original system state estimation error,For disturbance state evaluated error.Obtain the evaluated error of augmented state
System：
If G12=0, G22=W makes augmented state be decoupled with interference external system state w (t), then has the estimation of augmented state
Error system：
Third walks, and is measured based on the State Viewpoint in full micr oprocessorism and disturbance-observer amount, design have Interference Cancellation effect
Systems by output feedback antidisturbance control rule：
Wherein, K is controller parameter to be designed,It is the estimated value of external disturbance d (t),It is original systemEstimated value,It is augmented system stateEstimated value,It is the estimated value of original system state x (t),It is interference system state w (t)
Estimated value, InDiagonal matrix is tieed up for n.Control law can be expressed as：
Therefore closed-loop system can be obtained：
Wherein,WithRespectively the state of system,
Control input, the external disturbance of control input channel, control export and measure output, To fit dimension parameter matrix known to system.
4th step is obtained according to the positive system Dynamic Output Feedback anti-interference controller based on positive full micr oprocessorism of design
Using the linear combination of former positive system state, state estimation error and Interference Estimation error as the augmentation closed-loop system of augmented state.
First withFor augmented state, closed loop augmented system is obtained：
To ensure the positivity feasibility of closed-loop system, with the linear combination of existing system mode
For system mode, closed-loop system can be obtained：
Wherein, H=BVWVTBT(BVVTBT)-1For known matrix, WithFor known suitable dimension parameter matrix, IqUnit matrix, I are tieed up for qnUnit matrix is tieed up for n.
Based on linearly the condition that closed-loop system is Asymptotic Stability positive system is provided together with positive Lyapunov functions, parameter square is solved
Battle array K, L and non-negative vectorSo that its satisfaction：
L≥≥0
-BK≥≥0
In+A-L1Cm+BK-G11≥≥0
H-BVL2Cm-BVG21≥≥0
BVG21≥≥0
C+DK≥≥0
-DK≥≥0
(In+A+BK)υ1-BKυ2+Iqυ3≤≤0
(In+A-L1Cm+BK-G11)υ1+(-BK+G11)υ2+Iqυ3≤≤0
(H-BVL2Cm-BVG21-(I+A+BK))υ1+(BVG21+BK)υ2+(H-In)υ3≤≤0
And by linear programming algorithm resolve controller and observer parameter matrix K,
So that closed loop augmented system is gradually under the positive system Dynamic Output Feedback anti-interference controller effect based on positive full micr oprocessorism
Closely stable positive system.Wherein,It is controller parameter matrix to be solved,
For observer gain matrix to be solved, ifWherein IfWhereinAc、Bc、A、B、C、D、Cm、Cmc, W and V be known system
Parameter matrix.If there is a matrixThere is Mij>=0, i, j=1 ..., n, MijFor matrix M the i-th row jth row element, then
Matrix M is referred to as Metzler matrixes, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j
=1 ..., n, NijFor matrix N the i-th row jth row element, then matrix N is referred to as nonnegative matrix, be expressed as N >=>=0.Using linear
Programming evaluation, it is K=[- 0.2556-0.5469], L=[1.24 1.85-3.87-5.41] that one group of feasible solution, which can be obtained,T、Wherein, it is asymptotic based on linearly closed-loop system is provided together with positive Lyapunov functions
Stablize positive system condition refer to：For a positive systemWherein AvfIt is systematic parameter matrix, CvfIt is
System output matrix, design one is linearly together with positive Lyapunov function V (t)=pTxvf(t), wherein p be one it is to be solved just
Vector, it is known that positive system state is just, then to have V (t)=pTxvf(t)>0, positive system be it is asymptotically stable, and if only ifThat is pTAvf<0 or Avf Tp<0。
The content that description in the present invention is not described in detail belongs to the prior art well known to professional and technical personnel in the field.
Claims (7)
1. a kind of positive system Dynamic Output Feedback anti-interference control method based on positive full micr oprocessorism, it is characterised in that：Including
Following steps：
The first step, for the LINEAR CONTINUOUS positive system containing external disturbance, with system mode and interference for augmented state, just by original
System obtains a positivity augmented system；
Second step can ensure the positive full micr oprocessorism that State Viewpoint measured value is always positive for the design of positivity augmented system, and obtain
To the evaluated error system of augmented state；
Third walks, and based on the state estimator and Interference Estimation amount obtained by full micr oprocessorism, design has Interference Cancellation effect
Positive system Dynamic Output Feedback antidisturbance control rule；
4th step is obtained according to the positive system Dynamic Output Feedback anti-interference controller based on positive full micr oprocessorism of design with original
The linear combination of positive system state, state estimation error and Interference Estimation error is the closed-loop system of state, based on linearly together with just
Lyapunov functions provide closed-loop system be Asymptotic Stability positive system condition, and by linear programming algorithm resolve controller and
Observer parameter so that closed-loop system is acted in the positive system Dynamic Output Feedback anti-interference controller based on positive full micr oprocessorism
It is asymptotically stable positive system down.
2. a kind of positive system Dynamic Output Feedback antidisturbance control side based on positive full micr oprocessorism according to claim 1
Method, it is characterised in that：The first step, for the LINEAR CONTINUOUS positive system containing external disturbance,
Wherein,WithThe respectively state of system, control
Input, the external disturbance of control input channel, control output and measurement output, WithTo fit dimension parameter matrix known to system, and A is Metzler matrixes, B, C, D and CmFor non-negative square
Battle array, wherein if there is a matrixThere is Mij>=0, i, j=1 ..., n, then matrix M is referred to as Metzler matrixes, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j=1 ..., n, then matrix N is referred to as non-negative square
Battle array, be expressed as N >=>=0, meanwhile, positivity external disturbance d (t) can be described by an external system, specific as follows：
Wherein,For external system state,For known systematic parameter matrix, and W is
Metzler matrixes, V are nonnegative matrix；
WithIt is that an augmentation is just being by original system and external disturbance system combination for augmented system state
System：
Wherein, It is system known matrix.
3. a kind of positive system Dynamic Output Feedback antidisturbance control side based on positive full micr oprocessorism according to claim 2
Method, it is characterised in that：The second step can ensure that State Viewpoint measured value is always just for the positivity augmented system design
Positive full micr oprocessorism：
Wherein,It is augmented system stateEstimated value,It is former system
The estimated value of system state x (t),It is the estimated value of interference system state w (t),To wait for
The observer gain matrix of solution；
For positive system, the state of system and interference are in t>0 be always just, thus design State Observer need to ensure
State estimation is always just just meaningful, and according to the Rule of judgment of positive system, that is, it is Metzler matrixes to need G, and L is non-
Negative matrix, ifWhereinIf
WhereinIt is observer system output matrix；If there is a matrixHave
Mij>=0, i, j=1 ..., n, then matrix M is referred to as Metzler matrixes, is expressed asB, C, D and CmFor nonnegative matrix,
Wherein, if there is a matrixThere is form Nij>0, i=1 ..., m j=1 ..., n, then matrix N is referred to as nonnegative matrix,
Be expressed as N >=>=0；
If augmented state evaluated errorWherein,For original
System state estimation error,For disturbance state evaluated error, the evaluated error system of augmented state is obtained
System：
If G12=0, G22=W makes augmented state be decoupled with interference external system state w (t), then has the evaluated error of augmented state
System：
4. a kind of positive system Dynamic Output Feedback antidisturbance control side based on positive full micr oprocessorism according to claim 3
Method, it is characterised in that：The Rule of judgment of positive system is systemIt is a positive system, and if only if A
For Metzler matrixes, B, C are nonnegative matrix, and wherein A and B are systematic parameter matrixes, and C is system output matrix, if there is a matrixThere is Mij>=0, i, j=1 ..., n, MijFor the element of matrix M the i-th row jth row, then matrix M is referred to as Metzler squares
Battle array, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j=1 ..., n, NijFor matrix
N the i-th row jth row element, then matrix N is referred to as nonnegative matrix, be expressed as N >=>=0.
5. a kind of positive system Dynamic Output Feedback antidisturbance control side based on positive full micr oprocessorism according to claim 1
Method, it is characterised in that：The third step, is measured based on the State Viewpoint in full micr oprocessorism and disturbance-observer amount, design have dry
Disturb the systems by output feedback antidisturbance control rule of negative function：
Wherein, K is controller parameter to be designed,It is the estimated value of external disturbance d (t),It is original systemEstimated value,It is augmented system stateEstimated value,It is the estimated value of original system state x (t),It is interference system state w (t)
Estimated value, InDiagonal matrix is tieed up for n, control law can be expressed as：
Therefore closed-loop system can be obtained：
Wherein,WithThe respectively state of system, control
Input, the external disturbance of control input channel, control output and measurement output, To fit dimension parameter matrix known to system.
6. a kind of positive system Dynamic Output Feedback antidisturbance control side based on positive full micr oprocessorism according to claim 1
Method, it is characterised in that：4th step, it is anti-interference according to the positive system Dynamic Output Feedback based on positive full micr oprocessorism of design
Controller is obtained using the linear combination of former positive system state, state estimation error and Interference Estimation error as the augmentation of augmented state
Closed-loop system, first withFor augmented state, closed loop augmented system is obtained：
To ensure the positivity feasibility of closed-loop system, with the linear combination of existing system modeTo be
System state can obtain closed-loop system：
Wherein, H=BVWVTBT(BVVTBT)-1For known matrix, WithFor known suitable dimension parameter matrix, IqUnit matrix, I are tieed up for qnUnit matrix is tieed up for n；
Based on linearly the condition that closed-loop system is Asymptotic Stability positive system is provided together with positive Lyapunov functions, solve parameter matrix K,
L and non-negative vectorSo that its satisfaction：
L≥≥0
-BK≥≥0
In+A-L1Cm+BK-G11≥≥0
H-BVL2Cm-BVG21≥≥0
BVG21≥≥0
C+DK≥≥0
-DK≥≥0
(In+A+BK)υ1-BKυ2+Iqυ3≤≤0
(In+A-L1Cm+BK-G11)υ1+(-BK+G11)υ2+Iqυ3≤≤0
(H-BVL2Cm-BVG21-(I+A+BK))υ1+(BVG21+BK)υ2+(H-In)υ3≤≤0
And by linear programming algorithm resolve controller and observer parameter matrix K,So that
Closed loop augmented system is asymptotic steady under the positive system Dynamic Output Feedback anti-interference controller effect based on positive full micr oprocessorism
Fixed positive system, whereinIt is controller parameter matrix to be solved,To wait asking
The observer gain matrix of solution, ifWherein IfWhereinAc、Bc、A、B、C、D、Cm、Cmc, W and V be known system
Parameter matrix, if there is a matrixThere is Mij>=0, i, j=1 ..., n, MijFor matrix M the i-th row jth row element, then
Matrix M is referred to as Metzler matrixes, is expressed asIf there is a matrixThere is form Nij>0, i=1 ..., m j
=1 ..., n, NijFor matrix N the i-th row jth row element, then matrix N is referred to as nonnegative matrix, be expressed as N >=>=0.
7. a kind of positive system Dynamic Output Feedback antidisturbance control side based on positive full micr oprocessorism according to claim 6
Method, it is characterised in that：Refer to based on linearly the condition that closed-loop system is Asymptotic Stability positive system is provided together with positive Lyapunov functions：
For a positive systemWherein AvfIt is systematic parameter matrix, CvfIt is system output matrix, designs one
Linearly together with positive Lyapunov function V (t)=pTxvf(t), wherein p is a positive vector to be solved, it is known that positive system state is
Just, then there is V (t)=pTxvf(t)>0, positive system be it is asymptotically stable, and if only if
That is pTAvf<0 or Avf Tp<0。
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| CN113359443A (en) * | 2021-05-28 | 2021-09-07 | 南京理工大学 | Composite anti-interference control method of generalized time-lag Markov jump system |
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| CN109991849A (en) * | 2019-04-03 | 2019-07-09 | 哈尔滨理工大学 | A kind of time lag LPV system has memory H ∞ output feedback controller design method |
| CN110187641A (en) * | 2019-07-12 | 2019-08-30 | 杭州电子科技大学 | A kind of control method of urban water affairs pipe network water system under external disturbance input |
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