CN106200382B - A kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems - Google Patents
A kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems Download PDFInfo
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Abstract
The present invention discloses a kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems, consider that there are sector bounded is non-linear for network control system, random packet loss, model parameter is not known, in the case of controller gain perturbations, initially set up the nonlinear networked control system model of closed loop, reconstruct appropriate Lyapunov function, utilize Lyapunov Theory of Stability and linear matrix inequality analysis method, obtain adequate condition existing for nonlinear network networked control systems meansquare exponential stability and uncatalyzed coking dissipative control device, it is solved using the tool box Matlab LMI, providing uncatalyzed coking dissipative control device gain matrix isThe present invention considers the packet drop between sensor-controller and controller-actuator, and the probability of happening of packet loss meets Bernoulli distribution and is more of practical significance, and is suitable for general dissipative control, including H∞Control reduces the conservative of non-fragile controller design.
Description
Technical field
The present invention relates to network control systems and dissipative control, more particularly to a kind of nonlinear network with packet loss
The uncatalyzed coking dissipative control method of networked control systems.
Background technique
Network control system (networked control systems is abbreviated NCSs) refers to and is closed by what network was formed
Ring feedback control system, this network-based control system have it is convenient for installation and maintenance, flexibility is high and be easy to reconstruct etc. it is excellent
Point.It is had the following problems however, the intervention of network results in system：1) packet loss：In data transmission procedure because network blockage and
The reasons such as resource contention can cause the problem of data-bag lost；2) network delay：Data are in communication network transmission because of network
The reasons such as blocking or external interference, so that there is network delay in network control system；3) system parameter is not true
It is qualitative：In order to carry out effective Control System Design, a complicated system must be described with a relatively simple model,
And to the certain characteristics of system or link lack enough understandings result in the mathematical model used all have it is certain uncertain
Property；4) uncertainty of controller gain：Industrial instrument, control element are influenced by physical characteristic itself and environmental factor,
Leading to controller parameter, there is a certain error or variation, and the small perturbation of controller parameter all may cause closed-loop system
It can decline or even stability is destroyed.In recent years, Passive Shape Control and H∞The hot spot that control becomes many scholar's researchs is asked
Topic.But Passive Shape Control only considered phase information, and H∞Control is only extracted the gain of information, and acquired results have larger
Conservative.And the analysis of the controller based on dissipative map theory has comprehensively considered the gain and phase of system with design problem
Position information, has carried out preferable compromise between gain and phase.Therefore, the dissipativeness of network control system and holding are studied
Preferable anti-interference ability has highly important theory significance and more practical value.
In recent years, numerous scholars expand numerous studies with regard to the dissipation issues of network control system, including linear system,
Discrete system determines system, uncertain system, even generalized ensemble, achieves some research achievements.But it existing grinds
Study carefully achievement and do not account for the influence of physical characteristic and environmental factor to controller gain, there is certain limitation, and controller is joined
The small perturbation of number all may cause Performance of Closed Loop System decline or even stability is destroyed.
Summary of the invention
For above-mentioned problems of the prior art, the present invention provides a kind of the non-of nonlinear network networked control systems
Fragile dissipative control method.Considering network control system, there are random packet loss, sector bounded is not non-linear, model parameter true
In the case of fixed, controller gain perturbations, uncatalyzed coking dissipative control device is devised, so that network control system is in these cases
Still it is able to maintain meansquare exponential stability, and strict dissipativity.
The technical scheme adopted by the invention is that：A kind of uncatalyzed coking dissipative control side of nonlinear network networked control systems
Method includes the following steps：
1) state feedback controller to nonlinear networked Control System Design based on observer, closed loop nonlinear network
Networked control systems are：
Wherein,For state vector,To control input quantity,To measure output quantity,For control
Output quantity processed,For external disturbance,It is the state estimation of nonlinear network networked control systems, system estimation error And rank (B)=m,WithIt is known
Constant matrices；Nonlinear Vector value functionMeet following fan-shaped boundary's condition：
[f(k,xk)-L1xk]T[f(k,xk)-L2xk]≤0
Wherein,It is known real constant matrix；Δ A is Parameter uncertainties part, has following form：
Δ A=H1F1(k)E1,
Wherein, γ1> 0,It is constant matrices,It is unknown real value time-varying matrix；WithIt is the gain matrix of observer and controller respectively,Δ K is the gain perturbation of controller,
With following form：
Δ K=H2F2(k)E2,
Wherein, γ2> 0,It is constant matrices,For additivity time-varying perturbation matrix.
αkIndicate the random packet loss situation occurred in sensor-controller passage, βkIt indicates to occur in controller-execution
Random packet loss situation on device channel, αkAnd βkFor the stochastic variable for meeting the distribution of Bernoulli 0-1 sequence：
2) Lyapunov function is constructed
Wherein,It is positive definite symmetric matrices.
It is as follows that definition can measure supply function E (w, z, T)：
Wherein,For known symmetrical matrix,For known constant matrix.
3) uncatalyzed coking dissipative control device gain matrix K is calculated
Adequate condition existing for system meansquare exponential stability and uncatalyzed coking dissipative control device is：
For following linear MATRIX INEQUALITIES：
Wherein,
Δ31=diag { -0.5 τ1(L1+
L2),-0.5τ2(L1+L2), Δ33=diag {-τ1I,-τ2I }, Π22=diag {-P ,-P ,-I ,-P ,-P ,-I }, Π33=diag
{-ε1I,-ε1I,-ε2I,-ε2I },
Wherein,N=PL, M=P1K,WithIt is orthogonal matrix,It is to angular moment
Battle array, P11, P22, M, N, τ1, τ2, ε1And ε2For known variables, dependent variable is all known.
It is solved using the tool box Matlab LMI, if there is symmetric positive definite matrix P11∈Rm×m, P22∈R(n -m)×(n-m), real matrix M ∈ Rm×n, N ∈ Rn×p, real number τ1>=0, τ2>=0, ε1> 0, ε2> 0, then nonlinear network networked control systems
It is meansquare exponential stability, and strict dissipativity, controller gain matrix areAnd step 4) can be continued；
If above-mentioned known variables do not solve, nonlinear network networked control systems are not meansquare exponential stabilities and cannot obtain non-crisp
Weak dissipative control device gain matrix, it is not possible to carry out step 4)；
4) uncatalyzed coking H is calculated∞Controller gain matrix K
According to γ=Σ (| | zk||)/Σ(||wk| |) find out corresponding system performance index γ, H∞(i.e. each square under control
Battle array parameter is taken as：Q=-I, R=γ2I, S=0) Optimal Disturbance Rejection ratio γoptThe condition of optimization is：
Enable e=γ2If following optimization problem is set up：
P11> 0, P22> 0, τ1>=0, τ2>=0, ε1> 0, ε2> 0
It then can get closed-loop system and meeting uncatalyzed coking H∞Under control condition, the Optimal Disturbance Rejection ratio of system
Uncatalyzed coking dissipative control device gain matrix K is optimised for simultaneously
Compared with prior art, the present invention has following advantageous effects：
1) present invention is directed to nonlinear network networked control systems, while considering the imperfect measurement factor in system and not
Determine factor, including packet loss present in network, external disturbance and due to model simplification or other physical factor brings
Uncertainty establishes the nonlinear networked control system model of closed loop by a series of derivation, conversion, gives the network
The design method of uncatalyzed coking dissipative control device under environment.
2) present invention considers the packet drop between sensor-controller and controller-actuator, the generation of packet loss
Probability meets Bernoulli distribution, is more of practical significance.
3) present invention is suitable for general dissipative control, including H∞Control, reduces the non-fragile controller design method
Conservative.
Detailed description of the invention
Attached drawing 1 is the flow chart of nonlinear network networked control systems uncatalyzed coking dissipative control method.
General uncatalyzed coking strictly dissipative control condition responsive figure when attached drawing 2 is γ=0.9151.
General uncatalyzed coking strictly dissipative control condition responsive figure when attached drawing 3 is γ=0.9944.
General uncatalyzed coking strictly dissipative control condition responsive figure when attached drawing 4 is γ=1.0285.
Attached drawing 5 is γoptUncatalyzed coking H when=4.5245∞State of a control response diagram.
Attached drawing 6 is γoptUncatalyzed coking H when=5.5322∞State of a control response diagram.
Attached drawing 7 is γoptUncatalyzed coking H when=6.8213∞State of a control response diagram.
Specific embodiment
The following further describes the specific embodiments of the present invention with reference to the drawings.
Referring to attached drawing 1, a kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems includes the following steps：
Step 1：Establish nonlinear networked control system model
Wherein,For state vector,To control input quantity,To measure output quantity,For control
Output quantity,For external disturbance,And rank (B)=m,WithFor known constant matrices；Δ A is Parameter uncertainties part, has following form：
Δ A=H1F1(k)E1,
Wherein, γ1> 0,It is constant matrices,It is unknown real value time-varying matrix.
Select αkIt describes to occur the random packet loss situation in sensor-controller passage, works as αkWhen=1, sensor is surveyed
The data measured are received by controller completely；Work as αkWhen=0, the data that sensor measurement obtains all are lost.Stochastic variable αk
For the stochastic variable for meeting the distribution of Bernoulli 0-1 sequence：
To system (1), the state feedback controller based on observer for designing following form is considered
Observer：
Controller:
Wherein,It is the state estimation of nonlinear network networked control systems (1),It is defeated for the control of observer
Enter,It is the control input of not random packet loss,WithIt is the gain square of observer and controller respectively
Battle array.Δ K is the gain perturbation of controller, its form is
Δ K=H2F2(k)E2,
Wherein, γ2> 0,It is constant matrices,For additivity time-varying perturbation matrix.
Select βkIt describes to occur the random packet loss situation in controller-actuator channel, works as βkWhen=1, controller end
There is no loss of data to actuator end；Work as βkWhen=0, the data of controller end to actuator end are all lost.Stochastic variable βkFor
Meet the stochastic variable of Bernoulli 0-1 sequence distribution：
Define system estimation error：
Convolution (1), (2), (3) and (4), obtains the nonlinear networked control system model of closed loop：
Wherein,
It is as follows that definition can measure supply function E (w, z, T)：
Wherein,For known symmetrical matrix,For known constant matrix, matrix Q, R, S meet
Following condition：
Step 2：Construct suitable Lyapunov function
Wherein,It is positive definite symmetric matrices.
As external disturbance wkWhen=0：
Wherein,Ω such as following formula：
Wherein,
According to S-procedure lemma, due to
If there is scalar τ1>=0, τ2>=0 makes
Ω-τ1Ω1-τ2Ω2< 0 (6)
It sets up, then
Wherein,It is known constant matrices.
Step 3：Based on the Lyapunov function that step 2 constructs, not using Lyapunov Theory of Stability and linear matrix
Equation analysis method obtains existing for nonlinear network networked control systems meansquare exponential stability and uncatalyzed coking dissipative control device sufficiently
Condition, steps are as follows：
Step 3.1：The stability for first determining whether nonlinear network networked control systems obtains nonlinear network networked control systems
The adequate condition of meansquare exponential stability.
Assuming that inequality (6) is set up, according to Schur lemma
Wherein,
Γ22=diag {-P-1,-P-1,-P-1,-P-1,
By formula (7)：
Wherein,0 < α < min { λmin(- Ω), σ }, σ:=max { λmax(P),λmax(Q)}。
By formula (7) and (9), have,
α||ηk||2< Vk≤σ||ηk||2
According to Lyapunov Theory of Stability, nonlinear network networked control systems Stochastic stable shown in formula (7) fills
Slitting part is：As external disturbance wkWhen=0, there are positive definite matrix P > 0, nonnegative real number τ1、τ2, so that linear matrix inequality
(7) it sets up.When the adequate condition of step 3.1 is set up, then execute step 3.2；If the adequate condition of step 3.1 is invalid,
Then system is not meansquare exponential stability and uncatalyzed coking dissipative control device is not present, and cannot execute step 3.2.
Step 3.2：To any wk≠ 0, definition
Wherein, ζk=[xk ek wk f(k,xk)Fk]T, Θ such as following formula
Wherein,
Similar to step 2, due to
If there is scalar τ1>=0, τ2>=0 makes
Θ-τ1Θ1-τ2Θ2< 0 (11)
It sets up, then
Wherein,
It sums to k from 0 to T, has under zero initial condition
Assuming that inequality (11) is set up, it is available with lower inequality according to Schur lemma：
Wherein,Σ22=diag {-P-1,-P-1,-I,-P-1,-P-1,-I },
Δ31=diag { -0.5 τ1(L1+
L2),-0.5τ2(L1+L2), Δ33=diag {-τ1I,-τ2I}。
According to Lyapunov Theory of Stability, nonlinear network networked control systems shown in formula (5) are consumed with uncatalyzed coking
Dissipating adequate condition existing for controller is：Work as wkWhen ≠ 0,It sets up.
Formula (12) can be write as the form of formula (13)
Wherein,Μ11=Σ11, Μ22=Σ22,
According to S-procedure lemma, formula (13) can be written as follow form
Wherein,
Assuming that matrixIt is sequency spectrum, i.e. rank (B)=m then has two orthogonal matrixesWithSo that
Wherein,B1=diag { b1,b2,…,bm, bi(i=1,2 ..., m) is the non-zero of B
Singular value.
Since there are matrixesMeetWherein, Then there is nonsingular matrixSo that matrix equality BP1=PB is set up.Pass through relationship BP1
=PB finds out matrix P
That is,
Therefore, have,
On the both sides of formula (14) simultaneously multiplied by diagonal matrix diag { I, I, I, I, I, P-1P-1,I,P-1,P-1,P-1,I,I,I,
I, I, I, I, I), while M=P1K, N=PL, then formula (14) can rewrite (15)
Wherein, Π11=Σ11, Π22=diag {-P ,-P ,-I ,-P ,-P ,-I }, Π33=diag {-ε1I,-ε1I,-ε2I,-
ε2I },
Wherein,Q_1/2Q_1/2=Q_=-Q.It is asked using the tool box Matlab LMI
Solution, there are positive definite matrix P11∈Rm×m, P22∈R(n-m)×(n-m), real matrix M ∈ Rm×n, N ∈ Rn×p, real number τ1>=0, τ2>=0, ε1>
0, ε2> 0 meets MATRIX INEQUALITIES (15), then works as wkWhen ≠ 0,It sets up.So system (5) meansquare exponential stability, and
And strict dissipativity, uncatalyzed coking dissipative control device gain matrixAnd step 4 can be continued；If above-mentioned
Known variables do not solve, then nonlinear network networked control systems are not meansquare exponential stability and strict dissipativity, cannot obtain non-crisp
Weak dissipative control device gain matrix cannot also carry out step 4.
Step 4：Q is worked as in consideration, the dissipative control problem of system when S, R choose different value, wherein H∞Control can be considered as one
As dissipative control a kind of special case.If it is Dissipative control, then using γ=Σ (| | zk||)/Σ(||wk| |) find out pair
The system performance index γ answered；If it is the H of standard∞Control, i.e., each matrix parameter are taken as：Q=-I, R=γ2I, S=
0, using γ=Σ (| | zk||)/Σ(||wk| |) corresponding system performance index γ is found out, provide H∞Control lower Optimal Disturbance suppression
System compares γoptThe condition of optimization is：
Enable e=γ2If following optimization problem is set up：
P11> 0, P22> 0, τ1>=0, τ2>=0, ε1> 0, ε2> 0
It then can get closed-loop system (5) and meeting uncatalyzed coking H∞Under control condition, the Optimal Disturbance Rejection ratio of systemUncatalyzed coking dissipative control device gain matrix K is optimised for simultaneously
Embodiment：
Using a kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems proposed by the present invention, not outer
In the case that boundary disturbs when i.e. w (k)=0, nonlinear closed loop's nonlinear network networked control systems are meansquare exponential stabilities.When depositing
In external disturbance, system be also meansquare exponential stability and strict dissipativity.Concrete methods of realizing is as follows：
Step 1：Controlled device is closed loop nonlinear network networked control systems, and state-space model is formula (5), is given
Its system parameter is
D3=0.5,
E1=[0.1 00 0], H2=1, E2=[0.5 0.5 0.5 0.5].
Assuming that disturbing signal is wk=1/ (1+k2), choose 3 kinds of packet loss situations.Situation 1：Sensor-controller and control
Device-actuator drop probabilities are 0.05；Situation 2：Sensor-controller and controller-actuator drop probabilities are
0.10；Situation 3：Sensor-controller and controller-actuator drop probabilities are 0.15.
Step 2：Different value is chosen, three kinds of different packet loss are provided according to step 1, pass through Matlab for Q, S, R
The tool box LMI solves controller parameter under different packet loss probability scenarios.
It is assumed that Dissipative controls, each matrix parameter is taken as：Q=-I, S=I, R=I, be utilized respectively γ=Σ (| | zk|
|)/Σ(||wk| |) the corresponding system performance index γ of different packet loss probability is found out, it is shown in Table 1.As it can be seen from table 1 with net
The performance indicator γ of the increase of drop probabilities in network channel, system is also increased with it.
It is assumed that H∞Control：Each matrix parameter is taken as：Q=-I, R=γ2I, S=0.It is solved by the tool box Matlab LMI
Parameter and H under different packet loss probability scenarios after controller optimization∞The horizontal γ o of Disturbance Rejectionpt, and utilization γ=Σ (| | zk|
|)/Σ(||wk| |) corresponding system performance index γ is found out, it is shown in Table 2.From table 2 it can be seen that with packet loss in network channel
The performance indicator γ of the increase of probability, system is also increased with it, and illustrates that drop probabilities are to have a major impact to the performance of system.And
And γ < γoptDifferent drop probabilities are set up, show that designed dissipative control device meets H∞Performance indicator.
1 controller parameter of table and Disturbance Rejection performance parameter compare
2 controller parameter of table and Disturbance Rejection performance parameter compare
Step 3：Given original state is x0=[0.2 0.3 0.1 0.06]T, utilize Matlab LMI tool in step 2
Case solve as a result, simulated under different packet loss probability scenarios with Matlab, system closed-loop system under Dissipative control
Condition responsive, as shown in Figures 2 to 4 and system is in H∞Lower closed loop states response is controlled, as shown in Figures 5 to 7.
It can be seen from Fig. 2 to Fig. 4 under the Parameter Perturbation and drop probabilities allowed, the closed loop states of system respond bent
Line is finally intended to zero, and the performance indicator γ bigger (drop probabilities are bigger) of system, and system reaches the stable time and gets over
It is long.The optimal i.e. γ of interference free performance γ it can be seen from Fig. 5 to Fig. 7 when systemoptWhen=4.5245, the system mode of Fig. 5
Response curve convergence rate ratio Fig. 6 and Fig. 7 is fast；When occurring random packet loss in a network it can be seen from Fig. 6 and Fig. 7, even if being
System is external to be disturbed, and mean square stability can still be maintained in system under the action of controller, and system has good resist
Jamming performance.
The above are preferred embodiments of the present invention, is not intended to limit the present invention in any form, all foundations
Technical spirit of the invention any simple modification, equivalent change and modification made to the above embodiment, belong to inventive technique
In the range of scheme.
Claims (1)
1. a kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems, which is characterized in that specifically include following step
Suddenly：
1) state feedback controller to nonlinear networked Control System Design based on observer, the nonlinear networked control of closed loop
System processed is：
Wherein,For state vector,To control input quantity,To measure output quantity,For control output
Amount,For external disturbance,It is the state estimation of nonlinear network networked control systems, system estimation error And rank (B)=m,For known constant square
Battle array；Nonlinear Vector value functionMeet following fan-shaped boundary's condition：
[f(k,xk)-L1xk]T[f(k,xk)-L2xk]≤0
Wherein,It is known real constant matrix；Δ A is Parameter uncertainties part, has following form：
Wherein, γ1> 0,It is constant matrices,It is unknown real value time-varying matrix；WithIt is the gain matrix of observer and controller respectively,Δ K is that the gain of controller is taken the photograph
It is dynamic, there is following form：
Wherein, γ2> 0,It is constant matrices,For additivity time-varying perturbation matrix；
αkIndicate the random packet loss situation occurred in sensor-controller passage, βkIt indicates to occur logical in controller-actuator
Random packet loss situation on road, αkAnd βkFor the stochastic variable for meeting the distribution of Bernoulli 0-1 sequence：
2) Lyapunov function is constructedWherein,It is positive definite symmetric matrices；
It is as follows that definition can measure supply function E (w, z, T)：
Wherein,For known symmetrical matrix,For known constant matrix；
3) uncatalyzed coking dissipative control device gain matrix K is calculated, existing for system meansquare exponential stability and uncatalyzed coking dissipative control device
Adequate condition is：
For following linear MATRIX INEQUALITIES：
Wherein,
Δ31=diag { -0.5 τ1(L1+L2),-
0.5τ2(L1+L2), Δ33=diag {-τ1I,-τ2I }, Π22=diag {-P ,-P ,-I ,-P ,-P ,-I }, Π33=diag {-ε1I,-ε1I,-ε2I,-ε2I },
Wherein,N=PL, M=P1K,WithIt is orthogonal matrix,It is to angular moment
Battle array, P11, P22, M, N, τ1, τ2, ε1And ε2For known variables, dependent variable is all known；Using the tool box Matlab LMI into
Row solves, if there is symmetric positive definite matrix P11∈Rm×m, P22∈R(n-m)×(n-m), real matrix M ∈ Rm×n, N ∈ Rn×p, real number τ1
>=0, τ2>=0, ε1> 0, ε2> 0, then nonlinear network networked control systems are meansquare exponential stabilities, and strict dissipativity, controller increase
Beneficial matrix isAnd step 4) can be continued；If above-mentioned known variables do not solve, non-linear net
Network networked control systems are not meansquare exponential stabilities and cannot obtain uncatalyzed coking dissipative control device gain matrix, it is not possible to be walked
It is rapid 4)；
4) uncatalyzed coking H is calculated∞Controller gain matrix K, according to γ=Σ (| | zk||)/Σ(||wk| |) find out corresponding system
Performance indicator γ, each matrix parameter are taken as：Q=-I, R=γ2I, S=0, H∞Control lower Optimal Disturbance Rejection ratio γoptOptimization
Condition is：
Enable e=γ2If following optimization problem is set up：
P11> 0, P22> 0, τ1>=0, τ2>=0, ε1> 0, ε2> 0
It then can get closed-loop system and meeting uncatalyzed coking H∞Under control condition, the Optimal Disturbance Rejection ratio of systemSimultaneously
Uncatalyzed coking dissipative control device gain matrix K is optimised for
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