CN109856970A - It is a kind of with network induce bounded time lag and loss of data it is limited when calm method - Google Patents
It is a kind of with network induce bounded time lag and loss of data it is limited when calm method Download PDFInfo
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Abstract
It is a kind of with network induce bounded time lag and loss of data it is limited when calm method, be related to network control system technical field.The problem of method of calming when the present invention solves existing limited is unable to Active Compensation network induction bounded time lag and loss of data, and the control performance for method of calming when leading to limited is affected.Status information of the present invention using forecast Control Algorithm prediction network control system current time, the influence of Active Compensation network induction bounded time lag and loss of data to network control system control performance when limited.Compared with the conventional method, calm method can induce time lag, time-varying bounded Internet-Game Addiction and loss of data with the fixed network of Active Compensation network control system forward path and feedback channel when of the invention limited, calm method when limited based on linear matrix inequality solution has been obtained, has achieved the purpose that Active Compensation network induction bounded time lag and loss of data.The present invention be suitable for Linear Network dynamical system it is limited when Stabilization.
Description
Technical field
The invention belongs to network control system technical fields, and in particular to there is one kind network to induce bounded time lag sum number
According to loss it is limited when calm method.
Background technique
Calm when limited be in control system it is a kind of it is important study a question, it can make control system have convergence rate
Fastly, the advantages that stable state accuracy is high, robustness is good.It is obtained in fields such as guided missile system, communications network system, robot control systems
It is widely applied.From the perspective of optimization, quelling control method is time optimal control method when limited, so-called limited
Shi Zhending, which refers to, controls system to equalization point in finite time, studies have shown that having interference and uncertain feelings in system
Under condition, quelling system often has better performance when limited.
Although it is existing for it is limited when calm method research make some progress, town when existing limited
The control of calm method when determining method and be still unable to Active Compensation network induction bounded time lag and loss of data, and then influencing limited
Performance.
Summary of the invention
The purpose of the present invention is to solve it is existing limited when calm method be unable to Active Compensation network induction bounded when
The problem of control performance of stagnant and loss of data, method of calming when leading to limited is affected.
It is of the present invention it is a kind of with network induce bounded time lag and loss of data it is limited when calm method, this method
Specific steps are as follows:
Step 1: establishing the linear dynamic mould with the network control system of network induction bounded time lag and loss of data
Type；
Step 2: the State Forecasting Model of the linear dynamic model of the network control system in establishment step one；
Step 3: the State Forecasting Model for the network control system linear dynamic model established according to step 2, to set
Count state feedback controller；
Step 4: obtaining the closed-loop system side of network control system according to the state feedback controller that step 3 obtains
Journey；
Step 5:, by liapunov's theorem of stability, obtaining state using the closed-loop system of network control system
Estimated gain matrix L and state feedback gain matrix K；
Step 6: the state estimation gain matrix L obtained in step 5 is substituted into the State Forecasting Model in step 2, it will
State feedback gain matrix K substitutes into the state feedback controller in step 3, realizes and induces bounded time lag sum number to network
According to loss network control system it is limited when it is calm.
The beneficial effects of the present invention are: inducing having for bounded time lag and loss of data with network the present invention provides a kind of
Calm method in limited time, status information of the present invention using forecast Control Algorithm prediction network control system current time, active
Compensate for network induction bounded time lag and loss of data to network control system it is limited when control performance influence, and it is existing
It is limited when calm method compare, calm method can be with Active Compensation network control system forward path when of the invention limited
With fixed network induction time lag, time-varying bounded Internet-Game Addiction and the data-bag lost of feedback channel, obtain based on linear
MATRIX INEQUALITIES solution it is limited when calm method, achieved the purpose that Active Compensation network induction bounded time lag and loss of data.
The minimum value of the ε obtained by the method for the invention isBounded time lag and data are induced less than no network
The minimum value ε obtained when lossmin=2.8, so the control for method of calming when effectively can avoid limited using method of the invention
Performance processed is influenced by Internet-Game Addiction and loss of data, and has the advantages that be easy to solve and realize.
Detailed description of the invention
Fig. 1 is the method for the invention flow chart；
Fig. 2 is the embodiment of the present invention in given δx, optimization ε when closed-loop system state trajectory x1(t) and state trajectory
x2(t) figure；
Wherein: δx 2For square of original state threshold value, ε2For square of SOT state of termination threshold value, x (0) represents original state,
xTIt (0) is the transposition of x (0), x (t) represents the original state of t moment, xT(t) transposition for being x (t), R is domain matrix；
Specific embodiment
Specific embodiment one, embodiment is described with reference to Fig. 1, and there is one kind described in present embodiment network induction to have
Boundary's time lag and loss of data it is limited when calm method, the specific steps of this method are as follows:
Step 1: establishing the linear dynamic mould with the network control system of network induction bounded time lag and loss of data
Type；
Step 2: the State Forecasting Model of the linear dynamic model of the network control system in establishment step one；
Step 3: the State Forecasting Model for the network control system linear dynamic model established according to step 2, to set
Count state feedback controller；
Step 4: obtaining the closed-loop system side of network control system according to the state feedback controller that step 3 obtains
Journey；
Step 5:, by liapunov's theorem of stability, obtaining state using the closed-loop system of network control system
Estimated gain matrix L and state feedback gain matrix K；
Step 6: the state estimation gain matrix L obtained in step 5 is substituted into the State Forecasting Model in step 2, it will
State feedback gain matrix K substitutes into the state feedback controller in step 3, realizes and induces bounded time lag sum number to network
According to loss network control system it is limited when it is calm.
Specific embodiment two, the present embodiment is different from the first embodiment in that, the specific mistake of the step 1
Journey are as follows:
The linear dynamic model with the network control system of network induction bounded time lag and loss of data is established, it is described
The state space form of linear dynamic model are as follows:
Wherein: x (t) is the state variable of the linear dynamic model of the network control system of t moment, and x (t+1) is t+1
The state variable of the linear dynamic model of the network control system at moment, u (t) are that the control of the controller of t moment inputs letter
Number, y (t) are the measurement output function of the sensor of t moment, and A is sytem matrix, and B is input matrix, and C is output matrix.Matrix
It is that can detect to (A, C)；
By network connection between sensor and controller, also by network connection between actuator and controller, pass through
The data band having time of network transmission is stabbed.Feedback channel (that is, channel between sensor to controller) and forward path
The upper bound of the network time service in (that is, channel between controller to actuator) is respectively nbAnd nf, feedback channel and forward path
The upper bound of data packet continual data package dropout number be nd；
Specific embodiment three, present embodiment are unlike specific embodiment two, the specific mistake of the step 2
Journey are as follows:
The State Forecasting Model of the linear dynamic model of network control system in establishment step one, the status predication
The concrete form of model are as follows:
In formula,The x obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment
(t-k- τ+i) is in the predicted value at t-k- τ+i moment, i=2,3 ..., k+ τ；
Y (t-k- τ) is the measurement output function at t-k- τ moment；
The x obtained for the measurement output function y (t-k- τ -1) based on t-k- τ -1 moment
(t-k- τ) is in the predicted value at t-k- τ moment；
X (the t-k- τ obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment
+ 1) in the predicted value at+1 moment of t-k- τ；
X (the t- obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment
K- τ+i-1) in the predicted value at t-k- τ+i-1 moment；
L is state estimation gain；U (t-k- τ) is the control input function of the controller at t-k- τ moment；u(t-k-τ+i-
It 1) is the control input function of the controller at t-k- τ+i-1 moment；
Feedback channel (that is, channel between sensor to controller) and forward path are (that is, from controller to actuator
Between channel) the upper bound of network time service be respectively nbAnd nf, the data packet continual data package dropout number of feedback channel and forward path
The upper bound be nd；Intermediate variable k=nb+nd, intermediate variable τ=nf+nd。
Specific embodiment four, present embodiment are unlike specific embodiment three, the specific mistake of the step 3
Journey are as follows:
According to the State Forecasting Model for the network control system linear dynamic model that step 2 is established, it is anti-to carry out design point
Present controller；
In formula,The x (t) obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment is in t
The predicted value at quarter, K are state feedback oscillator.
Specific embodiment five, present embodiment are unlike specific embodiment four, the specific mistake of the step 4
Journey are as follows:
Formula (3) are substituted into formula (1), obtain the closed-loop system equation of network control system:
ξ (t+1)=Acξ(t) (4)
In formula, ξ (t) is state variable of the closed-loop system in t moment of network control system, and ξ (t+1) is networking control
State variable of the closed-loop system of system processed at the t+1 moment；ξ (t)=[xT(t) ET(t)]T, xT(t) for state variable x's (t)
Transposition, ET(t) transposition for being error vector E (t), E (t)=[eT(t) eT(t-1)...eT(t-k-τ+1)]T, eTIt (t) is e (t)
Transposition, e (t) be t moment state estimation error, and For based on the t-1 moment
Predicted value of the x (t) that measurement output function y (t-1) obtains in t moment, AcIt is for the closed-loop system of network control system
System matrix；
MatrixWherein, InUnit square is tieed up for n
Battle array, In(k+τ)Unit matrix is tieed up for n (k+ τ),For the tensor product of matrix.
Specific embodiment six, present embodiment obtain shape in the step 5 unlike specific embodiment five
State estimated gain matrix L and state feedback gain matrix K, detailed process are as follows:
Feedback coupling matrix X is obtained by formula (5), (6) and (7)1With estimation coupling matrix X2, and X1And X2It is pair
Claim positive definite matrix；Q1Represent input coupling matrix, Q2Represent output coupling matrix；R is domain matrix；
Intermediate variable matrixAre as follows: Represent matrixConditional number, ForMaximum eigenvalue,ForMinimal eigenvalue, γ
>=1, and γ is normal number, δxFor original state threshold value, ε is SOT state of termination threshold value, 0 < δx< ε, and δxIt is normal number, N with ε
For known positive integer；
State estimation gain matrix L is calculated by formula (8)；
State feedback gain matrix K is calculated by formula (9)；
Specific embodiment seven, the present embodiment is different from the first embodiment in that, Li Ya described in step 5
Pu Nuofu stability theorem are as follows:
V1(x (t+1)) < γ V1(x(t)) (10)
Wherein,
V1(x (t))=xT(t)P1x(t) (11)
In formula, V1(x (t)) is the Liapunov function of t moment, V1(x (t+1)) is the Liapunov letter at t+1 moment
Number, xT(t) transposition for being x (t), P1For Liapunov symmetric positive definite matrix.
Embodiment
It is emulated using the method for the invention:
System parameter:
C=[2 1]
In addition, given N=4,δxThe initial value of=1, ε are 30；
In the following, it is calm when carrying out limited to network control system using the method for the invention, and parameter ε is carried out excellent
Change:
Situation 1: feedback channel and forward path are without induction network time service, feedback channel and the equal no data packet of forward path
It loses, that is, nb=0, nf=0, nd=0；
State estimation gain matrix L and state feedback gain matrix K is solved:
Formula (5), formula (6), formula (7) and formula (9) are solved, obtaining state feedback gain matrix K is such as
Lower form
K=[1.02 1.54]
To no network induce the network control system of bounded time lag and loss of data it is limited when control effect:
Formula (5), formula (6) and formula (7) are solved, the minimum value for obtaining ε is εmin=2.8.
Situation 2: feedback channel and forward path have network to induce bounded time lag, and feedback channel and forward path have number
According to packet loss, that is, the upper bound of the network time service of feedback channel is nb=3, the upper bound of the network time service of forward path is nf=2, instead
The upper bound of the data packet continual data package dropout number in feedthrough road and forward path is nd=1；
State estimation gain matrix L and state feedback gain matrix K is solved:
Formula (5), formula (6), formula (7), formula (8) and formula (9) are solved, state estimation gain square is obtained
Battle array L and state feedback gain matrix K is following form
K=[1.00 1.60]
To the network control system that bounded time lag and loss of data are induced with network it is limited when control effect:
Formula (5), formula (6) and formula (7) are solved, the minimum value for obtaining ε is
For result as it can be seen that when inducing bounded time lag and loss of data with network, use is of the present invention from the above analysis
The minimum value of ε that method obtains isIts minimum obtained when inducing bounded time lag and loss of data less than no network
Value εmin=2.8.So for the network control system with network induction bounded time lag and loss of data, it is of the present invention
Method can effectively Active Compensation network induction bounded time lag and loss of data, network control system it is limited when control effect
Situation of the fruit better than no Internet-Game Addiction and loss of data.In turn, it intuitively, visually illustrates as shown in Figure 2 in the present invention
Under the action of the state feedback controller of the method design, the closed network with network induction bounded time lag and loss of data
The state trajectory x of networked control systems1(t) and x2(t) stable control effect when reaching limited, invented it is limited when calm side
Method can effectively Active Compensation network induction bounded time lag and loss of data.
Claims (7)
1. it is a kind of with network induce bounded time lag and loss of data it is limited when calm method, which is characterized in that this method
Specific steps are as follows:
Step 1: establishing the linear dynamic model with the network control system of network induction bounded time lag and loss of data；
Step 2: the State Forecasting Model of the linear dynamic model of the network control system in establishment step one；
Step 3: the State Forecasting Model for the network control system linear dynamic model established according to step 2, to design shape
State feedback controller；
Step 4: obtaining the closed-loop system equation of network control system according to the state feedback controller that step 3 obtains；
Step 5:, by liapunov's theorem of stability, obtaining state estimation using the closed-loop system of network control system
Gain matrix L and state feedback gain matrix K；
Step 6: the state estimation gain matrix L obtained in step 5 is substituted into the State Forecasting Model in step 2, by state
Feedback gain matrix K substitutes into the state feedback controller in step 3, realizes and induces bounded time lag and data to lose to network
The network control system of mistake it is limited when it is calm.
2. it is according to claim 1 it is a kind of with network induce bounded time lag and loss of data it is limited when calm method,
It is characterized in that, the detailed process of the step 1 are as follows:
The linear dynamic model with the network control system of network induction bounded time lag and loss of data is established, it is described linear
The state space form of dynamic model are as follows:
Wherein: x (t) is the state variable of the linear dynamic model of the network control system of t moment, and x (t+1) is the t+1 moment
Network control system linear dynamic model state variable, u (t) be t moment controller control input function, y
It (t) is the measurement output function of the sensor of t moment, A is sytem matrix, and B is input matrix, and C is output matrix.
3. it is according to claim 2 it is a kind of with network induce bounded time lag and loss of data it is limited when calm method,
It is characterized in that, the detailed process of the step 2 are as follows:
The State Forecasting Model of the linear dynamic model of network control system in establishment step one, the State Forecasting Model
Concrete form are as follows:
In formula,X (the t-k- obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment
τ+i) in the predicted value at t-k- τ+i moment, i=2,3 ..., k+ τ；
Y (t-k- τ) is the measurement output function at t-k- τ moment；
X (the t-k- obtained for the measurement output function y (t-k- τ -1) based on t-k- τ -1 moment
τ) in the predicted value at t-k- τ moment；
Exist for the obtained x (t-k- τ+1) of the measurement output function y (t-k- τ) based on the t-k- τ moment
The predicted value at+1 moment of t-k- τ；
Obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment x (t-k- τ+
I-1) in the predicted value at t-k- τ+i-1 moment；
L is state estimation gain；U (t-k- τ) is the control input function of the controller at t-k- τ moment；U (t-k- τ+i-1) is
The control input function of the controller at t-k- τ+i-1 moment；
The upper bound of the network time service of feedback channel and forward path is respectively nbAnd nf, the data packet of feedback channel and forward path
The upper bound of continual data package dropout number is nd；Intermediate variable k=nb+nd, intermediate variable τ=nf+nd。
4. it is according to claim 3 it is a kind of with network induce bounded time lag and loss of data it is limited when calm method,
It is characterized in that, the detailed process of the step 3 are as follows:
According to the State Forecasting Model for the network control system linear dynamic model that step 2 is established, carry out design point feedback control
Device processed；
In formula,The x (t) obtained for the measurement output function y (t-k- τ) based on the t-k- τ moment is in t moment
Predicted value, K are state feedback oscillator.
5. it is according to claim 4 it is a kind of with network induce bounded time lag and loss of data it is limited when calm method,
It is characterized in that, the detailed process of the step 4 are as follows:
Formula (3) are substituted into formula (1), obtain the closed-loop system equation of network control system:
ξ (t+1)=Acξ(t) (4)
In formula, ξ (t) is state variable of the closed-loop system in t moment of network control system, and ξ (t+1) is control based on network system
State variable of the closed-loop system of system at the t+1 moment；ξ (t)=[xT(t) ET(t)]T, xT(t) turn for state variable x (t)
It sets, ET(t) transposition for being error vector E (t), E (t)=[eT(t) eT(t-1)…eT(t-k-τ+1)]T, eT(t) for e's (t)
Transposition, e (t) they are the state estimation error of t moment, and For the survey based on the t-1 moment
Predicted value of the x (t) that amount output function y (t-1) obtains in t moment, AcFor the system of the closed-loop system of network control system
Matrix；
MatrixWherein, InUnit matrix is tieed up for n,
In(k+τ)Unit matrix is tieed up for n (k+ τ),For the tensor product of matrix.
6. it is according to claim 5 it is a kind of with network induce bounded time lag and loss of data it is limited when calm method,
It is characterized in that, obtaining state estimation gain matrix L and state feedback gain matrix K, detailed process in the step 5 are as follows:
Feedback coupling matrix X is obtained by formula (5), (6) and (7)1With estimation coupling matrix X2, and X1And X2It is symmetric positive definite
Matrix；Q1Represent input coupling matrix, Q2Represent output coupling matrix；R is domain matrix；
Intermediate variable matrixAre as follows: Represent matrixConditional number, ForMaximum eigenvalue,ForMinimal eigenvalue, γ
>=1, and γ is normal number, δxFor original state threshold value, ε is SOT state of termination threshold value, 0 < δx< ε, and δxIt is normal number, N with ε
For known positive integer；
State estimation gain matrix L is calculated by formula (8)；
State feedback gain matrix K is calculated by formula (9)；
7. it is according to claim 1 it is a kind of with network induce bounded time lag and loss of data it is limited when calm method,
It is characterized in that, liapunov's theorem of stability described in step 5 are as follows:
V1(x (t+1)) < γ V1(x(t)) (10)
Wherein,
V1(x (t))=xT(t)P1x(t) (11)
In formula, V1(x (t)) is the Liapunov function of t moment, V1(x (t+1)) is the Liapunov function at t+1 moment,
xT(t) transposition for being x (t), P1For Liapunov symmetric positive definite matrix.
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