CN107728480A - Control of Nonlinear Systems method and device - Google Patents

Control of Nonlinear Systems method and device Download PDF

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CN107728480A
CN107728480A CN201710945092.4A CN201710945092A CN107728480A CN 107728480 A CN107728480 A CN 107728480A CN 201710945092 A CN201710945092 A CN 201710945092A CN 107728480 A CN107728480 A CN 107728480A
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fuzzy
matrix
models
control gain
control
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CN107728480B (en
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赵涛
霍光尧
佃松宜
李传龙
梁伟博
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Sichuan University
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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
    • G05B13/0265—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
    • G05B13/0275—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 using fuzzy logic only
    • 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.Methods described is included based on the primary nonlinear system got, establishes T S fuzzy models；When the T S fuzzy models meet default Stabilization Conditions, control gain matrix corresponding to every fuzzy rule in the T S fuzzy models is obtained；The control gain matrix is then based on, fuzzy static output feedback controller is obtained, nonlinear system is approached by T S fuzzy models with this, and solves the problems, such as output control, more effectively.

Description

Control of Nonlinear Systems method and device
Technical field
The present invention relates to Control of Nonlinear Systems technical field, in particular to a kind of Control of Nonlinear Systems method And device.
Background technology
Network control system is because cost is low, in light weight, power is low and the simple concern for causing people is safeguarded in installation. Under network environment, data transfer is probably the communications conduit between the system component of wide apart.Therefore, networked system is all Nonlinear system, more complicated, bad processing.
The content of the invention
It is an object of the invention to provide a kind of Control of Nonlinear Systems method and device, to improve above mentioned problem.In order to Realize above-mentioned purpose, the technical scheme that the present invention takes is as follows：
In a first aspect, the embodiments of the invention provide a kind of Control of Nonlinear Systems method, methods described includes being based on obtaining The primary nonlinear system got, establishes T-S fuzzy models；When the T-S fuzzy models meet default Stabilization Conditions, obtain Control gain matrix corresponding to every fuzzy rule in the T-S fuzzy models；Based on the control gain matrix, obscured Static output feedback controller.
Second aspect, the embodiments of the invention provide 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 default Stabilization Conditions, obtaining the T-S and obscuring Control gain matrix corresponding to every fuzzy rule in model.Second obtaining unit, for based on the control gain matrix, obtaining 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, establish T-S fuzzy models；When the T-S fuzzy models meet default Stabilization Conditions, the T-S fuzzy models are obtained In every fuzzy rule control gain matrix；The control gain matrix is then based on, obtains fuzzy Static Output Feedback control Device processed, nonlinear system is approached by T-S fuzzy models with this, and solve the problems, such as output control, more effectively.
Other features and advantages of the present invention will illustrate in subsequent specification, also, partly become from specification It is clear that or 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 obtained in bright book, claims and accompanying drawing.
Brief description of the drawings
In order to illustrate the technical solution of the embodiments of the present invention more clearly, below by embodiment it is required use it is attached Figure is briefly described, it will be appreciated that the following drawings illustrate only certain embodiments of the present invention, therefore be not construed as pair The restriction of scope, for those of ordinary skill in the art, on the premise of not paying creative work, can also be according to this A little accompanying drawings obtain other related accompanying drawings.
Fig. 1 is a kind of structured flowchart for the electronic equipment that can be applied 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 border 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 in Fig. 5 from k=50；
Fig. 8 is that 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 structured flowchart of Control of Nonlinear Systems device provided in an embodiment of the present invention.
Embodiment
To make the purpose, technical scheme and advantage of the embodiment of the present invention clearer, below in conjunction with the embodiment of the present invention In accompanying drawing, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is Part of the embodiment of the present invention, rather than whole embodiments.The present invention implementation being generally described and illustrated herein in the accompanying drawings The component of example can be configured to arrange and design with a variety of.Therefore, the reality of the invention to providing in the accompanying drawings below The detailed description for applying example is not intended to limit the scope of claimed invention, but is merely representative of the selected implementation of the present invention Example.Based on the embodiment in the present invention, what those of ordinary skill in the art were obtained under the premise of creative work is not made Every other embodiment, belongs to the scope of protection of the invention.
It should be noted that：Similar label and letter represents similar terms in following accompanying drawing, therefore, once a certain Xiang Yi It is defined, then it further need not be defined and explained in subsequent accompanying drawing in individual accompanying drawing.Meanwhile the present invention's In description, term " first ", " second " etc. are only used for distinguishing description, and it is not intended that instruction or hint relative importance.
Fig. 1 shows a kind of structured flowchart for the electronic equipment 100 that can be applied in the embodiment of the present invention.As shown in figure 1, Electronic equipment 100 can include memory 102, storage control 104, one or more (one is only shown in Fig. 1) processors 106th, 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 electrically connected between block 112, display module 114,116 each element of radio-frequency module, with realize the transmission of data or Interaction.For example, electrical connection can be realized by one or more communication bus or signal bus between these elements.Nonlinear system System control method can be stored in memory 102 including at least one in the form of software or firmware (firmware) respectively Software function module, such as the software function module or computer program that the Control of Nonlinear Systems device includes.
Memory 102 can store various software programs and module, the nonlinear system provided such as the embodiment of the present application Programmed instruction/module corresponding to control method and device.Processor 106 is by running the software journey of storage in the memory 102 Sequence and module, so as to perform various function application and data processing, that is, realize the nonlinear system in the embodiment of the present application 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 PLDs, discrete gate or transistor logic, discrete hardware components.It can To realize or perform 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 processors etc..
Various input/output devices are coupled to processor 106 and memory 102 by the Peripheral Interface 108.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.
Input/output module 110 is used to be supplied to user input data to realize interacting for 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 COBBAIF, and it may include 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 referred to for display image data to user.In the present embodiment, the display module 114 can be liquid crystal display or touch Control display.If touch control display, it can be that the capacitance type touch control screen or resistance-type for supporting single-point and multi-point touch operation touch Control screen etc..Single-point and multi-point touch operation is supported to refer to that touch control display can sense on the touch control display one or more Individual opening position is with caused touch control operation, and the touch control operation that this is sensed transfers to processor 106 to be calculated and handled.
Radio-frequency module 116 is used to receiving and sending electromagnetic wave, realizes the mutual conversion of electromagnetic wave and electric signal, so that 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 more than shown in Fig. 1 or Less component, or there is the configuration different from shown in Fig. 1.Each component shown in Fig. 1 can use 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 personal computer, mobile phone, notebook computer, intelligent television, set top box, vehicle-mounted The terminal devices such as terminal.
Referring to Fig. 2, the embodiments of the invention provide a kind of Control of Nonlinear Systems method, methods described 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 be the T-S fuzzy models number of fuzzy rules, 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) represents the packet loss of data transfer, H (k) is delay function, and 0<hm≤h(k)≤hM, hm、hMIt is default positive integer.
In the present embodiment, RnAnd Rm×nN × n peacekeepings n × m dimension real matrixes are represented respectively；SnWithIt is symmetrical matrix respectively And positive definite matrix；InRepresent n × n unit matrix；X>0(<0) positive definite (negative definite) matrix is represented；X⊥Represent X kernel Base.Diag { ... } represents (block) diagonal matrix；Sym { X } represents 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 represented with *.X[f(t)]Represent square Battle array X[f(t)]Element contain f (t) scalar value.
Step S210：When the T-S fuzzy models meet default Stabilization Conditions, obtain every in the T-S fuzzy models Control gain matrix corresponding to bar fuzzy rule.
Further, when the T-S fuzzy models meet default Stabilization Conditions, LMI is obtained；Solve The LMI, obtain the first intermediary matrix and the second intermediary matrix；Based on first intermediary matrix and described Second intermediary matrix, obtain control gain matrix corresponding to every fuzzy rule in the T-S fuzzy models.
Further, it is based onObtain in the T-S fuzzy models corresponding to every fuzzy rule 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, fuzzy static output feedback controller is obtained.
Further, it is based onFuzzy static output feedback controller is obtained, u (k) is represented The fuzzy static output feedback controller, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) represents 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 Bernoulli Jacob, which is distributed in description data transmission procedure, has data-bag lost phenomenon.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 For control input amount, y (k) ∈ RpTo control output quantity, φ (k) is primary condition, θ (k)=[θ1(k),θ2..., θ (k)r (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 satisfaction 0<hm≤h(k)≤hM, hm、hMIt is default positive integer.
Assuming that former piece variable is as follows independent of control input amount, fuzzy membership functions form：
In formula (2), l ∈ S, ψij(θj(k)) it is ΘijThe degree of membership of middle θ (k).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 transfer, and Therefore, Static output is obscured Feedback controller represents 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) represents the packet loss of data transfer, H (k) is delay function, and 0<hm≤h(k)≤ hM, hm、hMIt is default 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 any 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 it is 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 the case of u (k)=0, scalar c be present>0 and Meet following condition, then fuzzy system Stochastic stable：
(8) in,And
Assuming that 1：For output matrix C ∈ Rp×n, nonsingular matrix J be present and meet CJ=[I 0].It is generally corresponding J value it is not unique, a kind of J calculation expression is described as：
J=[CT(CCT)-1 C⊥] (9)
(9) in, C⊥Referred to as null space matrix C orthogonal basis, meets CC⊥=0.
For convenience, the related symbol of theorem 1 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 cause 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, being h during k=1m, it is during k=2 hM。
It is as follows to prove that chooses Lyapunov-Krasovskii functions：
V (k)=V1(k)+V2(k)+V3(k) (12)
(12) in, And
OrderAnd the difference for defining V (k) is Δ V (k)=E { V (k+1) }-V (k), it is calculated 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), can obtain：
(20) in,To ξ1 (k), ξ2,1And ξ (k)2,2(k) lemma 1 is applied, can be obtained：
Wherein,β (k)=1- α (k).(22) and (23) are applied with lemma 2, Arbitrary Matrix N ∈ R2n×2n Meet with lower inequality (24), and meetAnd Ω>0.
Therefore Δ V (k) new coboundary is obtained：
Wherein,
DefinitionWithIt can obtainBy (10), can obtain：
Wherein,
It can be obtained by lemma 3 and (26)：
Wherein,
Understand scalar ρ be present according to (27)>0 causes (28) to set up：
Rq[h(k)]<diag{-ρIn,0n,...,0n} (28)
In view of (28), to all x (k) ≠ 0, can obtain：
Therefore, for arbitrary integer N>1, (30) both sides are added up and can obtained from k=0 to k=N：
Obtain：
Obtained according to the Lyapunov-Krasovskii functionals of aforementioned definitions：
(33), (34) and (35) are summed, obtained：
Obtained by formula (31) and (36)：
Wherein,
ObviouslyAnd it can be seen from defining 1, 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 cause system (5) to exist hm<h(k)<hMUnder the conditions of Stochastic stable adequate condition be exist H1∈Rp×p, H2∈R(n-p)×p, H3∈R(n-p)×(n-p),Meet following linear inequality：
Wherein,It is F in h (k) bordersijq[h(k)]Two vectors, such as be h during k=1m, it is h during 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⊥].T=diag { X, G, G } and its device are multiplied by inequality (10) left and right, wherein, X= [e1GT,e2GT,e3GT,e4GT,e5GT, e6GT,e7GT,e8GT,e9GT,e10GT].Obtain following LMI：
Inequality (42) is reconfigured as follows：
LMI (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 LMI (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 Exemplified by 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 can not use.Make 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) can accurately be represented 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 represent 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 border is as shown in Table 1.As shown in figure 4, from On down ,+represent hmMaximum delay border h corresponding to=22M；* h is representedmMaximum delay border h corresponding to=12M, circle table Show hmMaximum delay border h corresponding to=8M, these show different hmCorresponding maximum delay border hM, wherein β is by multiple Circulation obtains the value on corresponding maximum delay border.Figure 4, it is seen that corresponding Delay boundary conditions hMChange be with β Increase gradually increase, reaches peak value in β=1.2, continues to increase with β, Delay boundary conditions hMIt is gradually reduced.H at that timem=8, LMI in Solution finding theorem 2, following static output feedback controller gain matrix can be obtained：{K1,K2}= {[-0.3580],[0.1629]}。
The different h of table 1mCorresponding maximum delay border
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 represents k=50, fuzzy static state is defeated Go out feedback controller u (k) applications action, packet random loss is as shown in figure 8, delay function h (k) is changed over time such as Fig. 9. In Figure 5, k is worked as<When 50, any outside 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 represents state variable x2, it is real Line represents 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 been 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 meet default Stabilization Conditions, every is obtained in the T-S fuzzy models Control gain matrix corresponding to fuzzy rule；The control gain matrix is then based on, obtains fuzzy static output feedback control Device, nonlinear system is approached by T-S fuzzy models with this, and solve the problems, such as output control, more effectively.
Referring to Fig. 10, the embodiments of the invention provide a kind of Control of Nonlinear Systems device 300, described device 300 can With including establishing unit 310, the obtaining unit 330 of first obtains unit 320 and second.
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 be the T-S fuzzy models number of fuzzy rules, 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) represents the packet loss of data transfer, H (k) is delay function, and 0<hm≤h(k)≤hM, hm、hMIt is default positive integer.
First obtains unit 320, for when the T-S fuzzy models meet default Stabilization Conditions, obtaining the T-S moulds Control gain matrix corresponding to every fuzzy rule in fuzzy model.
The first obtains unit 320 can include first and obtain subelement 321.
First obtains subelement 321, for when the T-S fuzzy models meet default Stabilization Conditions, obtaining linear moment Battle array inequality；The LMI is solved, obtains the first intermediary matrix and the second intermediary matrix；In described first Between matrix and second intermediary matrix, obtain in the T-S fuzzy models control gain matrix corresponding to every fuzzy rule.
Described first obtains subelement 321, is additionally operable to be based onObtain in the T-S fuzzy models Control gain matrix, K corresponding to every fuzzy rulei∈Rm×pFor the control gain matrix of the i-th fuzzy rule,For described One intermediary matrix,For the inverse of second intermediary matrix.
Second obtaining unit 330, for based on the control gain matrix, obtaining fuzzy static output feedback controller.
Second obtaining unit 330 can include second and obtain subelement 331.
Second obtain subelement 331, for based onObtain fuzzy Static Output Feedback control Device processed, u (k) represent 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 transfer, y (k) ∈ R are representedpFor 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.
Above each unit can be that now, above-mentioned each unit can be stored in memory 102 by software code realization. Above each unit can equally be realized by hardware such as IC chip.
Control of Nonlinear Systems device 300 provided in an embodiment of the present invention, its realization principle and caused technique effect and Preceding method embodiment is identical, and to briefly describe, device embodiment part does not refer to part, refers in preceding method embodiment Corresponding contents.
In several embodiments provided herein, it should be understood that disclosed apparatus and method, can also pass through Other modes are realized.Device embodiment described above is only schematical, for example, flow chart and block diagram in accompanying drawing Show the device of multiple embodiments according to the present invention, method and computer program product architectural framework in the cards, Function and operation.At this point, each square frame in flow chart or block diagram can represent the one of a module, program segment or code Part, a part for the module, program segment or code include one or more and are used to realize holding for defined logic function Row instruction.It should also be noted that at some as in the implementation replaced, the function that is marked in square frame can also with different from The order marked in accompanying drawing occurs.For example, two continuous square frames can essentially perform substantially in parallel, they are sometimes It can perform in the opposite order, this is depending on involved function.It is it is also noted that every in block diagram and/or flow chart The combination of individual square frame and block diagram and/or the square frame in flow chart, function or the special base of action as defined in performing can be used Realize, or can be realized with the combination of specialized hardware and computer instruction in the system of hardware.
In addition, each functional module in each embodiment of the present invention can integrate to form an independent portion Point or modules individualism, can also two or more modules be integrated to form an independent part.
If the function is realized in the form of software function module and is used as independent production marketing or in use, can be with It is stored in a computer read/write memory medium.Based on such understanding, technical scheme is substantially in other words The part to be contributed to prior art or the part of the technical scheme can be embodied in the form of software product, the meter Calculation machine software product is stored in a storage medium, including some instructions are causing a computer equipment (can be People's computer, server, or network equipment etc.) perform all or part of step of each embodiment methods described of the present invention. And foregoing storage medium includes：USB flash disk, mobile hard disk, read-only storage (ROM, Read-Only Memory), arbitrary access are deposited Reservoir (RAM, Random Access Memory), magnetic disc or CD etc. are various can be with the medium of store program codes.Need Illustrate, herein, such as first and second or the like relational terms be used merely to by an entity or operation with Another entity or operation make a distinction, and not necessarily require or imply between these entities or operation any this reality be present The relation or order on border.Moreover, term " comprising ", "comprising" or its any other variant are intended to the bag of nonexcludability Contain, so that process, method, article or equipment including a series of elements not only include those key elements, but also including The other element being not expressly set out, or also include for this process, method, article or the intrinsic key element of equipment. In the absence of more restrictions, the key element limited by sentence "including a ...", it is not excluded that including the key element Process, method, other identical element also be present in article or equipment.
The preferred embodiments of the present invention are the foregoing is only, are not intended to limit the invention, for the skill of this area For art personnel, the present invention can have various modifications and variations.Within the spirit and principles of the invention, that is made any repaiies Change, equivalent substitution, improvement etc., should be included in the scope of the protection.It should be noted that：Similar label and letter exists Similar terms is represented in following accompanying drawing, therefore, once being defined in a certain Xiang Yi accompanying drawing, is then not required in subsequent accompanying drawing It is further defined and explained.
The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all be contained Cover within protection scope of the present invention.Therefore, protection scope of the present invention described should be defined by scope of the claims.
It should be noted that herein, such as first and second or the like relational terms are used merely to a reality Body or operation make a distinction with another entity or operation, and not necessarily require or imply and deposited between these entities or operation In any this actual relation or order.Moreover, term " comprising ", "comprising" or its any other variant are intended to Nonexcludability includes, so that process, method, article or equipment including a series of elements not only will including those Element, but also the other element including being not expressly set out, or it is this process, method, article or equipment also to include Intrinsic key element.In the absence of more restrictions, the key element limited by sentence "including a ...", it is not excluded that Other identical element also be present in process, method, article or equipment including the key element.

Claims (10)

  1. A kind of 1. Control of Nonlinear Systems method, it is characterised in that methods described includes：
    Based on the primary nonlinear system got, T-S fuzzy models are established；
    When the T-S fuzzy models meet default Stabilization Conditions, it is corresponding to obtain every fuzzy rule in the T-S fuzzy models Control gain matrix；
    Based on the control gain matrix, fuzzy static output feedback controller is obtained.
  2. 2. according to the method for claim 1, it is characterised 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, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are institute State the number of fuzzy rules of T-S fuzzy models, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×nIt is predetermined system matrix, Ki∈Rm×p For the control gain matrix of the i-th fuzzy rule,Bij=BiKjC,E (k) represents data The packet loss of transmission,H (k) is to prolong Slow function, and 0<hm≤h(k)≤hM, hm、hMIt is default positive integer.
  3. 3. according to the method for claim 2, it is characterised in that when the T-S fuzzy models meet default Stabilization Conditions, Control gain matrix corresponding to every fuzzy rule in the T-S fuzzy models is obtained, including：
    When the T-S fuzzy models meet default Stabilization Conditions, LMI is obtained；
    The LMI is solved, obtains the first intermediary matrix and the second intermediary matrix；
    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. 4. according to the method for claim 3, it is characterised in that based on first intermediary matrix and the second middle square Battle array, control gain matrix corresponding to every fuzzy rule in the T-S fuzzy models is obtained, including：
    It is based onControl gain matrix corresponding to every fuzzy rule in the T-S fuzzy models is obtained, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule,For first intermediary matrix,For the described second middle square Battle array it is inverse.
  5. 5. according to the method described in claim any one of 1-4, it is characterised in that based on the control gain matrix, obtain mould Static output feedback controller is pasted, including：
    It is based onFuzzy static output feedback controller is obtained, u (k) represents the fuzzy static state Output feedback controller, Ki∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) represents the packet loss of data transfer, 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.
  6. 6. a kind of Control of Nonlinear Systems device, it is characterised 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 default Stabilization Conditions, obtaining the T-S fuzzy models In control gain matrix corresponding to every fuzzy rule；
    Second obtaining unit, for based on the control gain matrix, obtaining fuzzy static output feedback controller.
  7. 7. device according to claim 6, it is characterised 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, μiFor i-th of fuzzy membership function,0≤μi≤ 1, s are institute State the number of fuzzy rules of T-S fuzzy models, Ai,Adi∈Rn×n、Bi∈Rn×m、C∈Rp×nIt is predetermined system matrix, Ki∈Rm×p For the control gain matrix of the i-th fuzzy rule,Bij=BiKjC,E (k) represents data The packet loss of transmission,H (k) is to prolong Slow function, and 0<hm≤h(k)≤hM, hm、hMIt is default positive integer.
  8. 8. device according to claim 6, it is characterised in that the first obtains unit includes：
    First obtains subelement, for when the T-S fuzzy models meet default Stabilization Conditions, obtaining linear matrix inequality technique Formula；The LMI is solved, obtains the first intermediary matrix and the second intermediary matrix；Based on first intermediary matrix With second intermediary matrix, control gain matrix corresponding to every fuzzy rule in the T-S fuzzy models is obtained.
  9. 9. device according to claim 8, it is characterised in that described first obtains subelement, is additionally operable to be based onObtain control gain matrix, K corresponding to every fuzzy rule 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.
  10. 10. according to the device described in claim any one of 6-9, it is characterised in that second obtaining unit includes：
    Second obtain subelement, for based onObtain fuzzy static output feedback controller, u (k) the fuzzy static output feedback controller, K are representedi∈Rm×pFor the control gain matrix of the i-th fuzzy rule, e (k) is represented The packet loss of data transfer, 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.
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