CN109062041A - The control method of T-S FUZZY NETWORK system based on event triggering - Google Patents
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Abstract
A kind of control method of the T-S FUZZY NETWORK system based on event triggering, has carried out stability and H for the non-linear NCSs based on event trigger mechanism∞The analysis of performance.System model is established by T-S fuzzy model.Based on this model, using the thought of relative error threshold value, the transmission strategy of event trigger mechanism (ETM) is given.Then, by introducing parallel distributed compensation (PDC) technology, corresponding state feedback controller is devised.Again by constructing suitable Lyapunov-Krasovskii functional based method, in conjunction with linear matrix inequality (LMI) theory, it is further guaranteed the adequate condition of system mean square stability and meets certain H∞Performance indicator.
Description
Technical field
The present invention relates to network control system field more particularly to a kind of T-S based on event triggering based on event triggering
The method processed of FUZZY NETWORK system.
Background technique
Due in the past few decades to automation, industrial stokehold, manufacture, robot and many other applications need
It asks and increases sharply, network control system (NCSs) is gradually promoted using status.In passing research, prolong caused by network
Late, data-bag lost and information confusion problem are mainly as caused by the finiteness of network bandwidth.In order to solve bandwidth institute band
The great number of issues come, it would be desirable to find the new method of one kind to improve system.
It is well known that Takagi-Sugeno (T-S) fuzzy model system has been widely used between the past few decades, it can
Substantially effectively indicate a kind of linear system.Nowadays complicated nonlinear function also may be by T-S fuzzy model
It generates, and only needs a small amount of fuzzy rule.The quantity of fuzzy rule is not only efficiently reduced in this way, and what is generated therefrom is huge
Advantage, the design problem of many controllers has been contemplated that using T-S model fuzzy system in a recent study.The most common control
Device design method processed, that is, so-called parallel distributed compensation (PDC) technology, controller and T-S fuzzy model are shared identical fuzzy
Former piece variable and membership function not only include state error therebetween, but also have also contemplated non-uniform temporal delay and obscure mould to T-S
The influence of type network and the rule for devising parallel distributed compensation fuzzy control.
Number of samples not only can be effectively reduced in event triggering control, while also maintaining the control performance of certain level
And with stable advantage compared with most of time triggering.By triggering control in the control of periodic sampling data and event
Between obtain balance to propose new event triggering control (ETC) strategy, here it is the triggerings of so-called recurrent event to control
(PETC), on the one hand advantage is to reduce resource utilization, and on the other hand, the condition of trigger event still has periodical spy
Sign.There is scholar to propose a kind of analysis time related method thereof, can be used for simulating contiguous network control system and the touching of dynamic event
Transmission plan is sent out, and simulates and analyze the discrete control system with event triggering.
Unless trigger conditions meet output sampled data otherwise it will be abandoned for any given trigger parameter
Remaining sampled data.There is scholar's use:
[x((k+j)h-x(kh)]TΩ[x((k+j)h)-x(kh)>σxT((k+j)hΩx((k+j)h)
Indicate trigger conditions, and trigger conditions are described as in other documentsWherein ikH and kh is sampling instant, and i is any positive integer, these conditions need
Consider time delay and interval segmentation problem.
Summary of the invention
The present invention is to solve prior art problem: establishing system model by T-S fuzzy model.Based on the mould
Type gives the transmission strategy of event trigger mechanism (ETM) using the thought of relative error threshold value.Then, parallel by introducing
Distributed compensation (PDC) technology, devises corresponding state feedback controller.Again by constructing suitable Lyapunov-
Krasovskii functional based method is further guaranteed the abundant of system mean square stability in conjunction with linear matrix inequality theory
Condition and meet certain H ∞ performance indicator it is a kind of based on event triggering T-S FUZZY NETWORK system method processed.
The particular content of the method for the present invention:
Step 1: event trigger mechanism being added in network control system, network-control system is established by event trigger mechanism
The closed-loop system model of system；The event trigger mechanism is that controller irregularly receives the output data from obscuring device；
Controlled device is a kind of nonlinear discrete object；
Step 1-1: a kind of nonlinear discrete object is described using T-S fuzzy model: if ζ1(k) it is
Mi1..., and ζsIt (k) is Mis, then the controlled device is described using formula (1):
Step 1-2: event trigger mechanism is the sampled data at a moment in comparisonAnd present sample
Data xi(k) relative error and deterministic schedule error threshold σ betweeni|xi(k) | between relationship adopted to determine
The new transmission value of sample data
Wherein, i=1,2 ..., n, σi∈ [0,1] is threshold parameter,And xiIt (k) is respectively to export and input letter
Number,Indicate newest primary transmission signal；
Step 1-3: one controller of design designs a state to controlled device (1) based on PDC technology and feeds back Fuzzy Control
Device processed, wherein the model of controller is as follows:
If ζ1It (k) is Mi1..., and ζsIt (k) is Mis,Formula
(4) in, u (k) is the output of controller, gain matrix Ki∈Rm×nBe it is to be designed, in conjunction with the final defeated of formula (3) controller
Out are as follows:
By the closed loop model of the available following non-linear NCS of formula (5) and formula (1):
Wherein,
Step 2: by constructing suitable Lyapunov-Krasovskii functional based method, being managed in conjunction with linear matrix inequality
By verifying this method guarantees that the T-S FUZZY NETWORK system of non-linear NCS meets certain H∞Performance indicator:
Step 2-1: for given matrix Q (x)=Q (x)T, R (x)=R (x)TWith S (x) so that following linear matrix
Inequality:
It sets up, is equivalent to MATRIX INEQUALITIES:
Q (x) < 0, R (x)-ST(x)Q(x)-1S (x) < 0,
R (x) < 0, Q (x)-S (x) R (x)-1ST(x) 0 <
Step 2-2: note V (k) is a Lyapunov function, if there is scalar μ > 0, the He of ν > 0, ε >=0
It can make:
μ||x(k)||2≤V(k)≤ν||x(k)||2 (10)
It sets up, then sequence meets:
Step 2-3: matrix Y is known given matrix and matrix M, N, F (k), FT(k) F (k)≤I is suitable dimension square
Battle array, if meeting Y+MF (k) N+NTF(k)TMTThen there is ε > 0 in < 0, so that Y+ ε MMT+ε-1NTN < 0；
Step 2-4: known matrix Y=YTIt is that given reality is symmetrical, and fits dimension matrix M, N, FT(k) F (k)≤I, under having
Column is set up
(1)Y+MF(k)N+NTF(k)TMT< 0；
(2) matrix W=W if it existsT> 0, then Y+MWMT+NTW-1N < 0.
The beneficial effects of the present invention are:
It 1, is to set out with the research of the NCSs based on T-S fuzzy model and the nonlinear Discrete-Time of event trigger mechanism
Point, using event trigger mechanism (ETM) strategy based on relative error, design one can reduce the state of sampled data transmission
Feedback controller.The mathematical model of non-linear NCSs is also successfully established under this strategy.
2, trigger conditions of the invention only need to calculate the opposite of each triggering moment in the triggering of above-mentioned event and miss
Poor threshold value, therefore the ETM condition in the method for the present invention not only has advantage in the use of network bandwidth, and at the place of NCSs
Cost has been saved in reason device calculating process, has reduced the traffic load in network.
Detailed description of the invention
Fig. 1: the network structure of the method for the present invention.
Fig. 2: system mode response diagram.
Fig. 3: controller state response diagram.
Fig. 4: sampled signal discharges time chart.
Fig. 5: sampled signal discharges time chart (not having ETM).
Specific embodiment
The controlled device being present in network as shown in Figure 1: is a kind of nonlinear discrete object, passes through T-S fuzzy model
It is described, which includes external disturbance ω (k), is controlled output vector sampler z (k), and come and actuator
Receive the control command that control input variable u (k) comes and holds；The state of the controlled device is adopted by the sampler based on time driving
Sample, and the sampling period is h；The sampler cooperates retainer, respectively by the sampled data x at current timei(k) and a upper moment
Sampled dataCompare the relative error between them by introducing event triggering quick-witted (ETM), is adopted with determination
Sample dataWhether should be transferred in controller.
The specific calculation control method of method in a computer is as detailed below:
Step 1: event trigger mechanism being added in network control system, network-control system is established by event trigger mechanism
The closed-loop system model of system；The event trigger mechanism is that controller irregularly receives the output data from obscuring device；
Controlled device is a kind of nonlinear discrete object；
Step 1-1: a kind of nonlinear discrete object is described using T-S fuzzy model: if ζ1(k) it is
Mi1..., and ζsIt (k) is Mis, then the controlled device is described using formula (1):
Wherein, i ∈ Sr；R indicates the number of fuzzy inference rule, x (k) ∈ Rn, u (k) ∈ RmWith z (k) ∈ RmIt respectively indicates
The controlled device state of system, control input and controlled output vector, external disturbance ω (k) meet ω (k) ∈ l2[0,∞)；Square
Battle array Ai,Bi,Ci,DiAnd Bωi(i∈Sr) it is suitable dimension and known, Mij(i∈Sr,j∈Ss) it is fuzzy set, pass throughOn be subordinate to
Function Mij(ζj(k)) it portrays, former piece variable ζ (k)=[ζ1(k),ζ2(k),...,ζs(k)]TIt is defined inOn x (k) known function.
The then final output of fuzzy system (1) are as follows:
Wherein,Mij(ζj(k))(i∈Sr,j∈SS)
It is ζj(k) belong to MijDegree of membership, and
Sensor used in communication network is based on time driving, and the sampling period is h, and controller and execution
Device is all based on event driven mode, and ZOH is for keeping sampled signal, until new sampled signal reaches controller.
The transmission strategy that we use is opposite between the sampled data and present sample data at a moment in comparison
Error, to determine whether sampled data should be transmitted.
Therefore, the design of event trigger mechanism is based on deterministic schedule error threshold:
Wherein, i=1,2 ..., n, σi∈ [0,1] is threshold parameter,And xiIt (k) is respectively to export and input letter
Number,Indicate newest primary transmission signal.
A controller is designed, a state is designed to controlled device (1) based on PDC technology and feeds back fuzzy controller,
Middle controller is the former piece part of shared T-S fuzzy model.
Therefore, the model of controller is as follows:
If ζ1It (k) is Mi1..., and ζsIt (k) is Mis, then
In formula, u (k) is the output of controller, gain matrix Ki∈Rm×nBe it is to be designed, convolution (2.4) controller
Final output are as follows:
By the closed loop model of the available following non-linear NCS of formula (4) and formula (1):
Wherein,
Step 2: by constructing suitable Lyapunov-Krasovskii functional based method, being managed in conjunction with linear matrix inequality
By verifying this method guarantees that the T-S FUZZY NETWORK system of non-linear NCS meets certain H∞Performance indicator:
Step 2-1 is lemma 1 (Schur benefit): for given matrix Q (x)=Q (x)T, R (x)=R (x)TWith S (x), make
Obtain LMI as follows
It sets up, is equivalent to MATRIX INEQUALITIES
Q (x) < 0, R (x)-ST(x)Q(x)-1S (x) < 0,
R (x) < 0, Q (x)-S (x) R (x)-1ST(x) 0. <
In solving most control problem methods, variable contained therein is usually all to be retouched with a matrix type
It states,
Such as the expression-form of MATRIX INEQUALITIES below
F (x)=ATX+XA+Q < 0 (8)
Wherein, matrix A is known given constant matrices, and meets A=AT, X is symmetrical unknown matrix,
Lemma is mended using Schur, above MATRIX INEQUALITIES can be converted into following expression-forms
At this moment, in formula (1) to set matrix X ∈ Rn×nIt can be found out using the previously described tool box LMI.
Step 2-2 is lemma 2: note V (k) is a Lyapunov function, if there is scalar μ > 0, the He of ν > 0, ε >=0It can make
μ||x(k)||2≤V(k)≤ν||x(k)||2 (10)
It sets up, then sequence meets
Step 2-3 is lemma 3: matrix Y is known given matrix and matrix M, N, F (k), FT(k) F (k)≤I is
Suitable dimension matrix, if meeting Y+MF (k) N+NTF(k)TMTThen there is ε > 0 in < 0, so that Y+ ε MMT+ε-1NTN < 0.
Step 2-4 is lemma 4: known matrix Y=YTIt is that given reality is symmetrical, and fits dimension matrix M, N, FT(k)F(k)≤
I has following formula to set up
(1)Y+MF(k)N+NTF(k)TMT< 0；
(2) matrix W=W if it existsT> 0, then Y+MWMT+NTW-1N < 0.
By constructing suitable Lyapunov-Krasovskii functional based method, managed in conjunction with linear matrix inequality (LMI)
By being further guaranteed the adequate condition of system mean square stability and meet certain H∞Performance indicator.
Theorem 2.1 is for given scalar γ > 0, if there is real matrix P=PT> 0, so that following LMI is set up
Wherein,
Π22=diag {-ε I ,-W }
It knows that nonlinear system (5) are mean square stabilities, and has reached certain H∞Performance.
It proves: defining Lyapunov function
V (k)=xT(k)Px(k) (14)
Wherein matrix P is symmetric positive definite matrix.Had according to closed-loop system
As ω (k)=0, can obtain
E V (k+1) | and V (k) }-E { V (k) }=xTΛx (16)
Lemma and (9) Shi Ke get are mended by schur
Equivalent variations are made to formula (17), both members respectively multiplied by
And its transposition, it can obtain
It is equivalent to
According to lemma 3, formula (19) is equivalent to
According to lemma 2, formula (16) is equivalent to
Wherein,
It is mean square stability from (20) available ω (k)=0 nonlinear system (5) as ε=0.When ω (k) ≠ 0
When, it can obtain
Wherein,
As Ψ < 0, lemma is mended by Schur, can be obtained
Using lemma 3, (24) are equivalent to
It is equivalent to
Φ2It substitutes into formula (27), using lemma 4, calculating process is similar to above, then can obtain
It is equivalent to formula (13).
Then it is mended by Schur, available Ψ < 0 and formula (13) sum from 0 to infinity to formula (15), available
Then the H of our an available improvement∞The nonlinear system (5) and satisfaction of performance indicator
Due to original state x (0)=0, then { V (0) }=0 E, wherein γ is given normal number
Then to ω (k) the ∈ L of any non-zero2[0 ,+∞) it sets up.Therefore, available nonlinear system (5) is that side is steady
Fixed, and the H with an improvement∞Performance indicator.
Prove that proposed method is effective by Numerical examples emulation:
We prove the validity of proposed method using the method for Numerical examples emulation.Consider following discrete time T-
S model system.
IfIt is M1, then
IfIt is M2, then
Wherein, the control input system matrix of state vector provides as follows
Bω1=[0 0.5]T,Bω2=[0 0.725]T,
C1=C2=[0 1], D1=D2=[0 0]
Membership function is given below:
Sampling period h=0.1s, it is σ that we, which select the parameter of event triggering transmission plan (2),i=0.06 performance level is
γ2=0.8452.Assuming that primary condition and disturbing signal are respectively x (0)=[1-1]T, ω (k) obeys equal between [1-1]
Even distribution.
Simulation example experimental result and analysis
According to theorem, it is as follows that we can obtain controller feedback oscillator:
K1=[- 1.0014-2.8927], K2=[- 0.4988-0.7221]
Fig. 2 and Fig. 3 illustrates the condition responsive of controlled device and controller respectively.Fig. 4 and Fig. 5 shows event touching
The distribution situation of the release moment point of hair mechanism.
2 and Fig. 3 is it can be clearly seen that system mode and controller state all reach after a period of time has passed from the graph
One stable state, it was demonstrated that mentioned method finally can achieve mean square stability in text.Although from fig. 4, it can be seen that only very
The measurement data of small scale is triggered and is sent to controller, but control system is with defined H∞The feelings of performance level
It is still under condition stable.In simulation time, measurement data only has 21.8% to be transferred to state feedback control by comparison diagram 4 and Fig. 5
Device processed, it means that required transmission data are greatly reduced, and network bandwidth is saved, it will be appreciated that the method proposed is
Effective and feasible.
Claims (1)
1. a kind of control method of the T-S FUZZY NETWORK system based on event triggering, comprising the following steps:
Step 1: event trigger mechanism being added in network control system, network control system is established by event trigger mechanism
Closed-loop system model；The event trigger mechanism is that controller irregularly receives the output data from obscuring device；It is controlled
Object is a kind of nonlinear discrete object；
Step 1-1: a kind of nonlinear discrete object is described using T-S fuzzy model: if ζ1(k) it is
Mi1..., and ζsIt (k) is Mis, then the controlled device is described using formula (1):
Step 1-2: event trigger mechanism is the sampled data at a moment in comparisonWith present sample data xi(k) it
Between relative error and deterministic schedule error threshold σi|xi(k) | between relationship determine the new transmission value of sampled data
Wherein, i=1,2 ..., n, σi∈ [0,1] is threshold parameter,And xi(k) be respectively output and input signal,Indicate newest primary transmission signal；
Step 1-3: one controller of design designs a state to controlled device (1) based on PDC technology and feeds back fuzzy control
Device, wherein the model of controller is as follows:
If ζ1It (k) is Mi1..., and ζsIt (k) is Mis,Formula (4)
In, u (k) is the output of controller, gain matrix Ki∈Rm×nBe it is to be designed, in conjunction with the final output of formula (3) controller
Are as follows:
By the closed loop model of the available following non-linear NCS of formula (5) and formula (1):
Wherein,
Step 2: by constructing suitable Lyapunov-Krasovskii functional based method, in conjunction with linear matrix inequality theory, testing
Card this method guarantees that the T-S FUZZY NETWORK system of non-linear NCS meets certain H∞Performance indicator:
Step 2-1: for given matrix Q (x)=Q (x)T, R (x)=R (x)TWith S (x) so that following linear matrix inequality technique
Formula:
It sets up, is equivalent to MATRIX INEQUALITIES:
Q (x) < 0, R (x)-ST(x)Q(x)-1S (x) < 0,
R (x) < 0, Q (x)-S (x) R (x)-1ST(x) 0 <
Step 2-2: note V (k) is a Lyapunov function, if there is scalar μ > 0, the He of ν > 0, ε >=0It can be with
So that:
μ||x(k)||2≤V(k)≤ν||x(k)||2 (10)
It sets up, then sequence meets:
Step 2-3: matrix Y is known given matrix and matrix M, N, F (k), FT(k) F (k)≤I is suitable dimension matrix, if
Meet Y+MF (k) N+NTF(k)TMTThen there is ε > 0 in < 0, so that Y+ ε MMT+ε-1NTN < 0；
Step 2-4: known matrix Y=YTIt is that given reality is symmetrical, and fits dimension matrix M, N, FT(k) F (k)≤I, there is following formula
Son is set up:
(1)Y+MF(k)N+NTF(k)TMT< 0；
(2) matrix W=W if it existsT> 0, then Y+MWMT+NTW-1N < 0.
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| CN112327616B (en) * | 2020-10-19 | 2022-09-16 | 江苏大学 | Network control system controller design method based on event triggering |
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| CN112882391A (en) * | 2021-01-26 | 2021-06-01 | 四川大学 | Double-end event triggered nonlinear control method |
| CN113093537B (en) * | 2021-03-24 | 2022-04-01 | 大连理工大学 | Event-triggered observer design method based on online asynchronous front-part reconstruction |
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| CN114706302A (en) * | 2022-03-16 | 2022-07-05 | 四川大学 | Modal event trigger control method of fuzzy switching system for actuator faults |
| CN114706302B (en) * | 2022-03-16 | 2022-11-22 | 四川大学 | Modal event trigger control method of fuzzy switching system for actuator faults |
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