CN118430243B - Highway network operation situation estimation method based on distributed observer - Google Patents
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Abstract
The embodiment of the invention discloses a highway network operation situation estimation method based on a distributed observer, which comprises the following steps: determining a dynamic model of traffic state of the expressway network according to interconnection relations among subsystems of the expressway network, wherein the traffic state comprises traffic flow density; under the condition that the dynamic model is an open-loop system, a distributed closed-loop observer of the traffic state of the highway network is constructed, wherein the distributed closed-loop observer consists of observers distributed in all subsystems, each observer is used for estimating the future traffic state of each subsystem according to the current estimation error, and the current estimation error is the difference between the current traffic state estimated by the observer and the real current traffic state; and measuring the real traffic state of each subsystem at any moment by using the sensing equipment of each subsystem, and estimating the future traffic state of each subsystem by each observer according to the measured real traffic state.
Description
Technical Field
The embodiment of the invention relates to the field of intelligent traffic, in particular to a highway network operation situation estimation method based on a distributed observer.
Background
Along with the development of intelligent highway construction in recent years, various intelligent devices are widely applied, the intelligent level of expressway traffic running state perception is continuously improved, the improvement of perception core algorithm is further promoted, and a state observer is used as a typical application tool and is more required to be improved. Meanwhile, along with the expansion of the scale of the expressway network, the realization of real-time monitoring of the road network level traffic state is more important for optimizing configuration and balanced utilization of resources, but is limited by the fact that a centralized state observer is difficult to bear the pressure of real-time calculation of a large-scale road network, so that the real-time performance is difficult to meet, and once a certain node of a centralized structure is in a problem, the whole network operation is blocked, so that the defects of the centralized structure are overcome, and the state observer of the distributed structure is selected.
The whole road network system is divided into a plurality of subsystems in the distributed structure, and each system is relatively independent, so that on one hand, the calculation pressure is greatly reduced, the instantaneity can be guaranteed, and on the other hand, the interference among the subsystems is small, and even if one subsystem fails, the normal operation of other subsystems can not be influenced. In addition, with diversification of data acquisition modes, in order to improve accuracy of the observer, an observer design method based on multi-source information may be adopted, for example, patent CN113053106B provides a traffic state estimation method and device based on multi-sensor information fusion, and patent CN113034903B provides a traffic state estimation method and device based on multi-source information fusion. However, the above patent does not consider the mutual influence of the traffic states among the subsystems, and the traffic states of the large-scale expressway network cannot be estimated accurately and comprehensively.
Disclosure of Invention
The embodiment of the invention provides a highway network running situation estimation method based on a distributed observer, which accurately and comprehensively estimates the traffic state of a highway network by considering the mutual influence of the traffic states of all subsystems.
In a first aspect, an embodiment of the present invention provides a method for estimating an operation situation of a highway network based on a distributed observer, including:
determining a dynamic model of traffic state of the expressway network according to interconnection relations among subsystems of the expressway network, wherein the traffic state comprises traffic flow density, each subsystem comprises at least one road section, and the dynamic model is used for representing dynamic change rules of the traffic state of each subsystem along with time;
Under the condition that the dynamic model is an open-loop system, a distributed closed-loop observer of the traffic state of the highway network is constructed, wherein the distributed closed-loop observer consists of observers distributed in all subsystems, each observer is used for estimating the future traffic state of each subsystem according to the current estimation error, and the current estimation error is the difference between the current traffic state estimated by the observer and the real current traffic state;
And measuring the real traffic state of each subsystem at any moment by using the sensing equipment of each subsystem, and estimating the future traffic state of each subsystem by each observer according to the measured real traffic state.
In a second aspect, an embodiment of the present invention provides an electronic device, including:
one or more processors;
A memory for storing one or more programs,
The one or more programs, when executed by the one or more processors, cause the one or more processors to implement the distributed observer-based highway network operation situation estimation method according to any of the embodiments.
In a third aspect, an embodiment of the present invention further provides a computer readable storage medium, where a computer program is stored, where the program when executed by a processor implements the method for estimating an operation situation of a highway network based on the distributed observer according to any embodiment.
The embodiment of the invention provides a highway network operation situation estimation method based on a distributed observer, which is characterized in that interconnection items among subsystems are defined through system modeling, a corresponding traffic state closed-loop observer is designed according to the interconnection items, the mutual influence of the traffic states among the subsystems is fully considered, and the traffic state of a large-scale highway network is accurately and comprehensively estimated.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a system architecture of a highway network distributed observer according to an embodiment of the present invention;
fig. 2 is a flowchart of a method for estimating an operation situation of a highway network based on a distributed observer according to an embodiment of the present invention;
Fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the invention, are within the scope of the invention.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should also be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
The embodiment of the invention provides a highway network running situation estimation method based on a distributed observer. To illustrate the method, a system architecture supporting the implementation of the method is preferentially introduced. Fig. 1 is a system architecture of a highway network distributed observer according to an embodiment of the present invention. In the figure, the highway network is regarded as a large system, and a control center is arranged; dividing the whole road network according to regions, wherein each region is a subsystem, and a control sub-center is arranged; the subsystem is divided into a plurality of road sections according to the positions of the entrance ramp, the ETC portal, the lane number change position and the like, and each road section is called a cell. Each road section is provided with at least one sensing device (such as a sensor) for sensing road end information; the divided cells can be sequentially calibrated with serial numbers, so that the arrangement positions of the sensing equipment can be marked conveniently. Each area corresponds to a set of state observers and is used for dynamically estimating the traffic state of each subsystem according to perceived road end information; the state observer of each area operates relatively independently, so that the calculation speed can be greatly improved, and the time delay caused by mass data transmission is reduced. The state observers of all the subsystems together form a distributed state observer of the whole road network, and the traffic states of the road network are estimated dynamically.
Based on the system architecture, fig. 2 is a flowchart of a highway network operation situation estimation method based on a distributed observer, which is provided by the embodiment of the invention, a new traffic state observer is constructed according to the interconnection relation among all subsystems, and the future traffic state of all the subsystems is comprehensively and accurately dynamically estimated. The method can be executed by the electronic equipment deployed in the control center or the control sub-center, as shown in fig. 2, and specifically comprises the following steps:
s110, determining a dynamic model of traffic state of the expressway network according to interconnection relations among subsystems of the expressway network, wherein the traffic state comprises traffic flow density, each subsystem comprises at least one road section, and the dynamic model is used for representing the dynamic change rule of the traffic state of each subsystem along with time.
In the whole highway network system, the traffic flow transmission between any two adjacent subsystems influences the traffic state of each other. In this embodiment, the traffic state dynamic equation of the subsystem i is constructed as follows, taking into consideration the interconnection relationship:
where N represents the number of subsystems, x i represents the traffic state vector of subsystem i, x i (t) and x i (t+1) represent the traffic state vectors of subsystem i at time t and time t+1, respectively, and x j (t) represents the traffic state vectors of all neighboring subsystems j of subsystem i at time t. For example, when the traffic state is the traffic flow density, x i (t) is a vector formed by the traffic flow density of each road section in the subsystem i at the time t, x i (t+1) and x j (t) are similar, and the time and subsystem labels in x i (t) are replaced by t+1 and j respectively. u i denotes the traffic demand of subsystem i, u i (t) denotes the traffic demand of subsystem i at time t, and u i (t) is a vector of traffic flow density variations of each road segment in subsystem i at time t when the traffic demand includes the incoming vehicles of each road segment, for example. y i represents the data acquired by the sensing devices of each road segment in the subsystem i, which is also called a measurement output vector, y i (t) represents the measurement output vector of the subsystem i at the time t, and the vector can be converted into the traffic state x i (t) of the subsystem i at the time t through the matrix C i. Matrix array C i The system matrix, input matrix, output matrix and affine term of subsystem i respectively,As a matrix associated with the adjacent subsystem j, Representing an upstream adjacent subsystem of subsystem i,Representing a downstream adjacent subsystem of subsystem i.C i Together reflecting the inherent properties of subsystem i which, when determined by the subsystem and its sensing devices, C i The values or expressions of the elements can be predetermined according to the road network structure and the general traffic flow transmission rule, and the specific process is the prior art and will not be repeated here.
Further, in order to facilitate the representation, the dynamic equations of the subsystems can be combined to obtain a dynamic model of the traffic state of the whole expressway network:
wherein x represents the traffic state of the highway network, X (t) and x (t+1) respectively represent traffic states of the highway network at the time t and the time t+1; u represents the traffic demand of the expressway network, u= [ u 1 T,…uN T]T, u (t) represents the traffic demand of the expressway network at the time t; y represents the measurement output of the highway network, y= [ y 1 T,...yN T]T, y (t) represents the measurement output of the highway network at the time t. A σ(t) is a system matrix of the highway network,Wherein, The block diagonal matrix is used for representing the transfer rule of the internal traffic state of each subsystem and is called as a decoupling block matrix of each subsystem; The method is used for representing the interaction of traffic states among the subsystems and is called an interconnection term among the subsystems. B σ(t) represents the input matrix of the highway network, C represents the output matrix c= blkdiag of the highway network (C i);Fσ(t) represents the affine term of the highway network,Likewise, the number of the cells to be processed,B σ(t), C, and F σ(t) collectively reflect the inherent properties of the highway network system and, when the highway Lu Wangji system and its sensing devices determine,B σ(t), C and F σ(t) are also known in advance.
S120, under the condition that the dynamic model is an open-loop system, a distributed closed-loop observer of the traffic state of the highway network is constructed, wherein the distributed closed-loop observer is composed of observers distributed in all subsystems, each observer is used for estimating the future traffic state of each subsystem according to the current estimation error, and the current estimation error is the difference between the current traffic state estimated by the observer and the real current traffic state.
As described above, the dynamic model shown in the formula (1) and (2) can reflect the rule of the traffic state of each subsystem changing with time, and when the measurement output y i (t) or y (t) of each subsystem at a certain moment is known, the traffic state x i (t) or x (t) of each subsystem at the moment can be obtained according to the model, so that the traffic state x i (t+1) or x (t+1) at the next moment can be estimated in combination with the traffic demand u i (t) or u (t) at the moment. However, since the dynamic model in the formulas (1) and (2) is an open-loop system and has a large error, the embodiment reconstructs a distributed closed-loop observer based on the model, gradually converges the estimation error (or referred to as the observation error) through the closed-loop idea, and accurately estimates the traffic states of all subsystems and the expressway network. In a specific embodiment, the construction process of the distributed closed-loop observer can include the following steps:
Step one, constructing a traffic state observer of a subsystem i based on a dynamic equation shown in a formula (1), wherein the traffic state observer is as follows:
Wherein, Representing the traffic state vector of subsystem i estimated by the observer of subsystem i,AndRepresenting the traffic state vectors of subsystem i at times t and t +1 estimated by the observer of subsystem i respectively,Representing the traffic state vector of the subsystem j estimated by the adjacent subsystem j of the subsystem i at the time t; representing the measured output vector of the observer of subsystem i, Representing the measured output vector of the observer at time t.An observer gain matrix representing subsystem i for characterizing traffic conditions of observer subsystem i at time tIs estimated for the traffic state of subsystem i at time t +1The influence of the estimation result of (2).For the unknown quantity to be determined, its value needs to be determined in a subsequent operation to ensure that the estimation error of the observer is closed-loop converged.
It can be seen that the distributed state observer of the present embodiment not only adopts all information of the subsystems themselves, but also interconnects information between the subsystemsIt is also contemplated that all available information of the road network system is contained as comprehensively as possible. Similarly, the traffic state observers of the subsystems can be combined to obtain the traffic state observer of the whole expressway network:
Wherein, Representing the traffic state of the expressway network estimated by each observer, AndRespectively representing traffic states of the expressway network estimated by each observer at the time t and the time t+1; Indicating that each observer is measuring the output, Representing the measurement output of each observer at the time t; k σ(t) denotes the observer gain matrix to be determined,
And step two, representing an estimation error system of the distributed state observer by using the observer gain matrix and the known interconnection. Specifically, the estimation error e of the observer is defined as the estimated value of the observer for each subsystem traffic stateThe difference from the true value x, i.eSubstituting equations (2) and (4) into the definition can be expressed as follows:
wherein e (t) and e (t+1) represent the estimated errors of the observer at time t and time t+1, respectively, K σ(t) is the unknown matrix to be determined, Is a known quantity. The formula represents the estimation error system as a matrix with respect to observer gainAnd interconnecting itemsIn the form of (c) provides the basis for the solution of K σ(t).
And thirdly, solving the gain of the observer according to the design principle of the estimation error system and the closed-loop observer with the convergence of the estimation error. Specifically, according to the design principle of the closed-loop observer, the observation error system shown in the formula (5) is required to be asymptotically stable; meanwhile, depending on the requirements of the observer design, if the system (A σ(t), C) is observable or detectable, it is certain to be able to design a set of gain matrices K σ(t) such that the matricesIs suler stable. But due to interconnecting terms in the error systemIs present even in a matrixIs sull stable and it is also difficult to ensure the stability of the error system (5). For this purpose, the present embodiment introduces an S-procedure and Lyapunov function to transform the stability problem of the error system (5) into a solution problem of the linear matrix inequality.
In a specific embodiment, a symmetric positive definite matrix P (P > 0) is first introduced, a lyapunov function V (e) =e T Pe is constructed, and the design principle of a closed-loop observer for estimating error convergence is converted into a constraint condition for estimating error energy attenuation along with time. In other words, if the equation (5) of the observation error system is asymptotically stable, the inequality (6) must be established:
Wherein e is an abbreviation of e (t) herein, equivalent to an estimated error at any instant; v is an abbreviation for v (t).
Meanwhile, v (t) satisfies the following quotients:
vTv≤λmaxeTe (7)
wherein lambda max is a matrix Can be defined by the maximum eigenvalue of (2)Solving to obtain the final product.
Combining inequality (6) (7) using the S-Procedure theorem yields: there must be a positive constant μ such that the following inequality holds:
Further, a quadratic inequality of the formula (9) is obtained:
I.e.
Wherein,
The matrix inequality (10) is not a linear matrix inequality and cannot be directly solved because of the presence of bilinear terms. Thus by variable substitution Q σ(t)＝PKσ(t),Converting equation (10) into a linear matrix inequality:
Wherein,
The inequality (11) is solved by using a linear matrix inequality solver to obtain P and Q σ(t). The observer gain K σ(t) is obtained by K σ(t)＝P- 1Qσ(t).
And fourthly, substituting the observer gain K σ(t) into the formula (4) to obtain the distributed closed-loop observer of the expressway network.
S130, measuring the real traffic state of each subsystem at any moment by using the sensing equipment of each subsystem, and estimating the future traffic state of each subsystem by each observer according to the measured real traffic state.
Along with the increase of the types of sensing devices, various data acquisition devices such as radar, video, floating car, ETC portal, microwave and other traffic sensors exist on the expressway at the same time, so that the steps utilize various sensing devices to measure real traffic states respectively, construct a distributed state observer for each type of sensing device by utilizing the operation of S110-S120, estimate the traffic states respectively by utilizing the observers corresponding to the measured values of each type of sensing device, and fuse and calculate the estimation results to obtain more accurate traffic running states.
Specifically, for different sensing devices, the output equation in the road network model can be expressed as follows:
yr(t)＝Crx(t)，r＝1,2,...,l (12)
Wherein l represents the type of traffic sensing equipment, y r (t) represents the measurement output of the class r sensing equipment at the moment t, and C r is a corresponding output matrix. Although traffic information perceived by different types of perception devices is different, the traffic information can be uniformly converted into a traffic state through corresponding conversion relations, and the ETC can acquire the instantaneous speed and the traffic flow of a vehicle, the video can acquire the traffic flow, and the traffic information can be respectively converted into traffic flow density as a measured value y r (t). Thus, the output matrices corresponding to different types of sensors can be unified as follows:
Where n represents the number of cells, k=1, …, n, i.e. as long as the sensor is arranged in the kth cell, its output matrix corresponds to a position element of 1, otherwise 0.
Based on such an output matrix, it can be determined by (A σ(t),Cr) whether the system is observable or detectable according to the observability criterion, if there are m systems observable or detectable, then m distributed state observers can be constructed. The traffic state converted from the sensing equipment data of the corresponding type is respectively substituted into m distributed state observers as y (t), and m estimated results can be obtained
And then, carrying out weighted summation calculation on the estimated values of the m distributed state observers by adopting a fusion algorithm. The method comprises the following steps: assume an estimate for each observer in subsystem iAll have a weight eta i-q, so that m weight combination pairs can be calculatedThe result of the weighted summation of traffic flow densitiesThe method comprises the following steps:
Respectively calculating estimation results of m observers in subsystem i And (3) withIs a difference Δ i-q between:
performing cyclic calculation in each sampling period of subsystem i to obtain m weight combination pairs corresponding to minimum values As final weights:
And substituting the weight combination corresponding to delta i into a formula (14) to obtain a final estimated value of the traffic state of the subsystem i, and obtaining the final estimated value of the traffic state of the whole expressway network.
In summary, the present embodiment provides a highway network operation situation estimation method based on a distributed observer, which defines an interconnection item between all subsystems through system modeling, designs a corresponding traffic state closed-loop observer according to the interconnection item, fully considers the mutual influence of the traffic states between the subsystems, and accurately and comprehensively estimates the traffic states of a large-scale highway network. Specifically, to ensure the solveability of the observer gain matrix, the present embodiment uses an interconnection matrixThe maximum eigenvalue lambda max of (a) is used for obtaining an inequality (7) which is required to be met by an estimation error and an interconnection term, the inequality (7) is applied to S-Procedure management together with an inequality (6) which is required to be gradually stabilized by an observation error system, and the inequality (formulas (8) - (11)) which is required to be jointly met by the interconnection term and an observer gain matrix is obtained, so that a traffic observer which meets the interconnection term is solved.
Fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, and as shown in fig. 3, the device includes a processor 60, a memory 61, an input device 62 and an output device 63; the number of processors 60 in the device may be one or more, one processor 60 being taken as an example in fig. 3; the processor 60, the memory 61, the input means 62 and the output means 63 in the device may be connected by a bus or other means, in fig. 3 by way of example.
The memory 61 is used as a computer readable storage medium for storing a software program, a computer executable program, and a module, such as a program instruction/module corresponding to the method for estimating the running situation of the highway network based on the distributed observer in the embodiment of the present invention. The processor 60 executes various functional applications of the device and data processing by running software programs, instructions and modules stored in the memory 61, i.e. implements the above-described method for estimating the running situation of the highway network based on the distributed observer.
The memory 61 may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, at least one application program required for functions; the storage data area may store data created according to the use of the terminal, etc. In addition, the memory 61 may include high-speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other non-volatile solid-state storage device. In some examples, memory 61 may further comprise memory remotely located relative to processor 60, which may be connected to the device via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The input means 62 may be used to receive entered numeric or character information and to generate key signal inputs related to user settings and function control of the device. The output 63 may comprise a display device such as a display screen.
The embodiment of the invention also provides a computer readable storage medium, on which a computer program is stored, which when being executed by a processor, implements the highway network running situation estimation method based on the distributed observer of any embodiment.
The computer storage media of embodiments of the invention may take the form of any combination of one or more computer-readable media. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or a combination of any of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
The computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, either in baseband or as part of a carrier wave. Such a propagated data signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination of the foregoing. A computer readable signal medium may also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.
Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.
Computer program code for carrying out operations of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, smalltalk, C ++ and conventional procedural programming languages, such as the C-language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any kind of network, including a Local Area Network (LAN) or a Wide Area Network (WAN), or may be connected to an external computer (for example, through the Internet using an Internet service provider).
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.
Claims (7)
1. A highway network operation situation estimation method based on a distributed observer is characterized by comprising the following steps:
according to the interconnection relation among subsystems of the expressway network, the following expressway network traffic state dynamic model is determined:
each subsystem comprises at least one road section, and x (t) and x (t+1) respectively represent traffic states of each subsystem at the time t and the time t+1, wherein the traffic states comprise traffic flow density; u (t) represents the traffic demand of each subsystem at the time t; y (t) represents the measurement output of each subsystem at the time t; The decoupling block matrix is used for representing the transmission rule of the internal traffic state of each subsystem; Representing the interconnection terms between the subsystems, The system is a known matrix constructed according to the transmission rule of the traffic state among all subsystems; b σ(t) is used for representing the influence of traffic demands of all subsystems on traffic states; c is used for representing the relation between the measurement output of each subsystem and the traffic state; f σ(t) represents an affine term;
In the case that the dynamic model is an open loop system, a distributed state observer is constructed as follows:
Wherein, AndRespectively representing the traffic states of the subsystems estimated by each observer at the time t and the time t+1; k σ(t) denotes the observer gain matrix to be determined;
the estimation error system of the distributed state observer is expressed as follows:
Wherein e (t) and e (t+1) respectively represent estimation errors of traffic states of the observer at the time t and the time t+1;
Solving the gain matrix of the observer according to the design principle of the estimation error system and the closed-loop observer with the convergence of the estimation error, and substituting the gain matrix into a formula (4) to obtain a distributed closed-loop observer of the traffic state of the expressway network, wherein the distributed closed-loop observer consists of observers distributed in subsystems;
And measuring the real traffic state of each subsystem at any moment by using the sensing equipment of each subsystem, and estimating the future traffic state of each subsystem by each observer according to the measured real traffic state.
2. The method of claim 1, wherein said solving the observer gain matrix according to the estimation error system and estimation error converging closed-loop observer design principle comprises:
introducing a symmetrical positive definite matrix P, and converting a design principle of a closed-loop observer with estimation error convergence into a constraint condition of energy attenuation of the estimation error along with time;
According to the estimation error system, the constraint condition is converted into the following inequality:
wherein e is an abbreviation for e (t);
Order the And solve forMaximum eigenvalue λ max, gives the inequality that v satisfies:
vTv≤λmaxeTe (7)；
Combining inequality (6) (7) using the S-Procedure theorem: there must be a positive constant μ, which makes the following inequality true:
solving inequality (8) to obtain the observer gain matrix.
3. The method of claim 2, wherein said solving inequality (8) for the observer gain matrix comprises:
converting inequality (8) into a matrix form gives:
Wherein, I represents an identity matrix;
let Q σ(t)＝PKσ(t), Converting inequality (10) into a linear matrix inequality:
Wherein,
Solving inequality (11) by using a linear matrix inequality solver to obtain P and Q σ(t);
Using K σ(t)＝P-1Qσ(t), the observer gain matrix K σ(t) is obtained.
4. The method of claim 1, wherein measuring the actual traffic condition of each subsystem at any one time using the sensing device of each subsystem comprises:
Judging the number m of observable systems in the subsystem i according to the observability judging criterion, and designing m corresponding state observers; estimated value for each observer Setting a weight eta i-q, and calculating the weighted summation result of the traffic states
Computing the estimation results of m observers in a circulating way in each sampling period of the subsystem iAnd (3) withAnd find the weight combination corresponding to the minimum value delta i as the final weight:
and calculating a final estimated value of the traffic state of the subsystem i according to the final weight.
5. The method of claim 1, wherein the sensing device comprises at least one of a radar, a video, a floating car, an ETC gantry, a microwave sensor.
6. An electronic device, comprising:
one or more processors;
A memory for storing one or more programs,
The one or more programs, when executed by the one or more processors, cause the one or more processors to implement the distributed observer-based highway network operation situation estimation method of any one of claims 1-5.
7. A computer readable storage medium, having stored thereon a computer program which when executed by a processor implements the distributed observer-based highway network operation situation estimation method according to any one of claims 1 to 5.
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| CN113538898A (en) * | 2021-06-04 | 2021-10-22 | 南京美慧软件有限公司 | Multisource data-based highway congestion management and control system |
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