CN107728480B - Control of Nonlinear Systems method and device - Google Patents
Control of Nonlinear Systems method and device Download PDFInfo
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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
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
Abstract
A kind of Control of Nonlinear Systems method and device provided in an embodiment of the present invention, is related to Control of Nonlinear Systems technical field.The method includes based on the primary nonlinear system got, establishing T S fuzzy models；When the T S fuzzy models, which meet, presets Stabilization Conditions, the corresponding control gain matrix of every fuzzy rule in the T S fuzzy models is obtained；It is then based on the control gain matrix, obtains and obscures static output feedback controller, nonlinear system is approached by T S fuzzy models with this, and solves output control problem, more effectively.
Description
Technical field
The present invention relates to Control of Nonlinear Systems technical fields, in particular to a kind of Control of Nonlinear Systems method
And device.
Background technology
Network control system is since at low cost, light-weight, power are low and installation maintenance simply causes the concern of people.
Under network environment, data transmission may be the communications conduit between the system component of wide apart.Therefore, networked system is all
Nonlinear system, more complicated, bad processing.
Invention content
The purpose of the present invention is to provide a kind of Control of Nonlinear Systems method and devices, to improve the above problem.In order to
Realize above-mentioned purpose, the technical solution adopted by the present invention is as follows：
In a first aspect, an embodiment of the present invention provides a kind of Control of Nonlinear Systems method, the method includes being based on obtaining
The primary nonlinear system got, establishes T-S fuzzy models；When the T-S fuzzy models, which meet, presets Stabilization Conditions, obtain
The corresponding control gain matrix of every fuzzy rule in the T-S fuzzy models；Based on the control gain matrix, obscured
Static output feedback controller.
Second aspect, an embodiment of the present invention provides a kind of Control of Nonlinear Systems device, described device includes establishing list
Member, first obtains unit and the second obtaining unit.Unit is established, for based on the primary nonlinear system got, establishing T-S
Fuzzy model.First obtains unit, for when the T-S fuzzy models meet and preset Stabilization Conditions, it is fuzzy to obtain the T-S
The corresponding control gain matrix of every fuzzy rule in model.Second obtaining unit is obtained for being based on the control gain matrix
Static output feedback controller must be obscured.
A kind of Control of Nonlinear Systems method and device provided in an embodiment of the present invention, based on the primary nonlinear got
System establishes T-S fuzzy models；When the T-S fuzzy models, which meet, presets Stabilization Conditions, the T-S fuzzy models are obtained
In every fuzzy rule control gain matrix；It is then based on the control gain matrix, obtains and obscures Static Output Feedback control
Device processed approaches nonlinear system with this by T-S fuzzy models, and solves output control problem, more effectively.
Other features and advantages of the present invention will be illustrated in subsequent specification, also, partly be become from specification
It is clear that by implementing understanding of the embodiment of the present invention.The purpose of the present invention and other advantages can be by saying what is write
Specifically noted structure is realized and is obtained in bright book, claims and attached drawing.
Description of the drawings
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below will be to needed in the embodiment attached
Figure is briefly described, it should be understood that the following drawings illustrates only certain embodiments of the present invention, therefore is not construed as pair
The restriction of range for those of ordinary skill in the art without creative efforts, can also be according to this
A little attached drawings obtain other relevant attached drawings.
Fig. 1 is a kind of structure diagram can be applied to the electronic equipment in the embodiment of the present invention；
Fig. 2 is the flow chart of Control of Nonlinear Systems method provided in an embodiment of the present invention；
Fig. 3 is the schematic diagram of data packetloss in Control of Nonlinear Systems method provided in an embodiment of the present invention；
Fig. 4 is the different h in Control of Nonlinear Systems method provided in an embodiment of the present inventionmCorresponding maximum delay boundary hM
Schematic diagram；
Fig. 5 is the condition responsive schematic diagram in Control of Nonlinear Systems method application example provided in an embodiment of the present invention；
The local state that Fig. 6 is Fig. 5 responds schematic diagram；
Fig. 7 is fuzzy static output feedback controller u (k) schematic diagram applied from k=50 in Fig. 5；
Fig. 8 is that data packet random loss is illustrated in Control of Nonlinear Systems method application example provided in an embodiment of the present invention
Figure；
Fig. 9 is delay function h (k) signals in Control of Nonlinear Systems method application example provided in an embodiment of the present invention
Figure；
Figure 10 is the structure diagram of Control of Nonlinear Systems device provided in an embodiment of the present invention.
Specific implementation mode
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.The present invention being usually described and illustrated herein in the accompanying drawings is implemented
The component of example can be arranged and be designed with a variety of different configurations.Therefore, below to the reality of the present invention provided in the accompanying drawings
The detailed description for applying example is not intended to limit the range of claimed invention, but is merely representative of the selected implementation of the present invention
Example.Based on the embodiments of the present invention, those of ordinary skill in the art are obtained without creative efforts
Every other embodiment, shall fall within the protection scope of the present invention.
It should be noted that：Similar label and letter indicate similar terms in following attached drawing, therefore, once a certain Xiang Yi
It is defined, then it further need not be defined and explained in subsequent attached drawing in a attached drawing.Meanwhile the present invention's
In description, term " first ", " second " etc. are only used for distinguishing description, are not understood to indicate or imply relative importance.
Fig. 1 shows a kind of structure diagram for the electronic equipment 100 that can be applied in the embodiment of the present invention.As shown in Figure 1,
Electronic equipment 100 may include memory 102, storage control 104, one or more (one is only shown in Fig. 1) processors
106, Peripheral Interface 108, input/output module 110, audio-frequency module 112, display module 114, radio-frequency module 116 and nonlinear system
System control device.
Memory 102, storage control 104, processor 106, Peripheral Interface 108, input/output module 110, audio mould
Directly or indirectly be electrically connected between block 112, display module 114,116 each element of radio-frequency module, with realize data transmission or
Interaction.For example, can realize electrical connection by one or more communication bus or signal bus between these elements.Nonlinear system
System control method respectively includes at least one to be stored in memory 102 in the form of software or firmware (firmware)
Software function module, such as software function module or computer program that the Control of Nonlinear Systems device includes.
Memory 102 can store various software programs and module, such as nonlinear system provided by the embodiments of the present application
Corresponding program instruction/the module of control method and device.Processor 106 is by running the software journey of storage in the memory 102
Sequence and module realize the nonlinear system in the embodiment of the present application to perform various functions application and data processing
Control method.
Memory 102 can include but is not limited to random access memory (Random Access Memory, RAM), only
Read memory (Read Only Memory, ROM), programmable read only memory (Programmable Read-Only
Memory, PROM), erasable read-only memory (Erasable Programmable Read-Only Memory, EPROM),
Electricallyerasable ROM (EEROM) (Electric Erasable Programmable Read-Only Memory, EEPROM) etc..
Processor 106 can be a kind of IC chip, have signal handling capacity.Above-mentioned processor can be general
Processor, including central processing unit (Central Processing Unit, abbreviation CPU), network processing unit (Network
Processor, abbreviation NP) etc.；It can also be digital signal processor (DSP), application-specific integrated circuit (ASIC), ready-made programmable
Gate array (FPGA) either other programmable logic device, discrete gate or transistor logic, discrete hardware components.It can
To realize or execute disclosed each method, step and the logic diagram in the embodiment of the present application.General processor can be micro-
Processor or the processor can also be any conventional processor etc..
The Peripheral Interface 108 couples various input/output devices to processor 106 and memory 102.At some
In embodiment, Peripheral Interface 108, processor 106 and storage control 104 can be realized in one single chip.Other one
In a little examples, they can be realized by independent chip respectively.
The interaction that input/output module 110 is used to that user input data to be supplied to realize user and electronic equipment 100.It is described
Input/output module 110 may be, but not limited to, mouse and keyboard etc..
Audio-frequency module 112 provides a user audio interface, may include that one or more microphones, one or more raises
Sound device and voicefrequency circuit.
Display module 114 provides an interactive interface (such as user interface) between electronic equipment 100 and user
Or it is referred to user for display image data.In the present embodiment, the display module 114 can be liquid crystal display or touch
Control display.Can be that the capacitance type touch control screen or resistance-type of single-point and multi-point touch operation is supported to touch if touch control display
Control screen etc..Single-point and multi-point touch operation is supported to refer to touch control display and can sense on the touch control display one or more
The touch control operation generated simultaneously at a position, and transfer to processor 106 to be calculated and handled the touch control operation that this is sensed.
Radio-frequency module 116 is used to receive and transmit electromagnetic wave, realizes the mutual conversion of electromagnetic wave and electric signal, thus with
Communication network or other equipment are communicated.
It is appreciated that structure shown in FIG. 1 is only to illustrate, electronic equipment 100 may also include it is more than shown in Fig. 1 or
Less component, or with the configuration different from shown in Fig. 1.Each component shown in Fig. 1 may be used hardware, software or its
Combination is realized.
In the embodiment of the present invention, electronic equipment 100 can be used as user terminal, or as server.User terminal
Can be PC (personal computer) computer, tablet computer, mobile phone, laptop, smart television, set-top box, vehicle-mounted
The terminal devices such as terminal.
Referring to Fig. 2, an embodiment of the present invention provides a kind of Control of Nonlinear Systems method, the method includes：Step
S200, step S210 and step S220.
Step S200：Based on the primary nonlinear system got, T-S fuzzy models are established.
The T-S fuzzy models arex(k)∈
RnFor the fringe amount at k moment, x (k+1) ∈ RnFor the fringe amount at k+1 moment, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are the number of fuzzy rules of the T-S fuzzy models, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×n
For predetermined system matrix, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule,Bij=BiKjC,E (k) indicates the packet loss of data transmission, H (k) is delay function, and 0<hm≤h(k)≤hM, hm、hMIt is preset positive integer.
In the present embodiment, RnAnd Rm×nIndicate that n × n peacekeepings n × m ties up real matrix respectively；SnWithIt is symmetrical matrix respectively
And positive definite matrix；InIndicate the unit matrix of n × n；X>0(<0) positive definite (negative definite) matrix is indicated；X⊥Represent the kernel of X
Base.Diag { ... } indicates (block) diagonal matrix；Sym { X } indicates X and XTSum；col{x1,…,xnIt is x1,…,xnRow to
Amount；For y1,…,ynThe set of composition.Symmetrical item and quadric form in symmetrical matrix will be indicated with *.X[f(t)]Indicate square
Battle array X[f(t)]Element contain the scalar value of f (t).
Step S210：When the T-S fuzzy models, which meet, presets Stabilization Conditions, obtain every in the T-S fuzzy models
The corresponding control gain matrix of fuzzy rule.
Further, when the T-S fuzzy models, which meet, presets Stabilization Conditions, linear matrix inequality is obtained；It solves
The linear matrix inequality obtains the first intermediary matrix and the second intermediary matrix；Based on first intermediary matrix and described
Second intermediary matrix obtains the corresponding control gain matrix of every fuzzy rule in the T-S fuzzy models.
Further, it is based onIt is corresponding to obtain every fuzzy rule in the T-S fuzzy models
Control gain matrix, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule,For first intermediary matrix,For institute
State the inverse of the second intermediary matrix.
Step S220：Based on the control gain matrix, obtains and obscure static output feedback controller.
Further, it is based onIt obtains and obscures static output feedback controller, u (k) is indicated
The fuzzy static output feedback controller, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) indicates that data pass
Defeated packet loss, y (k) ∈ RpFor the control output quantity at k moment, μiFor i-th of fuzzy membership function,0≤μi
≤ 1, s are the number of fuzzy rules of the T-S fuzzy models.
In the present embodiment, the primary nonlinear system can be nonlinear time-varying delay system.Consider a kind of communication
The control problem of nonlinear time-varying delay system under limited case, non-linear controlled device are approached by T-S fuzzy models.Pass through
There are data-bag lost phenomenons in Bernoulli Jacob's distribution description data transmission procedure.Detailed process is as shown in Figure 3.
Based on T-S fuzzy models description controlled device be：Regular i：If θ1(k) it is Θi1,……,θr(r) it is Θir, then
Have：
In formula (1), i ∈ S={ 1,2 ..., s }, s are number of fuzzy rules, x (k) ∈ RnFor fringe amount, u (k) ∈ Rm
Input quantity in order to control, y (k) ∈ RpOutput quantity in order to control, φ (k) are primary condition, θ (k)=[θ1(k),θ2(k) ..., θr
(k)] it is measurable former piece variable, ΘijFor fuzzy set, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×nIt is predetermined system matrix, h
(k) it is delay function, is time-varying and meets 0<hm≤h(k)≤hM, hm、hMIt is preset positive integer.
Assuming that former piece variable does not depend on control input quantity, fuzzy membership functions form is as follows：
In formula (2), l ∈ S, ψij(θj(k)) it is ΘijThe degree of membership of middle θ (k).It is calculated to simplify, by μi(θ (k)) table
It is shown as μi。
Be distributed the obtained controller of description random loss process using Bernoulli Jacob, it then follows fuzzy control rule it is as follows：
Regular i：If θ1(k) it is Θi1,……,θr(r) it is Θir, then have：
U (k)=e (k) Kiy(k) (3)
In formula (3), Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) is a Bernoulli process, table
Show the packet loss of data transmission, and Therefore, Static output is obscured
Feedback controller indicates as follows：
In formula (4), fuzzy membership functions meets0≤μi≤1.Based on formula (1) and (4), described in acquisition
T-S fuzzy models are：
In expression formula (5), x (k) ∈ RnFor the fringe amount at k moment, x (k+1) ∈ RnFor the fringe at k+1 moment
Amount, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are the number of fuzzy rules of the T-S fuzzy models,
Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×nIt is predetermined system matrix, Ki∈Rm×pFor the control gain square of the i-th fuzzy rule
Battle array,Bij=BiKjC,E (k) indicates the packet loss of data transmission, H (k) is delay function, and 0<hm≤h(k)≤
hM, hm、hMIt is preset positive integer.
Lemma 1：For matrixInteger a<B, vectorial z:U→Rn, and U={ a, a+1 ..., b-1, b }, then with
Lower inequality is set up：
(6) in, σ=b-a+1,And
Lemma 2：For arbitrary vectorMatrixM∈Rn×n, real number scalarMeet α1+α2
=1, even αi=0 xi=0.Then following inequality is set up：
Lemma 3：Meet x ∈ Rn, R ∈ Sn, M ∈ Rm×n, and rank { M }<N, for Arbitrary Matrix L ∈ Rn×m, then following
Inequality is of equal value：xTRx<0,x≠0；R+sym(LM)<0；(M⊥)TRM⊥<0。
Define 1：For the T-S fuzzy systems containing data packetloss, if in u (k)=0, there are scalar c>0 and
Meet the following conditions, then fuzzy system Stochastic stable：
(8) in,And
Assuming that 1：For output matrix C ∈ Rp×n, there are nonsingular matrix J to meet CJ=[I 0].It is corresponding under normal circumstances
J value it is not unique, a kind of calculation expression of J is described as：
J=[CT(CCT)-1 C⊥] (9)
(9) in, C⊥The referred to as orthogonal basis of null space matrix C, meets CC⊥=0.
For convenience, 1 related symbol of theorem is expressed as：hd=hM-hm, τ1(k)=h (k)-hm, τ2(k)=hM-h
(k),
f1=[e1,e5-e1,e6+e7-e2-e3], f7,ij=e1(BiKjC)T, f8
=[e1,e5-e2,e6+e7-e2-e4], f9,ij=[f6,ij, 0,0], f10=[e1, 0], f11,ij=[0, f6,ij], f12=[I, 0,0],
f13=[0, I], Δ1=[e5-e1,e1-e2], Δ2=[(hm+1)(e1-e5)+2e8,(hm+1)(e1+e2)-2e5],
Λ1=[e6-e2,e2-e3,e2-e6+2e9,e2+e3-2e6,e7-e3,e3-e4,e3-e7+2e10,e3+e4-2e7], Λ2[h(k)]=[0,
0,τ1(k)(e2-e6),τ1(k)(e2+e3),0,0,τ2(k)(e3-e7),τ2(k)(e3+e4)], Matrix-block,
Theorem 1：Consider fuzzy system (5), it is assumed that the gain K of controller (4)iIt is known.For known positive integer hmAnd hM
And ensure hm<hM, to make system (5) in hm<h(k)<hMUnder the conditions of Stochastic stable adequate condition be exist{Si}i∈S∈S3n, N=[Nij]i,j∈1,2∈R4n×4n, meet following linear square
Battle array inequality：
Fijq,k<0, k=1,2, i, j, q ∈ S (10)
Wherein,It is F in h (k) Delay boundary conditionsijq[h(k)]Two vectors, for example, when k=1 be hm, when k=2 is
hM。
It is as follows to prove that chooses Lyapunov-Krasovskii functions：
V (k)=V1(k)+V2(k)+V3(k) (12)
(12) in, And
It enablesAnd the difference for defining V (k) is Δ V (k)=E { V (k+1) }-V
(k), it calculates as follows：
Wherein,
In addition, there is following inequality to set up：
Choose (l1, l2) it is respectively (0, hm), (hm, h (k)), (h (k), hM), it can obtain：
Above formula is added to Δ V3(k), it can obtain：
(20) in,To ξ1
(k), ξ2,1(k) and ξ2,2(k) lemma 1 is applied, can be obtained：
Wherein,β (k)=1- α (k).Lemma 2, Arbitrary Matrix N ∈ R are applied to (22) and (23)2n×2n
Meet with lower inequality (24), and meetsAnd Ω>0.
Therefore the new coboundary of Δ V (k) is obtained：
Wherein,
DefinitionWithIt can obtainBy (10), can obtain：
Wherein,
It can be obtained by lemma 3 and (26)：
Wherein,
According to (27) it is found that there are scalar ρ>0 so that (28) are set up：
Rq[h(k)]<diag{-ρIn,0n,...,0n} (28)
In view of (28) can obtain all x (k) ≠ 0：
Therefore, for arbitrary integer N>1, (30) both sides are added up and can be obtained from k=0 to k=N：
It obtains：
It is obtained according to the Lyapunov-Krasovskii functionals of aforementioned definitions：
It sums, obtains to (33), (34) and (35)：
It is obtained by formula (31) and (36)：
Wherein,
ObviouslyAnd according to definition 1 it is found that fuzzy system (5) is Stochastic stable.
When controlling known to gain, theorem 1 mainly gives the stable condition of system.Further, it is assumed that control gain
It is unknown, on the basis of theorem 1, give corresponding Stabilization Conditions and control gain calculating method.
Theorem 2：For known positive integer hmAnd hMAnd ensure hm<hMAnd a scalar β, to make system (5) exist
hm<h(k)<hMUnder the conditions of Stochastic stable adequate condition be existH1∈Rp×p, H2∈R(n-p)×p, H3
∈R(n-p)×(n-p),Meet following linear inequality：
Wherein,It is F in the boundaries h (k)ijq[h(k)]Two vectors, such as when k=1 be hm, it is h when k=2M。 f14=[I, 0], f15
=[0 ,-I ,-I], f16=[0,0 ,-I], f17=[0, I, 0],J=[CT(CCT)-1,C⊥], GT=
JHT,
Prove that defines matrixAnd GT=JHT, wherein H1∈Rp×p, H2∈Rp×(n-p), H3∈R(n -p)×(n-p)With J=[CT(CCT)-1C⊥].It is multiplied by T=diag { X, G, G } and its device in inequality (10) left and right, wherein X=
[e1GT,e2GT,e3GT,e4GT,e5GT, e6GT,e7GT,e8GT,e9GT,e10GT].Obtain following linear matrix inequality：
Inequality (42) is reconfigured as follows：
Linear matrix inequality (39) and (40) can be obtained based on (43).(41) proof procedure is similar to above-mentioned side
Method.The solution of Stabilization provides in theorem 2, if parameter it is known that if can directly solve linear matrix inequality
(39), the feasibility problems of (40) and (41), to obtain suitable stability controller gain.
Further, in order to illustrate the validity of Fuzzy Control of Nonlinear Systems method provided in an embodiment of the present invention, with
For one Henon chaos system, explanation is illustrated.
Henon chaos systems：
In Henon chaos systems (44), c ∈ [0,1] are constant coefficient.Assuming that state variable can not be surveyed, therefore existing shape
State feedback cannot use.Enable θ (k)=cx1(k)+(1-c)x1(k-h (k)), it is assumed that θ (k) ∈ [- m, m], m>0.It is non-
Linear term θ2(k) it can accurately be indicated by following formula：θ2(k)=μ1(θ(k))(-m)θ(k)+μ2(θ (k)) m θ (k), member functionMeet μ1(θ(k))+μ1(θ (k))=1,
Therefore, primary nonlinear system such as Henon chaos systems can indicate as follows by T-S fuzzy models：
Rule 1:If θ (k)=- m, x (k+1)=A1x(k)+Ad1x(k-h(k))+B1u*(k)。
Rule 2：If θ (k)=m, x (k+1)=A2x(k)+Ad2x(k-h(k))+B2u*(k), wherein u*(k)=1.4
+ u (k) and
By setting c=0.8 and m=0.6, different hmCorresponding maximum delay boundary is as shown in Table 1.As shown in figure 4, from
On down ,+indicate hm=22 corresponding maximum delay boundary hM；* h is indicatedm=12 corresponding maximum delay boundary hM, circle table
Show hm=8 corresponding maximum delay boundary hM, these show different hmCorresponding maximum delay boundary hM, wherein β is by multiple
Cycle obtains the value on corresponding maximum delay boundary.Figure 4, it is seen that corresponding Delay boundary conditions hMVariation be with β
Increase and gradually increase, reaches peak value in β=1.2, continue to increase with β, Delay boundary conditions hMIt is gradually reduced.H at that timem=8,
Linear matrix inequality in Solution finding theorem 2 can obtain following static output feedback controller gain matrix：{K1,K2}=
{[-0.3580],[0.1629]}。
The different h of table 1mCorresponding maximum delay boundary
Further, in order to show the validity of Control of Nonlinear Systems method provided in an embodiment of the present invention, from k=50
Condition responsive from k=40 to 60 local states as shown in figure 5, respond as shown in fig. 6, when Fig. 7 indicates k=50, fuzzy static state is defeated
Go out feedback controller u (k) applications action, data packet random loss is as shown in figure 8, delay function h (k) is changed over time such as Fig. 9.
In Figure 5, work as k<When 50, any external input is not applied；Since k=50, the fuzzy Static Output Feedback that gets
Controller u (k) starts application effect.Fig. 5-Fig. 9 abscissas are time k, and in Fig. 5-Fig. 6, dotted line indicates state variable x2, real
Line indicates state variable x1, it is unstable for can be seen that original Henon systems from Fig. 5, Fig. 6 and Fig. 7, passes through the mould of acquisition
Paste static output feedback controller has calmed and has had the unstable Henon systems of time_varying sequence and data packetloss.Solving has
The fuzzy output control problem of time_varying sequence and data packetloss Discrete-time Nonlinear Systems.
A kind of Control of Nonlinear Systems method provided in an embodiment of the present invention, based on the primary nonlinear system got,
Establish T-S fuzzy models；When the T-S fuzzy models, which meet, presets Stabilization Conditions, every is obtained in the T-S fuzzy models
The corresponding control gain matrix of fuzzy rule；It is then based on the control gain matrix, obtains and obscures static output feedback control
Device approaches nonlinear system with this by T-S fuzzy models, and solves output control problem, more effectively.
Referring to Fig. 10, an embodiment of the present invention provides a kind of Control of Nonlinear Systems device 300, described device 300 can
To include establishing unit 310, first obtains unit 320 and the second obtaining unit 330.
Unit 310 is established, for based on the primary nonlinear system got, establishing T-S fuzzy models.
The T-S fuzzy models arex(k)∈
RnFor the fringe amount at k moment, x (k+1) ∈ RnFor the fringe amount at k+1 moment, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are the number of fuzzy rules of the T-S fuzzy models, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×n
For predetermined system matrix, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule,Bij=BiKjC,E (k) indicates the packet loss of data transmission, H (k) is delay function, and 0<hm≤h(k)≤hM, hm、hMIt is preset positive integer.
First obtains unit 320, for when the T-S fuzzy models meet and preset Stabilization Conditions, obtaining the T-S moulds
The corresponding control gain matrix of every fuzzy rule in fuzzy model.
The first obtains unit 320 may include the first acquisition subelement 321.
First obtains subelement 321, for when the T-S fuzzy models meet and preset Stabilization Conditions, obtaining linear moment
Battle array inequality；The linear matrix inequality is solved, the first intermediary matrix and the second intermediary matrix are obtained；In described first
Between matrix and second intermediary matrix, obtain the corresponding control gain matrix of every fuzzy rule in the T-S fuzzy models.
Described first obtains subelement 321, is additionally operable to be based onIt obtains in the T-S fuzzy models
The corresponding control gain matrix of every fuzzy rule, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule,It is described
One intermediary matrix,For the inverse of second intermediary matrix.
Second obtaining unit 330 obtains for being based on the control gain matrix and obscures static output feedback controller.
Second obtaining unit 330 may include the second acquisition subelement 331.
Second obtains subelement 331, for being based onIt obtains and obscures Static Output Feedback control
Device processed, u (k) indicate the fuzzy static output feedback controller, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e
(k) packet loss of data transmission, y (k) ∈ R are indicatedpFor the control output quantity at k moment, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are the number of fuzzy rules of the T-S fuzzy models.
The above each unit can be by software code realization, at this point, above-mentioned each unit can be stored in memory 102.
The above each unit can equally be realized by hardware such as IC chip.
The technique effect of Control of Nonlinear Systems device 300 provided in an embodiment of the present invention, realization principle and generation and
Preceding method embodiment is identical, and to briefly describe, device embodiment part does not refer to place, can refer in preceding method embodiment
Corresponding contents.
In several embodiments provided herein, it should be understood that disclosed device and method can also pass through
Other modes are realized.The apparatus embodiments described above are merely exemplary, for example, the flow chart in attached drawing and block diagram
Show the device of multiple embodiments according to the present invention, the architectural framework in the cards of method and computer program product,
Function and operation.In this regard, each box in flowchart or block diagram can represent the one of a module, section or code
Part, a part for the module, section or code, which includes that one or more is for implementing the specified logical function, to be held
Row instruction.It should also be noted that at some as in the realization method replaced, the function of being marked in box can also be to be different from
The sequence marked in attached drawing occurs.For example, two continuous boxes can essentially be basically executed in parallel, they are sometimes
It can execute in the opposite order, this is depended on the functions involved.It is also noted that every in block diagram and or flow chart
The combination of box in a box and block diagram and or flow chart can use function or the dedicated base of action as defined in executing
It realizes, or can be realized using a combination of dedicated hardware and computer instructions in the system of hardware.
In addition, each function module in each embodiment of the present invention can integrate to form an independent portion
Point, can also be modules individualism, can also two or more modules be integrated to form an independent part.
It, can be with if the function is realized and when sold or used as an independent product in the form of software function module
It is stored in a computer read/write memory medium.Based on this understanding, technical scheme of the present invention is substantially in other words
The part of the part that contributes to existing technology or the technical solution can be expressed in the form of software products, the meter
Calculation machine software product is stored in a storage medium, including some instructions are used so that a computer equipment (can be
People's computer, server or network equipment etc.) it performs all or part of the steps of the method described in the various embodiments of the present invention.
And storage medium above-mentioned includes：USB flash disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), arbitrary access are deposited
The various media that can store program code such as reservoir (RAM, Random Access Memory), magnetic disc or CD.It needs
Illustrate, herein, relational terms such as first and second and the like be used merely to by an entity or operation with
Another entity or operation distinguish, and without necessarily requiring or implying between these entities or operation, there are any this realities
The relationship or sequence on border.Moreover, the terms "include", "comprise" or its any other variant are intended to the packet of nonexcludability
Contain, so that the process, method, article or equipment including a series of elements includes not only those elements, but also includes
Other elements that are not explicitly listed, or further include for elements inherent to such a process, method, article, or device.
In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that including the element
Process, method, article or equipment in there is also other identical elements.
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field
For art personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, any made by repair
Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.It should be noted that：Similar label and letter exist
Similar terms are indicated in following attached drawing, therefore, once being defined in a certain Xiang Yi attached drawing, are then not required in subsequent attached drawing
It is further defined and is explained.
The above description is merely a specific embodiment, but scope of protection of the present invention is not limited thereto, any
Those familiar with the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all contain
Lid is within protection scope of the present invention.Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
It should be noted that herein, relational terms such as first and second and the like are used merely to a reality
Body or operation are distinguished with another entity or operation, are deposited without necessarily requiring or implying between these entities or operation
In any actual relationship or order or sequence.Moreover, the terms "include", "comprise" or its any other variant are intended to
Non-exclusive inclusion, so that the process, method, article or equipment including a series of elements is not only wanted including those
Element, but also include other elements that are not explicitly listed, or further include for this process, method, article or equipment
Intrinsic element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that
There is also other identical elements in process, method, article or equipment including the element.
Claims (8)
1. a kind of Control of Nonlinear Systems method, which is characterized in that the method includes：
Based on the primary nonlinear system got, T-S fuzzy models are established；
When the T-S fuzzy models, which meet, presets Stabilization Conditions, obtains every fuzzy rule in the T-S fuzzy models and correspond to
Control gain matrix；
Based on the control gain matrix, obtains and obscure static output feedback controller；
Based on the control gain matrix, obtains and obscure static output feedback controller, including：
It is based onIt obtains and obscures static output feedback controller, u (k) indicates the fuzzy static state
Output feedback controller, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) indicates the packet loss of data transmission, y
(k)∈RpFor the control output quantity at k moment, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are described
The number of fuzzy rules of T-S fuzzy models.
2. according to the method described in claim 1, it is characterized in that, the T-S fuzzy models arex(k)∈RnFor the fringe amount at k moment, x (k
+1)∈RnFor the fringe amount at k+1 moment, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×nIt is predetermined system matrix,Bij=BiKjC,
H (k) is delay function, and 0<hm≤h(k)≤hM, hm、hMIt is preset positive integer.
3. according to the method described in claim 2, it is characterized in that, when the T-S fuzzy models meet preset Stabilization Conditions when,
The corresponding control gain matrix of every fuzzy rule in the T-S fuzzy models is obtained, including：
When the T-S fuzzy models, which meet, presets Stabilization Conditions, linear matrix inequality is obtained；
The linear matrix inequality is solved, the first intermediary matrix and the second intermediary matrix are obtained；
Based on first intermediary matrix and second intermediary matrix, every fuzzy rule in the T-S fuzzy models is obtained
Corresponding control gain matrix.
4. according to the method described in claim 3, it is characterized in that, being based on first intermediary matrix and the second intermediate square
Battle array, obtains the corresponding control gain matrix of every fuzzy rule in the T-S fuzzy models, including：
It is based onObtain the corresponding control gain matrix of every fuzzy rule, K in the T-S fuzzy modelsi
∈Rm×pFor the control gain matrix of the i-th fuzzy rule,For first intermediary matrix,For second intermediary matrix
It is inverse.
5. a kind of Control of Nonlinear Systems device, which is characterized in that described device includes
Unit is established, for based on the primary nonlinear system got, establishing T-S fuzzy models；
First obtains unit, for when the T-S fuzzy models meet and preset Stabilization Conditions, obtaining the T-S fuzzy models
In the corresponding control gain matrix of every fuzzy rule；
Second obtaining unit obtains for being based on the control gain matrix and obscures static output feedback controller；
Second obtaining unit includes：
Second obtains subelement, for being based onIt obtains and obscures static output feedback controller, u
(k) the fuzzy static output feedback controller, K are indicatedi∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) is indicated
The packet loss of data transmission, y (k) ∈ RpFor the control output quantity at k moment, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are the number of fuzzy rules of the T-S fuzzy models.
6. device according to claim 5, which is characterized in that the T-S fuzzy models arex(k)∈RnFor the fringe amount at k moment, x (k
+1)∈RnFor the fringe amount at k+1 moment, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×nIt is predetermined system matrix,Bij=BiKjC,
H (k) is delay function, and 0<hm≤h(k)≤hM, hm、hMIt is preset positive integer.
7. device according to claim 5, which is characterized in that the first obtains unit includes：
First obtains subelement, for when the T-S fuzzy models meet and preset Stabilization Conditions, obtaining linear matrix inequality technique
Formula；The linear matrix inequality is solved, the first intermediary matrix and the second intermediary matrix are obtained；Based on first intermediary matrix
With second intermediary matrix, the corresponding control gain matrix of every fuzzy rule in the T-S fuzzy models is obtained.
8. device according to claim 7, which is characterized in that described first obtains subelement, is additionally operable to be based onObtain the corresponding control gain matrix of every fuzzy rule, K in the T-S fuzzy modelsi∈Rm×pFor
The control gain matrix of i-th fuzzy rule,For first intermediary matrix,For the inverse of second intermediary matrix.
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