CN113823085A - Traffic flow estimation method of comprehensive management system of public parking lot - Google Patents

Traffic flow estimation method of comprehensive management system of public parking lot Download PDF

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CN113823085A
CN113823085A CN202110989520.XA CN202110989520A CN113823085A CN 113823085 A CN113823085 A CN 113823085A CN 202110989520 A CN202110989520 A CN 202110989520A CN 113823085 A CN113823085 A CN 113823085A
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parking lot
management system
filter
time
comprehensive management
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CN113823085B (en
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李临敏
张俊锋
张石涛
孙振洋
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Hangzhou Dianzi University
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/065—Traffic control systems for road vehicles by counting the vehicles in a section of the road or in a parking area, i.e. comparing incoming count with outgoing count
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/14—Traffic control systems for road vehicles indicating individual free spaces in parking areas
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
    • H03H17/00—Networks using digital techniques
    • H03H17/02—Frequency selective networks

Abstract

The invention discloses a traffic flow estimation method of a public parking lot comprehensive management system. The invention comprises the following steps: step 1, establishing a state space model of a parking lot comprehensive management system with state saturation; step 2, constructing an event triggering condition of vehicle congestion at an entrance and an exit of the parking lot; and 3, designing an event trigger asynchronous filter of the comprehensive management system of the public parking lot. The invention models a public parking lot comprehensive management system based on a positive switching system with state saturation, and designs an asynchronous filter based on an event trigger strategy, wherein the asynchronous filter is used for traffic flow estimation of each large public parking lot. The method can accurately estimate the traffic flow of the entrance and the exit of each parking lot in real time, help parking users to select vehicle parking places more conveniently, effectively solve the problem of entrance and exit congestion of the parking lot caused by the capacity limitation of the parking lot and the road traffic condition, and improve the utilization rate of the parking space of the parking lot.

Description

Traffic flow estimation method of comprehensive management system of public parking lot
Technical Field
The invention belongs to the field of automation technology and modern control, and particularly relates to an event trigger filtering method of a direct switching system based on state saturation, which can be applied to a management system of a public parking lot.
Background
Along with the rapid increase of population density and the number of private cars in China, the process of urban road traffic motorization is accelerated, and the accompanying parking problem is increasingly serious. Many large public parking lots have tense berths, no effective parking prompt information exists, guidance and control of a parking management mode are lacked, parking users face severe road traffic conditions, parking space searching in nearby parking lots has long turnover time, and entrances and exits are often in a blocked state in peak hours. The sharing of parking space information among all parking lots in a city is not smooth, the partial parking lots are in full use, and the partial parking lots still have a large number of vacant parking spaces, so that the resource waste of the parking lots is large, the utilization rate of the parking spaces is not high, and therefore, the estimation of the traffic flow at the entrance and the exit of the parking lots becomes an important factor influencing the operation efficiency of the management system. The traditional parking lot management system mode cannot adapt to the traffic transportation condition of a future city and the fast and efficient parking requirement, the parking problem cannot be solved by increasing the scale or the quantity of the parking lot, but the leading-edge technology of more intelligent transportation fields and automation control fields needs to be introduced urgently, the parking lot automation management system is further perfected, the parking planning management is optimized, a parking user can know the use condition of the parking places of the public parking lot more timely and conveniently in a nearby range, the extra traffic flow brought by queuing and roundabout driving during parking is reduced, and therefore the use efficiency of the existing parking lot is improved. The invention mainly aims at a public parking lot management system in a city to dynamically acquire data information of remaining parking spaces of each parking lot, and provides a design method of a filter based on an automation technology, which is used for dynamically estimating the traffic flow of an entrance and an exit of each parking lot, reasonably arranging vehicles to select the parking lots and avoiding the occurrence of a parking lot jam phenomenon in a peak period.
Because the traffic flow of the parking lot entrance and exit is always a non-negative value, the positive system modeled by the positive variable can accurately depict the traffic flow of the parking lot. Furthermore, a one-class switching system is modeled based on the management systems of the parking lots, data information of the parking lots can be collected simultaneously, traffic flow information of each parking lot can be matched with parking space information by utilizing the data, and a driver can select parking places more conveniently and reasonably. FIG. 1 is a schematic diagram of a parking lot doorway management system; fig. 2 is a system block diagram of a switching system with state saturation and an event triggered asynchronous filter. Generally, the remaining number of vehicles in the existing parking lot is detected by a sensing device according to a system at an entrance and exit, and then displayed on a display screen. Because large-scale public parking area layout structure is complicated, the driver can't master the quantity of the vehicle that will drive away from in the parking area, when the parking stall is not enough, probably causes the phenomenon that many cars berth and wait, has not only reduced parking efficiency, has more aggravated the condition of blocking up in parking area. At the moment, the problem of congestion caused by the fact that the traffic flow near the entrance and the exit of the parking lot is saturated can be effectively solved by designing the event triggering conditions. The event triggering strategy can effectively reduce the resource consumption of the system by designing the event triggering conditions, and the filter based on the event triggering strategy can estimate the traffic flow in real time, so that the vehicle can be helped to master the predicted use condition of the parking spaces of each parking lot, a driver can conveniently and reasonably select the parking place, and the phenomenon of vehicle congestion caused by the fact that the vehicle queues up near the parking lot is avoided. Therefore, the method aims to adopt a tangent switching system with state saturation to model a parking lot comprehensive management system, design an asynchronous filter based on an event trigger mechanism, estimate the traffic flow of each parking lot in real time and improve the utilization rate of the berths of each parking lot.
Disclosure of Invention
In order to solve the defects of the prior art, realize the modeling of a public parking lot management system by using a positive switching system with state saturation and design an asynchronous filter based on an event triggering strategy, the invention adopts the following technical scheme:
a traffic flow estimation method of a comprehensive management system of a public parking lot comprises the following steps:
step 1, establishing a state space model of a parking lot comprehensive management system with state saturation;
step 2, constructing an event triggering condition of vehicle congestion at an entrance and an exit of the parking lot;
step 3, designing an event trigger asynchronous filter of the comprehensive management system of the public parking lot;
further, in the step 1, firstly, data acquisition is performed on traffic flow at an entrance and an exit of the parking lot, and a state space model of the parking lot integrated management system is established by using the acquired data, wherein the form is as follows:
x(k+1)＝sat(Aσ(k)x(k))+Bσ(k)ω(k)，(1)
y(k)＝Cσ(k)x(k)+Dσ(k)ω(k)，
z(k)＝Eσ(k)x(k)+Fσ(k)ω(k)，
wherein the content of the first and second substances,
Figure BDA0003232011810000031
representing the number of remaining parking lots in the parking lot at the kth sampling time, n representing the number of parking lots,
Figure BDA0003232011810000032
m represents the number of berths in the parking lot for the number of vehicles driving into the parking lot,
Figure BDA0003232011810000033
represents the estimate of y (k) at time k, i.e., the number of vehicles expected to enter the parking lot, s represents the number of exits and entrances of the parking lot, ω (k) is the external disturbance affecting the traffic flow at the exits and entrances of the parking lot, and
Figure BDA0003232011810000034
is a saturation function, defined as sat (u) ═ sat (u)1)，sat(u2)，…，sat(um)]T，sat(ui)＝sgn(ui)min{|uiI, 1, i ∈ m, σ (k) is the switching signal, which takes values in a finite set S ═ {1, 2, …, J }, J ∈ Z+，
Figure BDA0003232011810000035
Figure BDA0003232011810000036
And
Figure BDA0003232011810000037
is a known system matrix that satisfies for σ (k) i, i ∈ S
Figure BDA0003232011810000038
And
Figure BDA0003232011810000039
further, in the step 2, an event triggering condition for vehicle congestion at the entrance and exit of the parking lot is established:
||ey(k)||1＞β||y(k)||1，(2)
where the constant beta is greater than 0, sampling error
Figure BDA00032320118100000310
Figure BDA00032320118100000311
Represents the sampling state, | · | non-woven vision1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all the elements in the vector.
Further, the step 3 comprises the following steps:
step 3.1, designing an event trigger asynchronous filter of the parking lot comprehensive management system, wherein the specific form is as follows:
Figure BDA00032320118100000312
Figure BDA00032320118100000313
wherein x isf(k) Is the state signal of the filter, zf(k) Is z (k)Estimate, Afi，Bfi，EfiAnd FfiThe gain matrix of the designed event-triggered asynchronous filter is in the following specific form:
Figure BDA0003232011810000041
wherein 1 isnIs an n-dimensional vector with all elements in the vector being 1,
Figure BDA0003232011810000042
an n-dimensional vector representing that only the iota-th element is 1 and the remaining elements are all 0, theta, h and xi are n-dimensional vectors, eta and xi
Figure BDA00032320118100000413
Is an m-dimensional vector, θT、ηT、ξTAnd
Figure BDA00032320118100000412
respectively represent theta, eta, xi and
Figure BDA00032320118100000411
the transposing of (1).
And 3.2, the parking lot comprehensive management system based on state saturation has a saturation function meeting the following requirements:
Figure BDA0003232011810000043
wherein the content of the first and second substances,
Figure BDA0003232011810000044
and | | | H | | non-conducting phosphor∞≤1，||·||∞Is an infinite norm, representing the maximum of the sum of the absolute values of the elements of each row in the matrix, DlAn n × n diagonal matrix representing diagonal elements of 0 or 1,
Figure BDA0003232011810000045
i denotes an identity matrix of appropriate dimensions.
Step 3.3, define xe(k)＝xf(k)-x(k),e(k)＝zf(k) -z (k). According to the step 1, the step 3.1 and the step 3.2, a state space model of the parking lot comprehensive management system and the event triggered asynchronous filter are expanded into an error system, and the method specifically comprises the following steps:
Figure BDA0003232011810000046
wherein the content of the first and second substances,
Figure BDA0003232011810000047
Figure BDA0003232011810000048
and
Figure BDA0003232011810000049
the gain matrix of the augmentation form is composed of a state space model of the parking lot comprehensive management system and a system matrix of the event triggered asynchronous filter, and the specific form is as follows:
Figure BDA00032320118100000410
wherein the content of the first and second substances,
Figure BDA0003232011810000051
and 3.4, designing the constraint condition that an error system consisting of the parking lot comprehensive management system with the saturated state and the filter operates stably under the event trigger mechanism as follows:
design constant 0 < mu1＜1,μ2> 1, λ > 1, γ > 0, if there is an n-dimensional vector
Figure BDA0003232011810000052
Figure BDA0003232011810000053
So that the following inequality(7) It is true that the first and second sensors,
Figure BDA0003232011810000054
then the error system is positive and is true under the designed event asynchronous trigger filter gain matrix
Figure BDA0003232011810000056
The gain is stable, and the inequality (7) is as follows:
Figure BDA0003232011810000055
and the switching rule of the system satisfies:
Figure BDA0003232011810000061
wherein, κ-(k0K) represents the total time for which the filter operates in synchronism with the system, k+(k0K) represents the total time for which the filter operates asynchronously with respect to the system, τaDenotes the mean residence time, ΔmRepresenting the maximum lag time of the filter lag for the corresponding subsystem, phi-I-beta 1m×m,Ψ＝I+β1m×m。
Further, the step 3 further comprises the following steps for verifying the positivity of the configured error system under the event triggering condition:
step 3.5, for any initial state
Figure BDA0003232011810000062
And
Figure BDA0003232011810000063
event trigger condition in step 2 is at k0The time meets the following conditions:
Figure BDA0003232011810000064
wherein 1 ism×mAn m × m matrix with all matrix elements 1 is represented.
Step 3.6, combine step 3.3 with step 3.5, when k ∈ [ k ]l，kl+Δl) In time, there are:
Figure BDA0003232011810000065
Figure BDA0003232011810000066
when k is equal to kl+Δl，kl+1) In time, there are:
Figure BDA0003232011810000067
Figure BDA0003232011810000068
wherein the content of the first and second substances,
Figure BDA0003232011810000069
and
Figure BDA00032320118100000610
the gain matrixes are respectively in the form of amplification of a lower-bound system in asynchronous time and synchronous time, and the specific form is as follows:
Figure BDA0003232011810000071
wherein the content of the first and second substances,
Figure BDA0003232011810000072
and i is p to represent that the filter is synchronous with the corresponding subsystem, i is q to represent that the filter is asynchronous with the corresponding subsystem, and the filter gain matrix at the corresponding moment is the matrix during synchronization or asynchronization.
The positivity of the lower bound gain matrix can be guaranteed according to the positive constraint in step 3.4, so that for any initial state
Figure BDA0003232011810000073
The lower bound system is positive and therefore the error system is positive.
Further, the step 3 further comprises the step of verifying the configured error system under the event triggering condition
Figure BDA00032320118100000711
Gain stability:
step 3.7, combine step 3.3 with step 3.5, when k ∈ [ k ]l，kl+Δl) In time, there are:
Figure BDA0003232011810000074
Figure BDA0003232011810000075
when k is equal to kl+Δl，kl+1) In time, there are:
Figure BDA0003232011810000076
Figure BDA0003232011810000077
definition of
Figure BDA0003232011810000078
Wherein the content of the first and second substances,
Figure BDA0003232011810000079
and
Figure BDA00032320118100000710
the gain matrixes are respectively in an amplification form of an upper-bound system in asynchronous time and synchronous time, and the specific form is as follows:
Figure BDA0003232011810000081
step 3.8, designing a linear complementary Li ya Punuo function:
Figure BDA0003232011810000082
wherein the content of the first and second substances,
Figure BDA0003232011810000083
step 3.9, in combination with step 3.4, step 3.7 and step 3.8, the handover of the lyapunov function satisfies:
Figure BDA0003232011810000084
wherein the content of the first and second substances,
Figure BDA0003232011810000085
thus, the above equation can be derived by recursion:
Figure BDA0003232011810000086
step 3.10, for time
Figure BDA0003232011810000087
The following inequality can be obtained by step 3.9 by recursion:
Figure BDA0003232011810000088
wherein N isσ(k0T) denotes the switching signal σ (k) at time [ k ]0Number of handovers within T) and is satisfied under the condition of average residence time
Figure BDA0003232011810000089
Step 3.11, because
Figure BDA0003232011810000091
Let M be T-1, then under zero initial conditions, the following holds:
Figure BDA0003232011810000092
step 3.12, multiplying both sides of the inequality in step 3.11 by
Figure BDA0003232011810000093
It is possible to obtain:
Figure BDA0003232011810000094
step 3.13, according to the average residence time conditions in step 3.4 and step 3.10, has:
Figure BDA0003232011810000095
thus, step 3.12 can be converted into:
Figure BDA0003232011810000096
the two sides of the above formula are summed simultaneously at [0, ∞) ] due to
Figure BDA0003232011810000097
The following inequality is obtained:
Figure BDA0003232011810000098
wherein the content of the first and second substances,
Figure BDA0003232011810000099
thus, the error system meets the performance index γ
Figure BDA00032320118100000910
Gain performance.
The invention has the advantages and beneficial effects that:
aiming at the problem of traffic jam caused by saturated traffic flow in the current parking lot during peak hours, a state space model of a comprehensive management system of the parking lot is established by using a modern control theory technology, and by designing an event trigger filter, the traffic flow of each parking lot is effectively estimated in real time, so that vehicles can select parking places to park vehicles reasonably in time, the parking places of each parking lot are guaranteed to be efficiently utilized, and the problem of parking difficulty is relieved.
Drawings
FIG. 1 is a schematic view of a parking lot doorway management system according to the present invention;
fig. 2 is a system block diagram of a switching system with state saturation and an event triggered asynchronous filter in accordance with the present invention.
Detailed Description
The present invention is further illustrated by the following examples, which are not intended to limit the invention to these embodiments. It will be appreciated by those skilled in the art that the present invention encompasses all alternatives, modifications and equivalents as may be included within the scope of the claims.
As shown in fig. 2, the present embodiment models a parking lot integrated management system based on a state-saturated positive switching system, and designs an event-triggered asynchronous filter for estimating traffic flow of each large public parking lot, which includes the following specific steps:
step 1, firstly, carrying out data acquisition on traffic flow of an entrance and an exit of a parking lot, and establishing a state space model of a comprehensive management system of the parking lot by using the acquired data, wherein the form is as follows:
x(k+1)＝sat(Aσ(k)x(k))+Bσ(k)ω(k)，
y(k)＝Cσ(k)x(k)+Dσ(k)ω(k)，
z(k)＝Eσ(k)x(k)+Fσ(k)ω(k)，
wherein the content of the first and second substances,
Figure BDA0003232011810000101
representing the number of remaining parking lots in the parking lot at the kth sampling time, n representing the number of parking lots,
Figure BDA0003232011810000102
m represents the number of berths in the parking lot for the number of vehicles driving into the parking lot,
Figure BDA0003232011810000103
represents the estimate of y (k) at time k, i.e., the number of vehicles expected to enter the parking lot, s represents the number of exits and entrances of the parking lot, ω (k) is the external disturbance affecting the traffic flow at the exits and entrances of the parking lot, and
Figure BDA0003232011810000104
is a saturation function, defined as sat (u) ═ sat (u)1)，sat(u2)，…，sat(um)]T，sat(ui)＝sgn(ui)min{|uiI, 1, i ∈ m, σ (k) is the switching signal, which takes values in a finite set S ═ {1, 2, …, J }, J ∈ Z+，
Figure BDA0003232011810000111
Figure BDA0003232011810000112
And
Figure BDA0003232011810000113
is alreadyGiven the system matrix, for σ (k) i, i ∈ S, the system matrix satisfies
Figure BDA0003232011810000114
And
Figure BDA0003232011810000115
step 2, establishing an event triggering condition of vehicle congestion at an entrance and an exit of the parking lot:
||ey(k)||1＞β||y(k)||1,
where the constant beta is greater than 0, sampling error
Figure BDA0003232011810000116
Figure BDA0003232011810000117
Represents the sampling state | · |1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all the elements in the vector.
Step 3, designing an event-triggered asynchronous filter of the parking lot comprehensive management system, which is characterized by comprising the following steps:
step 3.1, designing an event trigger asynchronous filter, wherein the specific form is as follows:
Figure BDA0003232011810000118
Figure BDA0003232011810000119
wherein x isf(k) Is the state signal of the filter, zf(k) Is an estimate of z (k), Afi,Bfi,EfiAnd FfiThe gain matrix of the designed event-triggered asynchronous filter is in the following specific form:
Figure BDA00032320118100001110
wherein 1 isnIs an n-dimensional vector with all elements in the vector being 1,
Figure BDA00032320118100001111
an n-dimensional vector representing that only the iota-th element is 1 and the remaining elements are all 0, theta, h and xi are n-dimensional vectors, eta and xi
Figure BDA00032320118100001112
Is an m-dimensional vector, θT、ηT、ξTAnd
Figure BDA00032320118100001114
respectively represent theta, eta, xi and
Figure BDA00032320118100001115
the transposing of (1).
And 3.2, the parking lot comprehensive management system based on state saturation has a saturation function meeting the following requirements:
Figure BDA00032320118100001113
wherein the content of the first and second substances,
Figure BDA0003232011810000121
and | | | H | | non-conducting phosphor∞≤1，||·||∞Is an infinite norm, representing the maximum of the sum of the absolute values of the elements of each row in the matrix, DlAn n × n diagonal matrix representing diagonal elements of 0 or 1,
Figure BDA0003232011810000122
i denotes an identity matrix of appropriate dimensions.
Step 3.3, define xe(k)＝xf(k)-x(k),e(k)＝zf(k) -z (k). According to the step 1, the step 3.1 and the step 3.2, a state space model of the parking lot comprehensive management system and the event triggered asynchronous filter are expanded into an error system, and the method specifically comprises the following steps:
Figure BDA0003232011810000123
Figure BDA0003232011810000124
wherein the content of the first and second substances,
Figure BDA0003232011810000125
Figure BDA0003232011810000126
and
Figure BDA0003232011810000127
the gain matrix of the augmentation form is composed of a state space model of the parking lot comprehensive management system and a system matrix of the event triggered asynchronous filter, and the specific form is as follows:
Figure BDA0003232011810000128
Figure BDA0003232011810000129
wherein the content of the first and second substances,
Figure BDA00032320118100001210
and 3.4, designing the constraint condition that an error system consisting of the parking lot comprehensive management system with the saturated state and the filter operates stably under the event trigger mechanism as follows:
design constant 0 < mu1＜1,μ2> 1, λ > 1, γ > 0, if there is an n-dimensional vector
Figure BDA00032320118100001211
Figure BDA00032320118100001212
Such that the following inequality:
Figure BDA0003232011810000131
Figure BDA0003232011810000132
Figure BDA0003232011810000133
Figure BDA0003232011810000134
Figure BDA0003232011810000135
Figure BDA0003232011810000136
Figure BDA0003232011810000137
Figure BDA0003232011810000138
Figure BDA0003232011810000139
Figure BDA00032320118100001310
Figure BDA00032320118100001311
Figure BDA00032320118100001312
Figure BDA00032320118100001313
Figure BDA00032320118100001314
Figure BDA00032320118100001315
Figure BDA00032320118100001316
Figure BDA00032320118100001317
Figure BDA00032320118100001318
if true, then the error system is positive under the designed event asynchronous triggered filter gain matrix, and is
Figure BDA00032320118100001321
The gain is stable. And the switching rule of the system satisfies:
Figure BDA00032320118100001319
Figure BDA00032320118100001320
wherein, κ-(k0K) represents the total time for which the filter operates in synchronism with the system, k+(k0K) represents the total time for which the filter operates asynchronously with respect to the system, τaDenotes the mean residence time, ΔmRepresenting the maximum lag time of the filter lag for the corresponding subsystem, phi-I-beta 1m×m，Ψ＝I+β1m×m。
Further, the step 3 further comprises the following steps for verifying the positivity of the configured error system under the event triggering condition:
step 3.5, for any initial state
Figure BDA0003232011810000141
And
Figure BDA0003232011810000142
event trigger condition in step 2 is at k0The time meets the following conditions:
Figure BDA0003232011810000143
wherein 1 ism×mAn m × m matrix with all matrix elements 1 is represented.
Step 3.6, combine step 3.3 with step 3.5, when k ∈ [ k ]l,kl+Δl) In time, there are:
Figure BDA0003232011810000144
Figure BDA0003232011810000145
when k is equal to kl+Δl,kl+1) In time, there are:
Figure BDA0003232011810000146
Figure BDA0003232011810000147
wherein the content of the first and second substances,
Figure BDA0003232011810000148
and
Figure BDA0003232011810000149
the gain matrixes are respectively in the form of amplification of a lower-bound system in asynchronous time and synchronous time, and the specific form is as follows:
Figure BDA00032320118100001410
Figure BDA00032320118100001411
Figure BDA00032320118100001412
Figure BDA00032320118100001413
wherein the content of the first and second substances,
Figure BDA00032320118100001414
and i is p to represent that the filter is synchronous with the corresponding subsystem, i is q to represent that the filter is asynchronous with the corresponding subsystem, and the filter gain matrix at the corresponding moment is the matrix during synchronization or asynchronization.
The positivity of the lower bound gain matrix can be guaranteed according to the positive constraint in step 3.4, so that for any initial state
Figure BDA00032320118100001415
The lower bound system is positive and therefore the error system is positive.
Further, the step 3 further comprises the step of verifying the configured error system under the event triggering condition
Figure BDA00032320118100001514
Gain stability:
step 3.7, combine step 3.3 with step 3.5, when k ∈ [ k ]l，kl+Δl) In time, there are:
Figure BDA0003232011810000151
Figure BDA0003232011810000152
when k is equal to kl+Δl，kl+1) In time, there are:
Figure BDA0003232011810000153
Figure BDA0003232011810000154
definition of
Figure BDA0003232011810000155
Wherein the content of the first and second substances,
Figure BDA0003232011810000156
and
Figure BDA0003232011810000157
the gain matrixes are respectively in an amplification form of an upper-bound system in asynchronous time and synchronous time, and the specific form is as follows:
Figure BDA0003232011810000158
Figure BDA0003232011810000159
Figure BDA00032320118100001510
Figure BDA00032320118100001511
step 3.8, designing a linear complementary Li ya Punuo function:
Figure BDA00032320118100001512
wherein the content of the first and second substances,
Figure BDA00032320118100001513
step 3.9, in combination with step 3.4, step 3.7 and step 3.8, the handover of the lyapunov function satisfies:
Figure BDA0003232011810000161
wherein the content of the first and second substances,
Figure BDA0003232011810000162
thus, the above equation can be derived by recursion:
Figure BDA0003232011810000163
step 3.10, for time
Figure BDA0003232011810000164
The following inequality can be obtained by step 3.9 by recursion:
Figure BDA0003232011810000165
wherein N isσ(k0T) denotes the switching signal σ (k) at time [ k ]0Number of handovers within T) and is satisfied under the condition of average residence time
Figure BDA0003232011810000166
Step 3.11, because
Figure BDA0003232011810000167
Let M be T-1, then under zero initial conditions, the following holds:
Figure BDA0003232011810000168
step 3.12, multiplying both sides of the inequality in step 3.11 by
Figure BDA0003232011810000169
It is possible to obtain:
Figure BDA00032320118100001610
step 3.13 consists of the average residence time conditions in step 3.4 and step 3.10:
Figure BDA00032320118100001611
thus, step 3.12 can be converted into:
Figure BDA0003232011810000171
the two sides of the above formula are summed simultaneously at [0, ∞) ] due to
Figure BDA0003232011810000172
The following inequality is obtained:
Figure BDA0003232011810000173
wherein the content of the first and second substances,
Figure BDA0003232011810000174
thus, the error system meets the performance index γ
Figure BDA0003232011810000175
Gain performance.

Claims (5)

1. A traffic flow estimation method of a comprehensive management system of a public parking lot comprises the following steps:
step 1, establishing a state space model of a parking lot comprehensive management system with state saturation;
step 2, constructing an event triggering condition of vehicle congestion at an entrance and an exit of the parking lot;
and 3, designing an event trigger asynchronous filter of the comprehensive management system of the public parking lot.
2. The traffic flow estimation method of the comprehensive management system for public parking lots according to claim 1, characterized in that the specific method in step 1 is:
firstly, carrying out data acquisition on traffic flow of an entrance and an exit of a parking lot, and establishing a state space model of a comprehensive management system of the parking lot by using the acquired data, wherein the form is as follows:
Figure FDA0003232011800000011
wherein the content of the first and second substances,
Figure FDA0003232011800000012
representing the number of remaining parking lots in the parking lot at the kth sampling time, n representing the number of parking lots,
Figure FDA0003232011800000013
m represents the number of berths in the parking lot for the number of vehicles driving into the parking lot,
Figure FDA0003232011800000014
represents the estimate of y (k) at time k, i.e., the number of vehicles expected to enter the parking lot, s represents the number of exits and entrances of the parking lot, ω (k) is the external disturbance affecting the traffic flow at the exits and entrances of the parking lot, and
Figure FDA0003232011800000015
is a saturation function, defined as sat (u) ═ sat (u)1),sat(u2),…,sat(um)]T，sat(ui)＝sgn(ui)min{|uiI, 1, i ∈ m, σ (k) is the switching signal, which takes values in a finite set S ═ 1, 2, …, J,
Figure FDA0003232011800000016
Figure FDA0003232011800000017
and
Figure FDA0003232011800000018
is a known system matrix that satisfies for σ (k) i, i ∈ S
Figure FDA0003232011800000019
And
Figure FDA00032320118000000110
3. the traffic flow estimation method of a comprehensive management system for public parking lots as claimed in claim 1 or 2, wherein in said step 2, an event triggering condition for vehicle congestion at entrance and exit of a parking lot is established:
||ey(k)||1＞β||y(k)||1, (2)
where the constant beta is greater than 0, sampling error
Figure FDA0003232011800000021
Figure FDA0003232011800000022
Represents the sampling state | · |1Represents the 1 norm of the vector, i.e., the sum of the absolute values of all the elements in the vector.
4. The event-triggered asynchronous filter of an integrated management system based on state-saturation-plus-switching system modeling according to claim 3, wherein: the design of the event-triggered asynchronous filter of the parking lot integrated management system in the step 3 comprises the following steps:
step 3.1, designing an event trigger asynchronous filter of the parking lot comprehensive management system, wherein the specific form is as follows:
Figure FDA0003232011800000023
Figure FDA0003232011800000024
wherein x isf(k) Is the state signal of the filter, zf(k) Is an estimate of z (k), Afi,Bfi,EfiAnd FfiThe gain matrix of the designed event-triggered asynchronous filter is in the following specific form:
Figure FDA0003232011800000025
wherein 1 isnIs an n-dimensional vector with all elements in the vector being 1,
Figure FDA0003232011800000026
an n-dimensional vector representing that only the iota-th element is 1 and the remaining elements are all 0, theta, h and xi are n-dimensional vectors, eta and xi
Figure FDA0003232011800000029
Is an m-dimensional vector, θT、ηT、ξTAnd
Figure FDA00032320118000000210
respectively represent theta, eta, xi and
Figure FDA00032320118000000211
transposing;
and 3.2, the parking lot comprehensive management system based on state saturation has a saturation function meeting the following requirements:
Figure FDA0003232011800000027
wherein the content of the first and second substances,
Figure FDA0003232011800000028
and | | | H | | non-conducting phosphor∞≤1，||·||∞Is an infinite norm, representing the maximum of the sum of the absolute values of the elements of each row in the matrix, DlAn n × n diagonal matrix representing diagonal elements of 0 or 1,
Figure FDA0003232011800000031
i represents an identity matrix of appropriate dimensions;
step 3.3, define xe(k)＝xf(k)-x(k),e(k)＝zf(k) -z (k); according to step 1, step 3.1 and step 3.2, the process will be describedThe state space model and the event triggered asynchronous filter of the parking lot comprehensive management system are expanded into an error system, and the method specifically comprises the following steps:
Figure FDA0003232011800000032
Figure FDA0003232011800000033
wherein the content of the first and second substances,
Figure FDA0003232011800000034
Figure FDA0003232011800000035
and
Figure FDA0003232011800000036
the gain matrix of the augmentation form is composed of a state space model of the parking lot comprehensive management system and a system matrix of the event triggered asynchronous filter, and the specific form is as follows:
Figure FDA0003232011800000037
Figure FDA0003232011800000038
wherein the content of the first and second substances,
Figure FDA0003232011800000039
and 3.4, designing the constraint condition that an error system consisting of the parking lot comprehensive management system with the saturated state and the filter operates stably under the event trigger mechanism as follows:
design constant 0 < mu1＜1,μ2> 1, λ > 1, γ > 0, if there is an n-dimensional vector
Figure FDA00032320118000000310
Figure FDA00032320118000000311
Such that the following inequality:
Figure FDA0003232011800000041
Figure FDA0003232011800000042
if true, then the error system is positive and is l under the designed event asynchronous triggered filter gain matrix1The gain is stable; and the switching rule of the system satisfies:
Figure FDA0003232011800000043
Figure FDA0003232011800000044
wherein, κ-(k0K) represents the total time for which the filter operates in synchronism with the system, k+(k0K) represents the total time for which the filter operates asynchronously with respect to the system, τaDenotes the mean residence time, ΔmRepresenting the maximum lag time of the filter lag for the corresponding subsystem, phi-I- α 1m×m，Ψ＝I+β1m×m；
Further, the step 3 further comprises the following steps for verifying the positivity of the configured error system under the event triggering condition:
step 3.5, for any initial state
Figure FDA0003232011800000051
And
Figure FDA0003232011800000052
event trigger condition in step 2 is at k0The time meets the following conditions:
-β1m×my(k0)≤ey(k0)≤β1m×my(k0), (10)
wherein 1 ism×mAn m × m matrix representing matrix elements all of 1;
step 3.6, combine step 3.3 with step 3.5, when k ∈ [ k ]l,kl+Δl) In time, there are:
Figure FDA0003232011800000053
Figure FDA0003232011800000054
when k is equal to kl+Δl,kl+1) In time, there are:
Figure FDA0003232011800000055
Figure FDA0003232011800000056
wherein the content of the first and second substances,
Figure FDA0003232011800000057
and
Figure FDA0003232011800000058
the gain matrixes are respectively in the form of amplification of a lower-bound system in asynchronous time and synchronous time, and the specific form is as follows:
Figure FDA0003232011800000059
Figure FDA00032320118000000510
Figure FDA00032320118000000511
Figure FDA00032320118000000512
wherein the content of the first and second substances,
Figure FDA00032320118000000513
i takes p to represent that the filter is synchronous with the corresponding subsystem, i takes q to represent that the filter is asynchronous with the corresponding subsystem, and the filter gain matrix at the corresponding moment is a matrix during synchronization or asynchronization;
the positivity of the lower bound gain matrix can be guaranteed according to the positive constraint in step 3.4, so that for any initial state
Figure FDA00032320118000000514
The lower bound system is positive and therefore the error system is positive.
5. The event-triggered asynchronous filter of an integrated management system based on state-saturation-plus-switching system modeling according to claim 4, wherein:
said step 3 further comprises the step of verifying i of the error system constructed under event triggering conditions1Gain stability:
step 3.7, combine step 3.3 with step 3.5, when k ∈ [ k ]l,kl+Δl) In time, there are:
Figure FDA0003232011800000061
Figure FDA0003232011800000062
when k is equal to kl+Δl,kl+1) In time, there are:
Figure FDA0003232011800000063
Figure FDA0003232011800000064
definition of
Figure FDA0003232011800000065
Wherein the content of the first and second substances,
Figure FDA0003232011800000066
and
Figure FDA0003232011800000067
the gain matrixes are respectively in an amplification form of an upper-bound system in asynchronous time and synchronous time, and the specific form is as follows:
Figure FDA0003232011800000068
Figure FDA0003232011800000069
Figure FDA00032320118000000610
Figure FDA00032320118000000611
step 3.8, designing a linear complementary Li ya Punuo function:
Figure FDA00032320118000000612
wherein the content of the first and second substances,
Figure FDA00032320118000000613
step 3.9, in combination with step 3.4, step 3.7 and step 3.8, the handover of the lyapunov function satisfies:
Figure FDA0003232011800000071
wherein the content of the first and second substances,
Figure FDA0003232011800000072
thus, the above equation can be derived by recursion:
Figure FDA0003232011800000073
step 3.10, for time
Figure FDA0003232011800000074
The following inequality can be obtained by step 3.9 by recursion:
Figure FDA0003232011800000075
wherein N isσ(k0T) denotes the switching signal σ (k) at time [ k ]0Number of handovers within T) and is satisfied under the condition of average residence time
Figure FDA0003232011800000076
Step 3.11, because
Figure FDA0003232011800000077
Let M be T-1, then under zero initial conditions, the following holds:
Figure FDA0003232011800000078
step 3.12, multiplying both sides of the inequality in step 3.11 by
Figure FDA0003232011800000079
It is possible to obtain:
Figure FDA00032320118000000710
step 3.13 consists of the average residence time conditions in step 3.4 and step 3.10:
Figure FDA0003232011800000081
thus, step 3.12 can be converted into:
Figure FDA0003232011800000082
the two sides of the above formula are summed simultaneously at [0, ∞) ] due to
Figure FDA0003232011800000083
The following inequality is obtained:
Figure FDA0003232011800000084
wherein the content of the first and second substances,
Figure FDA0003232011800000085
thus, the error system satisfies l at the performance index γ1Gain performance.
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