CN108427273A - A kind of Feedback Control Design method reducing traffic congestion phenomenon - Google Patents
A kind of Feedback Control Design method reducing traffic congestion phenomenon Download PDFInfo
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Abstract
The invention discloses a kind of Feedback Control Design methods reducing traffic congestion phenomenon.The present invention includes the following steps：Step 1, the state-space model for establishing urban road junction；Step 2, design matrix A (k), B (k)；Step 3, due to crossing number of vehicles x (k) with drive into vehicle u (k) be it is controlled, design road vehicle number and drive into vehicle satisfaction constraints；Step 4, the minimum performance index for the PREDICTIVE CONTROL that designs a model；Step 5, the Model Predictive Control state feedback control law for designing road vehicles information.The present invention passes through the means such as road data acquisition, model foundation, constraint control, performance evaluation, the present invention can alleviate main line vehicle flowrate it is big and caused by congestion problems, ensure that urban road junction vehicle is steady, under the premise of safe operation, there is good control effect.
Description
Technical field：
The invention belongs to technical field of automation, it is proposed that a kind of state reducing city merging road traffic congestion phenomenon
Feedback Control Design method.Optimize the technologies such as analysis, design of control law by Model Predictive Control, constraint control, performance, realizes
Effective control to the crossing automobile quantity that easily gets congestion reduces congestion in road, can be used for Road Transportation industry.
Background technology：
Traffic congestion has become worldwide problem and is concerned, and many countries are all to some extent by this problem
Puzzlement.Traffic congestion can cause traffic delay to increase, and running speed reduces, and even result in urban transportation paralysis.In the congestion phase
Between, vehicle fuel consumption and exhaust emissions amount can be increased, aggravate energy shortage crisis and environmental degradation.Usually, there are two do
Method can alleviate traffic congestion phenomenon：First, the quantity of restricting vehicle and going out line frequency；Second is that improving road infrastructure, improve
The traffic capacity.But all there is the limitation of oneself factor in both methods, cannot effectively solve congestion problems.Odd-and-even license plate rule,
The work efficiency that limitation resident's private car trip will certainly reduce is increased, the quality of life and level of the people are reduced.For one
For city, conservation of natural environment is considered, production and living infrastructure land used, the path space for construction is also very limited
's.Therefore, rational vehicle scheduling operating mechanism is selected, the most important thing that road congestion is only urban construction and development is reduced.
The main reason for leading to urban traffic blocking is that automobile utilization rate increases.It is gone on a journey and is facilitated due to automobile, lead to city
Urban district vehicle flowrate increasingly increases, and whenever rush hour, working, tourism, shopping vehicle pours into urban district from eight hair of four sides.Vapour
The disadvantage of vehicle is exactly to occupy path space, and road capacity is insufficient in addition, design is improper, intersection is excessive, and urban district is caused to hand over
Logical congestion phenomenon is frequent occurrence.
With the introducing of intelligent transportation system, that is, advanced electronic information is used, communicates, automatically control, computer network
Etc. technologies distribute time of traffic lights so that urban road congestion problem is obtained by reasonably controlling, dispatch buses
It is obviously improved, but there are still most main lines and major trunk roads, and traffic jam issue occurs in festivals or holidays or morning and evening peak period.With
Automobile quantity and people go out the increase of line frequency, and this congestion phenomenon is bound to become increasingly severe.Based on positive system model
Predict-feedback control design method, it can be achieved that city road crossing vehicle parameter closed-loop control.
Invention content：
The purpose of the present invention is the intelligent transportation systems in being built for current smart city, provide a kind of reduction traffic and gather around
The Feedback Control Design method of stifled phenomenon.
The step of the method for the present invention includes：
Step 1, the state-space model for establishing urban road junction, specific method are：
Certain vehicle data for easily causing congestion phenomenon crossing is acquired first, and the shape of road trolley quantity is established using the data
State space model, form are as follows：
X (k+1)=A (k) x (k)+B (k) u (k),
Wherein, x (k)=[x1(k),x2(k),...,xn(k)]TIndicate by path sensor the k moment it is collected certain
One road trolley quantity, n indicate considered road way, u (k) ∈ RrThe vehicle that is driven into toward this crossing for the k moment or defeated
Enter vehicle, r is the crossing number considered, RrReal number column vector is tieed up for r, A (k), B (k) indicate that k moment sensors collect composition
Appropriate dimension constant matrices.Consider road traffic automobile quantity orthotropicity, i.e. x (k), u (k) be always it is non-negative, this
In assume that constructed road traffic control system is a kind of positive system model, i.e., collected number of vehicles is all non-negative always
, consider A (k), all elements all have nonnegativity (referred to as in B (k) matrixes),It is to be directed to square
Battle array interior element is more than for being less than.
Step 2, design matrix A (k), B (k), concrete methods of realizing are：
Due to factors such as road is complicated and changeable, sensor ageing and statistical errors, sensor is united to road vehicle quantity
In meter, it inevitably will appear statistic bias or the acquisition of different acquisition point obtain one group with a road section and differs the uncertainties such as data,
Detailed k moment A (k) are obtained, B (k) time-varying matrixes are A (k) that is very difficult, designing here, and B (k) matrixes have not really
Qualitative, including section, more cell spaces both uncertain factors, this design method is also more suitable for complicated intersection and builds
Mould meets following condition respectively：
2.1, bounded-but-unknown uncertainty can indicate Ω1：
Wherein, A1,A2Indicate the bound matrix of A (k), B1,B2The bound matrix for indicating B (k), between matrixRepresenting matrix corresponding element magnitude relationship.Due to the nonnegativity of sensor collection vehicle information, it is evident that
2.2, more cell space uncertainties can indicate Ω2：
Wherein, p=1,2 ..., J, J are the number that positive integer indicates vertex matrix, [Ap|Bp] represent matrix A, the pth of B
A vertex matrix.0≤γp≤ 1 is known constant, and value can change with the difference of p, can be according to sensor actual acquisition feelings
Condition provides, and meetsDue to the nonnegativity of sensor collection vehicle information, it is evident that
Step 3, in actual life, a certain right-angled intersection vehicle flowrate is limited with vehicle is driven into, thus design
Crossing number of vehicles x (k) is controlled with vehicle u (k) is driven into, and specific method is：
A certain road vehicle number constraint satisfaction：
Wherein,Γ∈Rn×nWithδ∈RnKnown given matrix and vector are indicated respectively, this tittle can root
According to real road can bearing capacity empirically give.Rn×nIndicate that n × n ties up real number matrix, RnIndicate that n ties up real number column vector, (It is also for the element size of vector, between vectorIndicate big existing for two vectorial corresponding elements
Small relationship).
It drives into vehicle and also referred to as controls input constraint satisfaction：
Here, l1,l2It indicates to give n dimension real number column vectors and l1Each element is less than zero, l in row2Each element is big in row
In zero.θ is also that each element is more than zero during given r ties up real number column vector and arranges.These given amounts in practice can be according to road
The bearing capacity that mouth drives into vehicle is given.F1,F2Real number matrix, F are tieed up for r × n1Each element is less than zero, F in matrix2In matrix
Each element is more than zero, F1,F2Meet for the model predictive controller gain matrix to be designed：
U (k+i | k)=(F1+F2) x (k+i | k), i=0,1 ..., N ..., ∞,
Wherein x (k+i | k) indicate that the k moment predicts the crossing number of vehicles situation at the following k+i moment, u (k+i | k) it indicates
The k moment drives into number of vehicles prediction to the following k+i moment, and N is that natural number indicates prediction step number.
Step 4, the minimum performance index for the PREDICTIVE CONTROL that designs a model, specific implementation step are：
Here performance index function：
WhereinIt indicates at the k moment to the following k+i moment control law u's (k+i | k)
Two components.ρ1,ρ2It indicates to give r dimension real number column vectors and ρ1Each element is less than zero, ρ in row2Each element is more than in row
Zero, the two given vectors can have solution analysis given according to follow-up optimization problem.It is every in indicating n dimension real number column vectors and arranging
A element is both greater than zero.A (k+i), B (k+i) indicate the sensor measurement matrix predicted at the k+i moment.
Step 5, the Model Predictive Control state feedback control law for designing road vehicles information, comprise the concrete steps that：
5.1, u (k+i | k)=(F is designed1+F2) x (k+i | k), and meet step 4 minimum performance index.Design one simultaneously
Linear remaining positive type Lyapunov functions shaped like：
V (x (k+i | k))=x (k+i | k)Tv,
Here, each element is more than zero during v indicates n dimension real number column vectors and arranges.To ensure the stability of system, calculating can
Its difference equation is obtained to meet：
Wherein,ρ1,ρ2It is defined within step 4.
5.2, for step 2.1 measurement, there are sections not to know, and following optimization problem is made to have solution：
x(k|k)Tv≤γ,
Wherein, 1r=[1 ..., 1]T∈Rr,1n=[1 ..., 1]T∈Rn, zIt is tieed up for n
Each element is both less than zero in real number column vector and row,Real vector is tieed up for n, μ is each member during r ties up real number column vector and arranges
Element both greater than zero,z (ε)Real vector is tieed up for n,Tie up real number column vector for n and in arranging each element be both greater than zero, ε ∈ 1,
2 ..., r }, T representing matrixes or vectorial transposition, x (k | k) indicate that the k moment predicts crossing vehicle-state when step number is zero.
γ ＞ 0, ρ ＞ 0 is constant to be asked.A1,A2,B1,B2It is defined within step 2.1, Γ, δ, l1,l2, θ be defined within constraints step
Rapid 3, ρ1,ρ2,Consistent with definition in step 4, v is defined within step 5.1.
5.3, for step 2.2 measurement, there are more cell spaces not to know, and following optimization problem is made to have solution：
x(k|k)Tv≤γ,
Wherein, Ap,BpIt is defined within step 2.2, other definition are consistent with the definition of step 5.2.
5.4, the difference inequalitie equation according to Lyapunov functions and calculating designed by step 5.1.If step 5.2 and
Optimization problem in step 5.3 has a solution, and it is stable to measure uncertain, more cell space closed-loop systems comprising section, can obtain it is following not
Equilibrium relationships：
Wherein, be related to parameter with it is defined above consistent.All it is non-negative state always according to the prediction of k+i moment vehiclesWithIt can be further converted to：
With
Wherein, 0≤γp≤1.
It can further obtain：
5.5, the condition according to optimization problem designed by step 5.2, can obtain following result：
It can further obtain：
5.6, consider number of vehicles state and input constraint condition in step 3, combine step 5.2 and step 5.3 again
In optimization problem in condition, following inequality relation can be obtained：
γ≥x(k)Tv≥ρx(k)T1n,
It may further obtain：
Wherein, ξ1For-l1Minimum component, ξ2Indicate l2Minimum component, ξ3Indicate the largest component of θ.||*||1It indicates
Matrix or vectorial 1 norm of standard, i.e., rectangular array and maximum absolute value value or vector element absolute value and.
5.7, consider that step 4 obtains minimum performance index, i.e. following formula is set up：
According to the inequality x (k | k) in step 5.2 and step 5.3TFollowing relationship establishment can be obtained in v≤γ：
V(x(k|k))≤γ.
It can further obtain：
5.8 combining step 5.4-5.7, can obtain：When sensor measurement is not known there are section or more cell spaces, urban road
There are identical forms, i.e. F=F for the model prediction STATE FEEDBACK CONTROL gain of trolley quantity1+F2, shaped like：
Beneficial effects of the present invention are as follows：
Method of the present invention is directed to urban road vehicle congestion problems, establishes the state-space model of vehicle parameter, constructs
One linear Lyapunov function, devises model prediction state feedback controller, effectively controls the number of congestion crossing vehicle
Amount, reduces congestion phenomenon.
Using a certain easy trolley quantity that congestion phenomenon section occurs as practical object, the vehicle parameter to drive into the section is
Input, to establish the dynamic model of vehicle fleet size.
The method of the present invention is based on positive system model prediction closed loop states Design of Feedback Controller, reduces traffic congestion phenomenon.
The method that the present invention uses Model Predictive Control implements urban highway traffic congestion phenomenon the closed loop control of vehicle flowrate
System.By to the means such as the data acquisition of road vehicle, model foundation, state and input constraint control, performance evaluation, establishing
A kind of model prediction state feedback controller design method reducing traffic congestion phenomenon, can alleviate terrain vehicle using this method
Flow it is big and caused by congestion problems, ensure that urban road junction vehicle is steady, under the premise of safe operation, have good
Control effect.
Specific implementation mode
Step 1, the state-space model for establishing urban road junction, specific method are：
Certain vehicle data for easily causing congestion phenomenon crossing is acquired first, and the shape of road trolley quantity is established using the data
State space model, form are as follows：
X (k+1)=A (k) x (k)+B (k) u (k),
Wherein, x (k)=[x1(k),x2(k),...,xn(k)]TIndicate by path sensor the k moment it is collected certain
One road trolley quantity, n indicate considered road way, u (k) ∈ RrThe vehicle that is driven into toward this crossing for the k moment or defeated
Enter vehicle, r is the crossing number considered, RrReal number column vector is tieed up for r, A (k), B (k) indicate that k moment sensors collect composition
Appropriate dimension constant matrices.Consider road traffic automobile quantity orthotropicity, i.e. x (k), u (k) be always it is non-negative, this
In assume that constructed road traffic control system is a kind of positive system model, i.e., collected number of vehicles is all non-negative always
, consider A (k), all elements all have nonnegativity (referred to as in B (k) matrixes),It is to be directed to
Matrix interior element is more than for being less than.
Step 2, design matrix A (k), B (k), concrete methods of realizing are：
Due to factors such as road is complicated and changeable, sensor ageing and statistical errors, sensor is united to road vehicle quantity
In meter, it inevitably will appear statistic bias or the acquisition of different acquisition point obtain one group with a road section and differs the uncertainties such as data,
Detailed k moment A (k) are obtained, B (k) time-varying matrixes are A (k) that is very difficult, designing here, and B (k) matrixes have not really
Qualitative, including section, more cell spaces both uncertain factors, this design method is also more suitable for complicated intersection and builds
Mould meets following condition respectively：
2.1, bounded-but-unknown uncertainty can indicate Ω1：
Wherein, A1,A2Indicate the bound matrix of A (k), B1,B2The bound matrix for indicating B (k), between matrixRepresenting matrix corresponding element magnitude relationship.Due to the nonnegativity of sensor collection vehicle information, it is evident that
2.2, more cell space uncertainties can indicate Ω2：
Wherein, p=1,2 ..., J, J are the number that positive integer indicates vertex matrix, [Ap|Bp] represent matrix A, the pth of B
A vertex matrix.0≤γp≤ 1 is known constant, and value can change with the difference of p, can be according to sensor actual acquisition feelings
Condition provides, and meetsDue to the nonnegativity of sensor collection vehicle information, it is evident that
Step 3, in actual life, a certain right-angled intersection vehicle flowrate is limited with vehicle is driven into, thus design
Crossing number of vehicles x (k) is controlled with vehicle u (k) is driven into, and specific method is：
A certain road vehicle number constraint satisfaction：
Wherein,Γ∈Rn×nWithδ∈RnKnown given matrix and vector are indicated respectively, this tittle can root
According to real road can bearing capacity empirically give.Rn×nIndicate that n × n ties up real number matrix, RnIndicate that n ties up real number column vector, (It is also for the element size of vector, between vectorIndicate big existing for two vectorial corresponding elements
Small relationship).
It drives into vehicle and also referred to as controls input constraint satisfaction：
Here, l1,l2It indicates to give n dimension real number column vectors and l1Each element is less than zero, l in row2Each element is big in row
In zero.θ is also that each element is more than zero during given r ties up real number column vector and arranges.These given amounts in practice can be according to road
The bearing capacity that mouth drives into vehicle is given.F1,F2Real number matrix, F are tieed up for r × n1Each element is less than zero, F in matrix2In matrix
Each element is more than zero, F1,F2Meet for the model predictive controller gain matrix to be designed：
U (k+i | k)=(F1+F2) x (k+i | k), i=0,1 ..., N ..., ∞,
Wherein x (k+i | k) indicate that the k moment predicts the crossing number of vehicles situation at the following k+i moment, u (k+i | k) it indicates
The k moment drives into number of vehicles prediction to the following k+i moment, and N is that natural number indicates prediction step number.
Step 4, the minimum performance index for the PREDICTIVE CONTROL that designs a model, specific implementation step are：
Here performance index function：
WhereinIt indicates at the k moment to the following k+i moment control law u's (k+i | k)
Two components.ρ1,ρ2It indicates to give r dimension real number column vectors and ρ1Each element is less than zero, ρ in row2Each element is more than in row
Zero, the two given vectors can have solution analysis given according to follow-up optimization problem.It is every in indicating n dimension real number column vectors and arranging
A element is both greater than zero.A (k+i), B (k+i) indicate the sensor measurement matrix predicted at the k+i moment.
Step 5, the Model Predictive Control state feedback control law for designing road vehicles information, comprise the concrete steps that：
5.1, u (k+i | k)=(F is designed1+F2) x (k+i | k), and meet step 4 minimum performance index.Design one simultaneously
Linear remaining positive type Lyapunov functions shaped like：
V (x (k+i | k))=x (k+i | k)Tv,
Here, each element is more than zero during v indicates n dimension real number column vectors and arranges.To ensure the stability of system, calculating can
Its difference equation is obtained to meet：
Wherein,ρ1,ρ2It is defined within step 4.
5.2, for step 2.1 measurement, there are sections not to know, and following optimization problem is made to have solution：
x(k|k)Tv≤γ,
Wherein, 1r=[1 ..., 1]T∈Rr,1n=[1 ..., 1]T∈Rn, zIt is tieed up for n
Each element is both less than zero in real number column vector and row,Real vector is tieed up for n, μ is each member during r ties up real number column vector and arranges
Element both greater than zero,z (ε)Real vector is tieed up for n,Tie up real number column vector for n and in arranging each element be both greater than zero, ε ∈ 1,
2 ..., r }, T representing matrixes or vectorial transposition, x (k | k) indicate that the k moment predicts crossing vehicle-state when step number is zero.γ ＞ 0, ρ ＞ 0 is constant to be asked.A1,A2,B1,B2It is defined within step 2.1, Γ, δ, l1,l2, θ is defined within constraint item
Part step 3, ρ1,ρ2,Consistent with definition in step 4, v is defined within step 5.1.
5.3, for step 2.2 measurement, there are more cell spaces not to know, and following optimization problem is made to have solution：
x(k|k)Tv≤γ,
Wherein, Ap,BpIt is defined within step 2.2, other definition are consistent with the definition of step 5.2.
5.4, the difference inequalitie equation according to Lyapunov functions and calculating designed by step 5.1.If step 5.2 and
Optimization problem in step 5.3 has a solution, and it is stable to measure uncertain, more cell space closed-loop systems comprising section, can obtain it is following not
Equilibrium relationships：
Wherein, be related to parameter with it is defined above consistent.All it is non-negative state always according to the prediction of k+i moment vehiclesWithIt can be further converted to：
With
Wherein, 0≤γp≤1.
It can further obtain：
5.5, the condition according to optimization problem designed by step 5.2, can obtain following result：
It can further obtain：
5.6, consider number of vehicles state and input constraint condition in step 3, combine step 5.2 and step 5.3 again
In optimization problem in condition, following inequality relation can be obtained：
γ≥x(k)Tv≥ρx(k)T1n,
It may further obtain：
Wherein, ξ1For-l1Minimum component, ξ2Indicate l2Minimum component, ξ3Indicate the largest component of θ.||*||1It indicates
Matrix or vectorial 1 norm of standard, i.e., rectangular array and maximum absolute value value or vector element absolute value and.
5.7, consider that step 4 obtains minimum performance index, i.e. following formula is set up：
According to the inequality x (k | k) in step 5.2 and step 5.3TFollowing relationship establishment can be obtained in v≤γ：
V(x(k|k))≤γ.
It can further obtain：
5.8 combining step 5.4-5.7, can obtain：When sensor measurement is not known there are section or more cell spaces, urban road
There are identical forms, i.e. F=F for the model prediction STATE FEEDBACK CONTROL gain of trolley quantity1+F2, shaped like：
Claims (6)
1. a kind of Feedback Control Design method reducing traffic congestion phenomenon, it is characterised in that include the following steps：
Step 1, the state-space model for establishing urban road junction；
Step 2, design matrix A (k), B (k)；
Step 3, due to crossing number of vehicles x (k) with drive into vehicle u (k) be it is controlled, design road vehicle number and
Drive into the constraints of vehicle satisfaction；
Step 4, the minimum performance index for the PREDICTIVE CONTROL that designs a model；
Step 5, the Model Predictive Control state feedback control law for designing road vehicles information.
2. a kind of Feedback Control Design method reducing traffic congestion phenomenon according to claim 1, it is characterised in that step
The state-space model for establishing urban road junction described in rapid 1, specific method are：
Certain vehicle data for easily causing congestion phenomenon crossing is acquired first, and the state that road trolley quantity is established using the data is empty
Between model, form is as follows：
X (k+1)=A (k) x (k)+B (k) u (k),
Wherein, x (k)=[x1(k),x2(k),...,xn(k)]TIt indicates through path sensor collected certain one at the k moment
Road trolley quantity, n indicate considered road way, u (k) ∈ RrThe vehicle or input vehicle driven into toward this crossing for the k moment
, r is the crossing number considered, RrReal number column vector is tieed up for r, A (k), B (k) indicate that k moment sensors collect the suitable of composition
When the constant matrices of dimension；Consider the orthotropicity of road traffic automobile quantity, i.e. x (k), u (k) are non-negative always, it is assumed that institute
The road traffic control system of structure is a kind of positive system model, i.e., collected number of vehicles is all non-negative always, considers A
(k), all elements all have nonnegativity in B (k) matrixes, referred to as It is to be directed to matrix interior element
More than less than for.
3. a kind of Feedback Control Design method reducing traffic congestion phenomenon according to claim 2, it is characterised in that step
Design matrix A (k) described in rapid 2, B (k), concrete methods of realizing are：
The A (k) of design, B (k) matrix have uncertainty, comprising section, more cell spaces both uncertain factors, distinguish
Meet following condition：
2.1, bounded-but-unknown uncertainty can indicate Ω1：
Wherein, A1,A2Indicate the bound matrix of A (k), B1,B2The bound matrix for indicating B (k), between matrixTable
Show matrix corresponding element magnitude relationship；Due to the nonnegativity of sensor collection vehicle information, it is evident that
2.2, more cell space uncertainties can indicate Ω2：
Wherein, p=1,2 ..., J, J are the number that positive integer indicates vertex matrix, [Ap|Bp] represent matrix A, p-th of top of B
Dot matrix；0≤γp≤ 1 is known constant, and value can change with the difference of p, can be given according to sensor actual acquisition situation
Go out, meetsDue to the nonnegativity of sensor collection vehicle information, it is evident that
4. a kind of Feedback Control Design method reducing traffic congestion phenomenon according to claim 3, it is characterised in that step
Rapid 3 are implemented as follows：
A certain road vehicle number constraint satisfaction：
Wherein,Γ∈Rn×nWithδ∈RnKnown given matrix and vector are indicated respectively, this tittle can be according to reality
Border road can bearing capacity empirically give；Rn×nIndicate that n × n ties up real number matrix, RnIndicate that n ties up real number column vector,It is also for the element size of vector, between vectorIndicate big existing for two vectorial corresponding elements
Small relationship；
It drives into vehicle and also referred to as controls input constraint satisfaction：
Here, l1,l2It indicates to give n dimension real number column vectors and l1Each element is less than zero, l in row2Each element is more than zero in row；
θ is also that each element is more than zero during given r ties up real number column vector and arranges；These given amounts can be driven into practice according to crossing
The bearing capacity of vehicle is given；F1,F2Real number matrix, F are tieed up for r × n1Each element is less than zero, F in matrix2Each member in matrix
Element is more than zero, F1,F2Meet for the model predictive controller gain matrix to be designed：
U (k+i | k)=(F1+F2) x (k+i | k), i=0,1 ..., N ..., ∞,
Wherein x (k+i | k) indicates crossing number of vehicles situation prediction of the k moment to the following k+i moment, when u (k+i | k) indicates k
It carves and number of vehicles prediction is driven into the following k+i moment, N is that natural number indicates prediction step number.
5. a kind of Feedback Control Design method reducing traffic congestion phenomenon according to claim 4, it is characterised in that step
The minimum performance index of the PREDICTIVE CONTROL that designs a model described in rapid 4, specific implementation step are：
Here performance index function：
WhereinIndicate two at the k moment to the following k+i moment control law u (k+i | k)
Component；ρ1,ρ2It indicates to give r dimension real number column vectors and ρ1Each element is less than zero, ρ in row2Each element is more than zero in row, this
Two given vectors can have solution analysis given according to follow-up optimization problem；Each element in indicating n dimension real number column vectors and arranging
Both greater than zero；A (k+i), B (k+i) indicate the sensor measurement matrix predicted at the k+i moment.
6. a kind of Feedback Control Design method reducing traffic congestion phenomenon according to claim 5, it is characterised in that step
The Model Predictive Control state feedback control law of design road vehicles information described in rapid 5, comprises the concrete steps that：
5.1, u (k+i | k)=(F is designed1+F2) x (k+i | k), and meet step 4 minimum performance index；Design simultaneously one is linear
Remaining positive type Lyapunov functions shaped like：
V (x (k+i | k))=x (k+i | k)Tv,
Here, each element is more than zero during v indicates n dimension real number column vectors and arranges；To ensure the stability of system, it can be calculated
Difference equation meets：
Wherein,ρ1,ρ2It is defined within step 4；
5.2, for step 2.1 measurement, there are sections not to know, and following optimization problem is made to have solution：
x(k|k)Tv≤γ,
Wherein, 1r=[1 ..., 1]T∈Rr,1n=[1 ..., 1]T∈Rn,Z is that n ties up real number
Each element is both less than zero in column vector and row,Real vector is tieed up for n, μ is each element during r ties up real number column vector and arranges
More than zero,z (ε)Real vector is tieed up for n,Tie up real number column vector for n and in arranging each element be both greater than zero, ε ∈ 1,2 ...,
R }, T representing matrixes or vectorial transposition, x (k | k) indicate that the k moment predicts crossing vehicle-state when step number is zero；
γ ＞ 0, ρ ＞ 0 is constant to be asked；A1,A2,B1,B2It is defined within step 2.1, Γ, δ, l1,l2, θ is defined within about
Beam condition step 3, ρ1,ρ2,Consistent with definition in step 4, v is defined within step 5.1；
5.3, for step 2.2 measurement, there are more cell spaces not to know, and following optimization problem is made to have solution：
x(k|k)Tv≤γ,
Wherein, Ap,BpIt is defined within step 2.2, other definition are consistent with the definition of step 5.2；
5.4, the difference inequalitie equation according to Lyapunov functions and calculating designed by step 5.1；If step 5.2 and step
Optimization problem in 5.3 has solution, and it is stable to measure uncertain, more cell space closed-loop systems comprising section, can obtain following inequality
Relationship：
Wherein, be related to parameter with it is defined above consistent；All it is non-negative state always according to the prediction of k+i moment vehiclesWithIt can be further converted to：
With
Wherein, 0≤γp≤1.
It can further obtain：
5.5, the condition according to optimization problem designed by step 5.2, can obtain following result：
It can further obtain：
5.6, consider number of vehicles state and input constraint condition in step 3, combine in step 5.2 and step 5.3 again
Condition in optimization problem can obtain following inequality relation：
γ≥x(k)Tv≥ρx(k)T1n,
It may further obtain：
Wherein, ξ1For-l1Minimum component, ξ2Indicate l2Minimum component, ξ3Indicate the largest component of θ；||*||1Representing matrix
Or vectorial 1 norm of standard, i.e., rectangular array and maximum absolute value value or vector element absolute value and；
5.7, consider that step 4 obtains minimum performance index, i.e. following formula is set up：
According to the inequality x (k | k) in step 5.2 and step 5.3TFollowing relationship establishment can be obtained in v≤γ：
V(x(k|k))≤γ.
It can further obtain：
5.8 combining step 5.4-5.7, can obtain：When sensor measurement is not known there are section or more cell spaces, urban road trolley
There are identical forms, i.e. F=F for the model prediction STATE FEEDBACK CONTROL gain of quantity1+F2, shaped like：
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