Hierarchical and distributed model predictive control method for traffic flow in large-scale urban road networks

Abstract

The present invention discloses a hierarchical and distributed model predictive control method for large-scale urban road network traffic flow, and relates to the technical field of urban road network traffic planning. The method can effectively utilize the MFD-related properties of road network traffic by combining hierarchical control strategy with distributed MPC. When the road network traffic is oversaturated, the control strategy is adopted to maintain the number of vehicles in the road network near an optimal value, and the traffic efficiency of the traffic in the road network is maximized under the premise of alleviating congestion, and the calculation efficiency is guaranteed. The specific scheme is as follows: the urban road network is divided into regions. Data is collected for the regions divided by the road network to obtain the MFD image and properties of the regional road network. The upper controller in the hierarchical MPC is optimized and solved. The lower MPC of the hierarchical strategy is optimized and solved in combination with the distributed MPC. The road network vehicle traffic continues, and from the current moment to the next moment, each sensor continues to collect data, and the optimization steps are repeated to achieve rolling optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of urban road network traffic planning, and in particular to a hierarchical and distributed model prediction and control method for large-scale urban road network traffic flow. Background Art

[0002] At present, the development of vehicle technology and the steady growth of civilian car ownership have led to an increase in traffic congestion. Given that the construction of major urban roads is both difficult and expensive, one of the most effective ways to alleviate congestion is to use traffic signal control to increase the efficiency of existing infrastructure. Reasonable traffic signal control can greatly reduce traffic congestion, thereby improving traffic conditions. In addition, the latest advances in electronics, sensing, information and communication technologies have made it possible to collect and process traffic data in real time and deploy intelligent controllers to achieve efficient operation of the traffic system. For road network control, in order to obtain the optimal traffic signal setting, the online traffic data detected by road sensors is used to obtain the signal light setting scheme that should be adopted at each intersection under the current road network state by solving optimization problems, and the traffic light time of the signal light is used to control the stopping and passing of traffic flow, thereby achieving the traffic efficiency of all sections and intersections under the large-scale road network of the entire city.

[0003] The Macroscopic Fundamental Diagram (MFD) considers the urban traffic network as a whole and describes the characteristics of the network from a general perspective. The introduction of this concept is of great significance for traffic research and management. MFD links the number (or density) of vehicles in the traffic network to the spatial average traffic flow. Therefore, if the urban traffic network is considered as a whole, the MFD can describe the characteristics of the network. On the one hand, these findings make it easier to establish a dynamic model of traffic flow at the network level. On the other hand, researchers can design real-time control strategies based on MFD to alleviate congestion and improve mobility in large-scale urban traffic networks. Model Predictive Control (MPC) is an advanced control method based on optimization ideas that can better cope with uncertainty and nonlinearity and explicitly handle control constraints. It has been widely used in the field of road network traffic flow control and vehicle-road collaboration in urban traffic. MPC methods can generally be divided into two categories: centralized control and distributed control. The centralized controller uses the number of vehicles on all sections of the road network and the duration of traffic lights at all intersections as input for calculation. It is relatively easy to design and can also obtain the global optimal control performance. However, as the scale of the road network increases, the amount of calculation of the centralized controller will increase dramatically, thus affecting the real-time performance of the control. The idea of ​​distributed control is to divide the entire control system into multiple subsystems. Each subsystem uses a traditional controller for a single object. The system is controlled by considering the objectives, constraints and interactions between the subsystems. It has strong scalability and practicality. At the same time, the hierarchical control strategy combines the control of different layers, passes the results to the lower layer after solving the optimization problem of the upper layer, and then continues to solve it. It can effectively realize the conversion between different control quantities and state quantities, and achieve more efficient and stable control effects. Applying MPC control strategy and hierarchical strategy to traffic flow control can effectively take advantage of the superior control performance of MPC.

[0004] Existing MPC traffic flow management methods face several limitations: 1) The combination of hierarchical and distributed control strategies often relies on complex traffic flow models, which become too complex when applied to large-scale urban road networks and need further improvement for better scalability and efficiency. 2) The unique properties of the road network described by MFD are usually ignored in the MPC framework. Therefore, the cost function cannot take into account the characteristics of the network, limiting the ability to fully utilize the network potential. Summary of the invention

[0005] In view of this, the present invention provides a hierarchical and distributed model predictive control method for large-scale urban road network traffic flow, which can effectively utilize the MFD-related properties of road network traffic by combining the hierarchical control strategy with distributed MPC. When the road network traffic is oversaturated, this control strategy is used to maintain the number of vehicles in the road network near a certain optimal value. This can maximize the traffic efficiency of the traffic in the road network while alleviating congestion and ensure computational efficiency.

[0006] To achieve the above object, the technical solution of the present invention is a hierarchical and distributed model predictive control method for traffic flow in a large-scale urban road network, wherein the road network includes a group of intersections connected by roads, and if the number of connected intersections is greater than 4, it is a large-scale urban road network. The method specifically includes the following steps:

[0007] Step 1: Divide the urban road network into regions.

[0008] Step 2: Collect data on the areas divided by the road network to obtain the MFD image and properties of the regional road network.

[0009] Step 3: Optimize and solve the upper-level controller in the hierarchical MPC.

[0010] Step 4: Combine distributed MPC to optimize the lower-level MPC solution of the hierarchical strategy.

[0011] Step 5: Vehicles continue to pass through the road network, moving from the current moment to the next moment, and each sensor continues to collect data, repeating steps 3 to 4 to achieve rolling optimization.

[0012] Furthermore, step 1: divide the urban road network into regions, specifically: divide the urban road network into three regions I, J, and L. The three regions are divided based on the same road network structure, and the division method is not unique; on this basis, the road network is further divided into multiple subsystems with the same structure in each region, and the number of intersections in each subsystem and the distribution method of each intersection are the same.

[0013] Furthermore, step 2: data is collected for the area divided by the road network to obtain the MFD image and properties of the regional road network, specifically:

[0014] In each road section, sensors are used to obtain the d The number of vehicles on each road section n z (k d ), z=1,2,3..., and the traffic volume q of each road section z (k d ), and use this to calculate at time k d The average number of vehicles N in the three areas i (k d ),N j(k d ),N l (k d ), the turning rate r of each lane w leading to the downstream section z wz ,w=1,2,3...Use sensors at the entrances and exits and connections of the area to obtain the traffic exchange volume Q of each area ij (k d ),Q ji (k d ),Q il (k d ),Q li (k d ),Q jl (k d ),Q lj (k d ) and the traffic volume Q flowing into and out of the road network i,in (k d ),Q i,out (k d ),Q j,in (k d ),Q j,out (k d ),Q l,in (k d ),Q l.out (k d ).

[0015] Where Q ij (k d ) is the time k d The traffic exchange volume from area I to area J, Q ji (k d ) is the time k d The traffic exchange volume from inner J area to I area, Q il (k d ) is the time k d The traffic exchange volume from inner I area to L area, Q li (k d ) is the traffic exchange volume from area L to area I, Q jl (k d ) is the traffic exchange volume from area J to area L, Q lj (k d ) is the traffic exchange volume from area L to area J; Q i,in (k d ) is the traffic volume flowing into area I, Q i,out (k d ) is the traffic volume outflowing from area I, Q j,in (k d ) is the traffic volume flowing into area J, Q j,out (k d) is the traffic volume outflowing from area J, Q l,in (k d ) is the traffic volume flowing into area L, Q l.out (k d ) is the traffic flow out of area L.

[0016] Set the value Q of the traffic flow in the road network in the three areas i,in ,Q j,in ,Q l,in A known constant at all times.

[0017] For the three areas I, J, and L divided by the road network, each has a corresponding MFD image and a functional relationship corresponding to the image. The MFD image represents two properties of the traffic flow in the road network. One is the fitting functional relationship between the number of existing vehicles and the passing traffic flow, and the other is the proportional relationship between the passing traffic flow and the traffic flow leaving the road network. The corresponding MFD image is obtained by collecting the relevant quantities of the road network and correspondingly fitting the curve on the coordinate axis. The number of vehicles N corresponding to the maximum passing traffic flow in the road network is further obtained from the functional relationship between the number of vehicles and the passing traffic flow. i,critical , it is known from the existing research on road network MFD that this value is unique.

[0018] Further, step 3: optimizing and solving the upper controller in the hierarchical MPC is performed, specifically:

[0019] The three areas I, J, and L together constitute the control object of the upper-level controller of the hierarchical MPC, with the number of vehicles in the three areas as the state quantity, and the traffic exchange volume between areas and the road network outflow as the control quantity; each subsystem in each area is the control object of the lower-level controller of the hierarchical MPC, and distributed MPC is used for optimization and solution, with the number of vehicles on each road in the subsystem as the state quantity, and the length of the green light time of the traffic lights at each intersection in the subsystem as the control quantity.

[0020] In the case of oversaturated road network, the upper controller uses the number of vehicles N in the current area as the i (k d ),N j (k d ),N l (k d ) is the system state quantity, the regional vehicle flow exchange volume and the road network outflow volume are the control quantities, and the optimization problem design is carried out according to the properties obtained from the MFD images of the three regions.

[0021] The goal of this optimization problem is to improve the vehicle traffic efficiency in each area by utilizing the characteristics of MFD, by maximizing the spatial average traffic flow; the designed objective function consists of two parts: 1) minimizing the number of vehicles in the area; 2) maintaining the number of vehicles in each area at the critical value of MFD to maximize the spatial average traffic flow; the objective function contains the target term of optimizing the number of vehicles and tracking N i,critical , N j,critical and N l,critical The penalty term; the optimization problem is solved by the fmincon solver in MATLAB, and the control sequence Q of the traffic flow is obtained i,out (k d +p|k d ),Q ij (k d +p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d );in is the upper layer prediction time domain, symbol (k d +p|k d ) represents the k-based d Step to k d + prediction of the system state in p steps;

[0022] A set of control sequences within the future p steps is obtained. The control sequence at each moment consists of 9 vehicle flows. The control sequence when p=0 is passed to the lower-level controller.

[0023] Furthermore, in step 3, the basis for judging whether the road network is oversaturated is k d In the step, whether the average number of vehicles in any of the three areas I, J, and L exceeds the number of vehicles corresponding to the maximum traffic flow.

[0024] Further, step 4: combining distributed MPC to optimize and solve the lower-level MPC of the hierarchical strategy, specifically:

[0025] For the three areas I, J, and L, the upper-level controller obtains the optimized control sequence and passes it to the lower-level controller for implementation. At the same time, the lower-level controller needs to specifically optimize the green light time length of the traffic lights in each direction of the intersection and coordinate the traffic capacity of each road in the road network.

[0026] Distributed MPC is used to design the lower-level controller, and the store-and-forward model is selected to establish the mathematical model of each road section.

[0027] For each area, it is further divided into multiple subsystems according to the structure of the road network. The number and distribution of intersections in each subsystem are required to be the same. A distributed MPC controller is designed in each subsystem.

[0028] The lower-level controller completes the following tasks at specific intersections through the control of traffic light signals: (1) the realization of the traffic flow control sequence obtained by the upper-level controller; and (2) the optimization of vehicle traffic on each road section. Therefore, the objective function of the optimization problem solved by the distributed MPC of each subsystem in the lower-level controller needs to be composed of two items.

[0029] After the subsystems are divided in each area, the road sections contained in each subsystem are divided into two categories:

[0030] The first type of road section is a road section that connects the area with the outside world and exchanges vehicles. The outside world here includes the external environment of the entire road network and the adjacent area according to the location of the area. The road section connected to the external environment of the entire road network and exchanges vehicles is controlled by controlling the green light duration of the traffic light to control Q i,out ,Q j,out and Q l,out The realization of the road section connecting adjacent areas and exchanging vehicles is to control the green light duration of the traffic light to control Q ij ,Q il ,Q ji ,Q jl ,Q lj and Q li Implementation.

[0031] The second type of road section is the other road sections connecting various intersections in the subsystem. This type of road section controls the passage of vehicles in the subsystem by controlling the green light duration of the signal, thereby improving the passage efficiency of vehicles in the subsystem.

[0032] In the optimization problem solved by distributed MPC, the cost function designed for the (1) type of road section is to achieve the solution result of the upper-level controller. i,out (k d +p|k d ),Q ij (k d+p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d ), take the control sequence at time p = 0, and the number of vehicles n in each road section z (k d ) is the state quantity, n z (k d ) represents the segment z at step k d The average number of vehicles in the intersection corresponds to the length of time g that the traffic light is green z (k d ) is the control variable, and the objective function of this part is designed; where z represents the road section, which is the (1)th type of road section in each subsystem.

[0033] In the optimization problem solved by distributed MPC, the cost function designed for the (2) type of road section is to optimize the control to improve the traffic efficiency of vehicles in the area, with the number of vehicles n in each road section as the goal. z (k d ) is the state quantity, corresponding to the length of the green light time g at the intersection z (k d ) is the control variable, and the objective function of this part is designed; where z represents the road section, which is the (2) type road section in each subsystem.

[0034] Through the design of objective functions corresponding to the two types of road sections, each road section in a subsystem has its corresponding objective function, and the objective function of the distributed MPC optimization problem that the subsystem needs to solve is obtained by adding the objective functions of each road section.

[0035] In each area, the alternating direction multiplier method ADMM is used to perform collaborative processing between subsystems on each solution result; the global optimization problem is decomposed into multiple sub-problems, local variables and global variables are allowed to be updated alternately, and gradually converge to the global optimum.

[0036] The alternating direction multiplier method ADMM is modified as follows:

[0037] 1) Local optimization: Take the green time of each link as an independent optimization variable, solve the objective function of each link, and obtain the local variable g z .

[0038] 2) Global coordination: The average green light time of all links in the area is introduced as the global variable g to ensure the coordination and balance setting between different links.

[0039] 3) Variable update: Update the Lagrange multiplier to gradually correct the difference between individual green light time and the global average time to ensure the coordination of the entire network.

[0040] Solve and obtain the green light duration control sequence of the traffic lights corresponding to each intersection:

[0041]

[0042] in, is the lower layer prediction time domain, Z is the last item of all road sections z; take the first column and get k d The green light duration at the +1 moment is designed to meet the traffic order, that is, a set of signal light schemes with non-conflicting phases are applied to each intersection. This method is manually designed and directly controls the setting of the signal lights for application.

[0043] Beneficial effects:

[0044] The hierarchical and distributed model predictive control method for traffic flow in a large-scale urban road network provided by the present invention provides a hierarchical and distributed model predictive control method for the problem of traffic flow control in a large-scale urban road network. First, the road network is divided into regions, and the MFD basic properties existing in each regional road network are used to obtain the number of vehicles corresponding to the optimal traffic flow of the road network under the condition of oversaturation of traffic flow passing through the road network, and the proportional relationship between the passing traffic flow and the traffic flow leaving the road network. Then, in the upper-level controller, a centralized MPC design optimization problem is adopted. After solving the inter-regional exchange traffic flow and the traffic flow leaving the road network in the upper-level controller, the relevant control quantity is transmitted to the lower-level controller for implementation. In the lower-level controller, a distributed MPC design optimization problem is adopted to optimize the traffic of vehicles in each section of the subsystem while realizing the upper-level transmission control sequence. The present invention uses MPC to design a control scheme, combined with the functional relationship properties of the road network itself, to achieve the adjustment of the road network traffic capacity through the allocation control of the signal light time scheme under oversaturation, alleviate congestion and optimize the road network traffic efficiency. It is an effective solution to the problem that most existing traffic flow control methods are based on local optimization of a small number of intersections, and their control strategies cannot be extended to large-scale road network traffic flow control in cities; or they directly use centralized or distributed control in large-scale road networks, which fails to fully release the potential of road network traffic in combination with the nature of the road network, and has defects such as complex calculations and poor optimization effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 To design large-scale urban road networks and their regional divisions;

[0046] Figure 2 A schematic diagram of the scale of a single subsystem and the road section structure for dividing the road network area;

[0047] Figure 3 It is a schematic diagram of the phase distribution of signal lights;

[0048] Figure 4 Schematic diagram of traffic exchange between three areas regulated by the upper controller;

[0049] Figure 5 This is the functional relationship between the number of vehicles and the spatial average traffic flow represented by the MFD of the road network under ideal conditions;

[0050] Figure 6(a) and Figure 6(b) are the MFD images of region i;

[0051] Figure 6(c) and Figure 6(d) are MFD images of regions j and l (the road networks in regions j and l have the same properties);

[0052] Figure 7 Designing a control method for the present invention uses a flow chart;

[0053] Figure 8 It is a schematic diagram of a two-layer hierarchical MPC controller;

[0054] Fig. 9 Schematic diagram of distributed MPC used by the lower-level controller;

[0055] Figure 10(a) is a schematic diagram showing the change of the number of vehicles in region i over time under different control strategies;

[0056] Figure 10(b) is a schematic diagram showing the change of the number of vehicles in region j over time under different control strategies;

[0057] Figure 10(c) is a schematic diagram showing the change of the number of vehicles in area l over time under different control strategies;

[0058] Figure 11(a) is a schematic diagram of the weighted traffic flow in area i changing over time under different control strategies;

[0059] Figure 11(b) is a schematic diagram of the weighted traffic flow in area j changing with time under different control strategies;

[0060] Figure 11(c) is a schematic diagram showing the variation of weighted traffic flow in area l over time under different control strategies;

[0061] Fig.12 This is a schematic diagram of the average speed of vehicles in the road network changing with time under different control strategies in the example verification;

[0062] Fig.13 A flow chart of the hierarchical and distributed model predictive control method for large-scale urban road network traffic flow provided by the present invention. DETAILED DESCRIPTION

[0063] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0064] The present invention provides a hierarchical and distributed model predictive control method for traffic flow in a large-scale urban road network provided by the present invention. The road network is a group of intersections connected by roads, two intersections are connected by multiple roads in two directions, and the set of vehicles traveling in the road connection is defined as the traffic flow in the road. When the number of connected intersections is greater than 4, it can be considered to meet the large-scale characteristics, and the number of intersections in a city-scale road network is generally considered to be greater than 10. The specific process of the method is as follows Fig.13 As shown, the technical solution includes:

[0065] Step 1: Divide the road network into regions for hierarchical and distributed control. In order to facilitate the expansion of this method, that is, to involve the exchange of traffic in more regions, the present invention chooses to divide it into three regions, so as to describe the exchange of traffic between multiple regions during the modeling process. Based on the road network structure, the existing large-scale urban road network is divided into three regions: i, j, and l. That is, in the road network, the three regions are divided based on the same road network structure, that is, each region can continue to be divided into a road network structure with the same structure, and the division method is not unique. On this basis, the road network is further divided into multiple subsystems with the same structure in each region, and the number of intersections of each subsystem and the distribution method of each intersection are required to be the same. After obtaining the number of vehicles in each road section in actual time through sensors in each road section, calculate: 1) in step k d (A simulation step actually represents [k d ·T u ,(k d +1)T u The number of vehicles n on each road section within the actual time interval of ] z (k d ), z = 1, 2, 3..., unit: vehicle (veh), obtained by calculating the average value of the number of vehicles in the time interval, where T u is the simulation time corresponding to a single step, which is equal to the duration of the traffic light cycle, in seconds (s); 2) The traffic flow q of each road section z (k d ), unit: veh / s, is calculated by calculating the ratio of the number of vehicles traveling in the road section to the time interval; 3) in step k d The average number of vehicles N in the three areas i (k d ),N j (k d ),N l (k d ), unit: veh, calculated by dividing the n of each road section in the area z (k d ) are added together to obtain the turning rate r of lane w leading to the downstream section z wz ,w=1,2,3..., w,z are two interconnected road sections, and the fixed values ​​that can be assumed in advance are obtained through historical data. At the connection between the entrance and exit of the road network and the outside world and between regions, sensors can also be used to obtain the traffic exchange volume Q of each region ij (k d ),Q ji (k d ),Q il (k d ),Q li (k d ),Q jl (kd ),Q lj (k d ), unit: veh / s, q passing the relevant road section z (k d ) is accumulated, and the traffic flow Q of the road network flowing into and out of the outside world i,in (k d ),Q i,out (k d ),Q j,in (k d ),Q j,out (k d ),Q l,in (k d ),Q l.out (k d ), which is calculated in the same way as the regional traffic exchange volume. Based on historical data, the present invention can also set the value Q of the traffic flow in the road network in the three regions i,in ,Q j,in ,Q l,in It is a known constant at all times. Taking the road network and the traffic flow within it as the control system, in the designed hierarchical and distributed model predictive control strategy, the present invention divides the system into two layers, the upper and lower layers, where the three regions i, j, and l together constitute the control object of the upper controller of the hierarchical MPC, with the number of vehicles in the three regions as the state quantity, and the traffic exchange volume between regions and the road network outflow as the control quantity; each subsystem in each region is the control object of the lower controller of the hierarchical MPC, and the distributed MPC is used for optimization and solution, with the number of vehicles on each road in the subsystem as the state quantity, and the length of the green light time of the signal light at each intersection in the subsystem as the control quantity.

[0066] Step 2: Collect data from the areas divided by the road network to obtain the MFD image and properties of the regional road network. For the three areas i, j, and l divided by the road network, each has a corresponding MFD image and the function relationship corresponding to the image. Taking area i as an example, the MFD image can represent two properties of the traffic flow in the road network. One is the number of vehicles N. i (k d )(unit: veh) and traffic volume (by step k d The q of the entire road network in the inner area z (k d ) is obtained by calculation, unit: veh / s) and the other is the fitting function relationship between the traffic volume (Unit: veh / s) and the vehicle flow D leaving the road network i (k d )(q through the relevant section z (k d) is accumulated, unit: veh / s). By collecting the relevant quantities of the road network and corresponding them on the coordinate axis and fitting the curve, the corresponding MFD image can be obtained. The functional relationship between the number of vehicles and the traffic flow can further obtain the number of vehicles N corresponding to the maximum traffic flow in the road network. i,critical , it is known from the existing research on road network MFD that this value is unique. The main purpose of the upper-level controller is to combine the MFD properties in the area and control the inflow and outflow of vehicles in the area to maintain the number of vehicles in the area at the number of vehicles N corresponding to the maximum traffic flow. i,critical When the road network is oversaturated with vehicles, the invented control strategy can be used to regulate the number of vehicles in each area to optimize the traffic flow.

[0067] The road network traffic flow state function obtained from the road network MFD image can be expressed as: 1)

[0069]

[0070] This means that taking area i as an example, the number of vehicles N in the area i (k d )(unit: veh) and traffic volume (Unit: veh / s). It means that the i region is in k d Traffic flow within the step and the number of vehicles in the area N i (k d ), which is obtained by fitting the MFD image. b are the coefficients of the fitted polynomial, and d is the highest order. 2)

[0072]

[0073] This represents the traffic volume in area i. (Unit: veh / s) and the traffic flow D leaving the area i (k d )(unit: veh / s). The traffic flow leaving the area includes two types of traffic flow: leaving the area to the adjacent area and leaving the area to the external environment of the road network. κ i is the proportional coefficient, which can be obtained by fitting the regional MFD image.

[0074] Step 3: Optimize the upper controller in the hierarchical MPC: In the case of oversaturation of the road network, the upper controller uses the number of vehicles N in the area in the current step i (k d ),Nj (k d ),N l (k d ) is the system state quantity, the regional vehicle flow exchange volume and the road network outflow vehicle flow are the control quantities, and the optimization problem is designed based on the properties obtained from the MFD images of the three regions. The goal of the present invention is to improve the vehicle traffic efficiency in each region by utilizing the characteristics of MFD, especially by maximizing the spatial average traffic flow. Therefore, the designed objective function consists of two parts: 1) Minimize the number of vehicles in the region to alleviate congestion and eliminate network oversaturation; 2) Maintain the number of vehicles in each region at the critical value of MFD to maximize the spatial average traffic flow. The objective function contains the target item of optimizing the number of vehicles and tracking N i,critical , N j,critical and N l,critical The optimization problem is solved by the fmincon solver in MATLAB, and the control sequence Q of the traffic flow is obtained. i,out (k d +p|k d ),Q ij (k d +p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d );in is the upper layer prediction time domain, symbol (k d +p|k d ) represents the k-based d Step to k d +p-step system state prediction. The present invention obtains a set of control sequences within the future p steps, and the control sequence at each moment consists of 9 vehicle flows. The control sequence when p=0 is passed to the lower controller

[0075] In step 3, the traffic volume By k dThe q of all road networks in the area within the step z (k d ) is obtained by calculation, which is specifically expressed as:

[0076]

[0077] is the set of regional road segments, l z is the length of the road segment.

[0078] Among them, in step 3, the basis for judging the oversaturation of the road network is k d In step i, j, l, is there any area with an average number of vehicles exceeding the number of vehicles N corresponding to the maximum traffic flow? i,critical , N j,critical and N l,critical .

[0079] Among them, in step 3, the upper controller performs inter-regional traffic exchange and outflow traffic control for the three regions, adopts centralized control, and the optimization problem is constructed as:

[0080] J upper =J TTS +αJ pen

[0081] in

[0082]

[0083] is the objective term for optimizing the number of vehicles.

[0084]

[0085] To track N i,critical , N j,critical and N l,critical α is the penalty term coefficient, M is the set of divided regions, T u is the actual time corresponding to the step control duration. The equality constraint corresponding to the optimization problem can be composed of the following parts.

[0086] The equality constraints formed by the prediction equation for the number of vehicles in the area are:

[0087] N i (k d +p+1|k d )=N i (k d +p|k d )+T u ·{[Q i,in (k d +p|k d )-Q i,out (kd +p|k d )]

[0088] +[Q ji (k d +p|k d )-Q ij (k d +p|k d )]+[Q il (k d +p|k d )-Q li (k d +p|k d )]}

[0089] N j (k d +p+1|k d )=N j (k d +p|k d )+T u ·{[Q j,in (k d +p|k d )-Q j,out (k d +p|k d )]+[Q ij (k d +p|k d )-Q ji (k d +p|k d )]+[Q lj (k d +p|k d )-Q jl (k d +p|k d )]}

[0090] N l (k d +p+1|k d )=N l (k d +p|k d )+T u ·{[Q l,in (k d +p|k d )-Q l,out (k d +p|k d )]+[Q il (k d +p|k d )-Q li (k d+p|k d )]+[Q jl (k d +p|k d )-Q lj (k d +p|k d )]}

[0091] The equality constraints formed by the road network properties obtained by the MFD image fitting function are:

[0092]

[0093] D i (k d +p|k d )=Q i,out (k d +p|k d )+Q ij (k d +p|k d )+Q il (k d +p|k d )

[0094]

[0095] D j (k d +p|k d )=Q j,out (k d +p|k d )+Q ji (k d +p|k d )+Q jl (k d +p|k d )

[0096]

[0097] D l (k d +p|k d )=Q l,out (k d +p|k d )+Q li (k d +p|k d )+Q lj (k d +p|k d ) bi ,a' bj and a' b ' lis the multi-term coefficient of the functional relationship between the number of vehicles and the traffic flow obtained from the MFD image, d i ,d j and d l is the highest term, κ i ,κ j and κ l It is the proportional coefficient between the traffic flow within the road network and the traffic flow leaving the road network.

[0098] The inequality constraints of the optimization problem are composed of the intervals of traffic flow in the region, with i → Take the inequality constraint of the traffic exchange volume in area j as an example:

[0099] 0≤Q ij (k d +p|k d )≤m ij ·q s,ij

[0100] Where m ij is the number of lanes for vehicles traveling from i to j, q s,ij is the maximum traffic flow of a lane for vehicles traveling from i to area j, and this value can be directly obtained through historical data. Similarly, the present invention can obtain the inequality constraints of the exchange direction of traffic between other areas and the outflow of traffic to the road network.

[0101] The objective function and constraints (equality constraints and inequality constraints) together constitute the optimization problem that the upper-level controller needs to solve. The solver is used to solve the optimization problem to obtain the required control sequence Q i,out (k d +p|k d ), Q ij (k d +p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ) and Q li (k d +p|k d), take the control sequence at time p=0 and pass it to the lower controller.

[0102] Step 4: Combine distributed MPC to optimize the lower-level MPC solution of the hierarchical strategy. For the three regions i, j, and l, after the upper-level controller obtains the optimized control sequence, it is passed to the lower-level controller for implementation. At the same time, the lower-level controller needs to specifically optimize the length of the green light time of the traffic lights in each direction of the intersection and coordinate the traffic capacity of each road in the road network. Although the overall road network has been divided into three regions, there are still a large number of road sections and intersections in each region. Directly using centralized control in the lower-level controller has the disadvantages of large computational complexity and complex interaction between each intersection. Therefore, distributed MPC is used to design the lower-level controller, and the store-and-forward model is used to establish the mathematical model of each road section. For each region, it is further divided into multiple subsystems according to the structure of the road network. The number and distribution of intersections in each subsystem are required to be the same. A distributed MPC controller is designed in each subsystem. The lower-level controller completes the following tasks at specific intersections through the control of traffic light signals: (1) the implementation of the traffic flow control sequence obtained by the upper-level controller; (2) the optimization of vehicle traffic in each section. Therefore, the objective function of the optimization problem solved by the distributed MPC of each subsystem in the lower-level controller needs to be composed of two terms.

[0103] After the subsystems are divided in each area, the road sections in each subsystem can be divided into two categories: (1) Road sections that connect the area with the outside world and exchange vehicles. The outside world here includes the external environment of the entire road network and adjacent areas according to the location of the area. The road sections that are connected to the external environment of the entire road network and exchange vehicles are controlled by controlling the green light duration of the signal light to control Q i,out ,Q j,out and Q l,out The realization of the road section connecting adjacent areas and exchanging vehicles is to control the green light duration of the traffic light to control Q ij ,Q il ,Q ji ,Q jl ,Q lj and Q li (2) The remaining sections connecting the intersections in the subsystem. This type of section controls the passage of vehicles in the subsystem by controlling the green light duration of the signal, thereby improving the passage efficiency of vehicles in the subsystem, such as the passage time and average speed. Therefore, in the optimization problem solved by the distributed MPC, the cost function designed for the section (1) should be aimed at achieving the solution result of the upper-level controller, according to the Q obtained by the upper-level MPC. i,out (k d +p|k d ),Q ij (k d +p|k d ),Qil (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d ), take the control sequence at time p = 0, and the number of vehicles n in each road section z (k d ) is the state quantity, n z (k d ) represents the segment z at step k d The average number of vehicles in the intersection corresponds to the length of time g that the traffic light is green z (k d ) is the control quantity, and the objective function of this part is designed. Where z represents the road section, which is the (1)th type of road section in each subsystem. In the optimization problem solved by distributed MPC, the cost function designed for the (2)th type of road section should be aimed at optimizing control to improve the traffic efficiency of vehicles in the area, with the number of vehicles n in each road section as the goal. z (k d ) is the state quantity, corresponding to the length of the green light time g at the intersection z (k d) is the control variable, and the objective function of this part is designed. Wherein z represents the road section, which is the (2)th type of road section in each subsystem. Through the design of the objective functions corresponding to the two types of road sections, each road section in a subsystem has its corresponding objective function, and the objective function of the distributed MPC optimization problem that the subsystem needs to solve can be obtained by adding the objective functions of each road section. In each area, due to the mutual dependence of traffic flows between road links, directly solving the distributed problem of each subsystem cannot guarantee the global optimal solution. In order to solve this problem, the present invention adopts the alternating direction multiplier method (ADMM) to perform collaborative processing between subsystems on each solution result. The global optimization problem is decomposed into multiple subproblems. This method allows local variables and global variables to be updated alternately and gradually converge to the global optimum. In order to make the traditional ADMM better adapt to the traffic flow optimization problem, the present invention makes the following modifications: 1) Local optimization: The green light time of each link is taken as an independent optimization variable, and the objective function of each link is solved to obtain the local variable g z 2) Global coordination: The present invention introduces the average green time of all links in the region as a global variable g to ensure coordination and balance between different links. 3) Variable update: The present invention updates the Lagrange multiplier to gradually correct the difference between individual green time and the global average time, ensuring the coordination of the entire network.

[0104] Solve and obtain the green light duration control sequence of the traffic lights corresponding to each intersection:

[0105]

[0106] in, is the lower layer prediction time domain, and Z is the last item of all road segments z. Take the first column and get k d The green light duration at the +1 moment is designed to meet the traffic order, that is, a set of signal light schemes with non-conflicting phases are applied to each intersection. This method is manually designed and directly controls the setting of the signal lights for application.

[0107] The store-and-forward model in step 4 can be described as:

[0108]

[0109] where n z (k d ) represents the segment z at step k d Average number of vehicles in is the lower layer prediction time domain; w, z are both road segments within the subsystem and the two road segments are connected to each other. represents w as an upstream segment of z; is the set of upstream sections of z; r wz represents the turning rate of lane w leading to the downstream section z, which is a constant value; q w and q z represents the departure flow of the two road segments, which is calculated as the average number of vehicles leaving the road segment within the simulation step in the actual time interval. The model also needs to meet the following constraints:

[0110] 1) The outgoing flow q converted from the green light time z The equality constraints are:

[0111] q z (k d +p|k d )=S z ·g z (k d +p|k d )

[0112]

[0113] Among them, S z is the saturated traffic flow of section z, which can be obtained from historical data, in units of veh / s. At an intersection, the traffic light cycle is divided into multiple phases, and the traffic lights of each section in each phase have different colors and times, so as to determine the traffic rules that will not cause traffic conflicts. z Represents the green light time allocated to section z, which is the sum of the green light times of section z in different phases within a traffic light cycle. Contains the phase when the downstream traffic light color of section z is green, g P Indicates the green light time corresponding to the P phase.

[0114] 2) To ensure that the green light time of road section z is fully utilized, it is necessary to wait for enough vehicles to pass through, so the inequality constraint must be satisfied:

[0115] q z (k d +p|k d )≤n z (k d +p|k d )

[0116] 3) To ensure that the vehicle meets the traffic conditions, the following inequality constraints exist:

[0117]

[0118] is the maximum number of vehicles that road section z can accommodate, which is a known constant.

[0119] 4) Inequality constraints on the range of green light duration:

[0120]

[0121] The maximum time that the green light at the downstream intersection can be set when vehicles pass through section z.

[0122] Among them, the distributed MPC optimization problem of each subsystem solved by the lower-level controller in step 4 can be described as the addition of the objective functions of the two types of road sections, and the same constraints are used.

[0123] The first type of road section in the subsystem is responsible for connecting the area with the outside world and exchanging vehicles. The outside world here includes the external environment of the entire road network and adjacent areas according to the location of the area. Traffic flow is controlled by traffic lights to achieve the control sequence obtained by the upper controller. Taking subsystem i1 in area i as an example, if there is a road section responsible for connecting areas i and j, its objective function is designed as:

[0124]

[0125] is the set of road segments connecting areas i and j in subsystem i1; Q ij The value of is the first item obtained from the corresponding upper layer, that is, Q ij (k d |k d );m ij Take the number of road sections connecting areas i and j in this subsystem, that is, The number of road segments.

[0126] By adding Q ij and m ij By replacing the corresponding values ​​of other (1)-type road sections, we can obtain the corresponding objective functions of all (1)-type road sections in each area and subsystem of the road network.

[0127]

[0128] represents the corresponding objective function of the road section connecting the two areas i and l in the subsystem i1. The present invention can thus design the objective function for each road section of type (1). In each subsystem, by adding the objective functions of all the road sections of type (1), the first term in the objective function of the distributed MPC optimization problem can be obtained, that is,

[0129] Ψ(k d )=Ψ (1) (k d )+Ψ (2) (k d )+...

[0130] The second type of road section in the subsystem belongs to all other road sections except the first type. It is responsible for connecting various intersections and controlling the passage of vehicles in the subsystem by controlling the green light duration of signals, thereby improving the passage efficiency of vehicles in it. For the second type of road section in one of the subsystems, its objective function is designed as:

[0131]

[0132] The objective function consists of the following items:

[0133]

[0134] is the set of the (2) type of road sections in the subsystem, is the maximum number of vehicles on road section z. Function Φ (1) (k d ) represents the occupancy rate of vehicles in the road section, Φ (2) (k d ) represents the travel time of vehicles in the road section, Φ (3) (k d ) represents the number of redundant vehicles (without driving action) in the road section, and the three are related by the coefficient α z,p , β z,p , γ z,p (determined by the target expected value of the above three functions, which is a constant) after transformation and superposition, they together form the target function of the second type of road section, that is, Φ(k d ) shown in the form.

[0135] Therefore, the objective function of the optimization problem that needs to be solved for a subsystem is expressed as:

[0136] J lower =Ψ(k d )+Φ(k d )

[0137] The constraints of this optimization problem are that each of the (2) type sections must satisfy all the constraints that the store-and-forward model shown above needs to satisfy. The optimization problem thus constructed uses the ADMM algorithm to handle the coupling and coordination problems of each subsystem, and uses MATLAB to write a program to call the solver for solving. The improved algorithm steps of the ADMM algorithm used are shown in the attached figure.

[0138] The distributed MPC problem solved by the lower controller has a state quantity of the number of vehicles n on each road section. z and traffic flow q z , the control quantity is the green light time length g of the traffic lights on each road section z It should be noted that q z(k d ) is defined in the lower controller as the time interval k d The number of vehicles leaving road section z in , unit: veh.

[0139] Step 5: Continue the vehicle traffic on the road network, starting from the current k d Time advances to k d At time +1, each sensor collects data, let k d +1→k d , repeat steps 3 to 4 to achieve rolling optimization.

[0140] Embodiment 1: This example is completed with the help of MATLAB and VISSIM simulation platform.

[0141] Step 1.1 Establish a simulated road network and divide it into areas and subsystems, and determine the phase of the traffic lights:

[0142] The urban road network is considered to be a set of intersections connected by roads. Each road consists of one or more lanes, and traffic lights are used at the intersections to control vehicles to pass in different directions. The road network is a set of intersections connected by roads, two intersections are connected by multiple roads in two directions, and the set of vehicles traveling within the road connection is defined as the traffic flow within the road. Here, the present invention defines an intersection as a common intersection area of ​​different roads, and traffic lights are used at the intersections to control traffic flows in different directions.

[0143] like Figure 1 , establish a large-scale urban traffic network in the VISSIM traffic simulation platform. Figure 1 The design shown includes a total of 32 intersections, each of which is connected by a two-way lane. Figure 1 The black dotted lines show that the road network is divided into three areas: i, j, and l. It can be seen that area i contains 16 intersections, and areas j and l each contain 8 intersections. The present invention defines the basic road segment connection as Figure 2 The structure shown is an example of a city network consisting of four intersections. By superimposing the same structure, the present invention can obtain Figure 1 The overall road network shown. Figure 1 The area enclosed by the white dashed line meets Figure 2 The structure of Figure 1 Other intersections are formed by overlapping and connecting these areas. Figure 2 The structure shown is a subsystem structure, which is divided into several subsystems for distributed MPC design. Figure 2 The four intersections and their interconnected sections are considered as a subsystem road network, and each subsystem has exactly the same road network structure. Figure 1 and Figure 2The design of all road sections and intersections in the simulated road network can be obtained. In a traffic light controlled node, a set of traffic flows needs to follow the different traffic permits issued by the traffic lights to avoid conflicts. Such a set of traffic light signal changes is called a signal phase. In a subsystem, the corresponding relationship between the signal phase and the corresponding traffic order is given by Figure 3 Listed, the subsequent steps of manually designing the signal light scheme need to be designed according to the green light time and the phase relationship. At the same time, the design introduces traffic flow at each entrance of the road network, Q i,in =14×800=11200veh / h, Q j,in =8×800=6400veh / h, Q l,in =6×800=6400veh / h. The maximum vehicle speed is designed to be 100km / h, and the distance between adjacent intersections is 500m. The traffic interaction between the three areas and between the road network and the outside world is as follows Figure 4 shown.

[0144] Step 2.1 Draw the MFD image to obtain the basic properties and parameters of the road network:

[0145] The MFD image of the road network traffic flow also includes the relationship between the traffic volume entering the road network and the traffic volume leaving the road network. Previous studies have shown that in a traffic network connected by multiple intersections and sections, certain state quantities of the traffic flow when vehicles pass through satisfy certain functional relationships, such as Figure 5 As shown in the ideal case, the functional relationship between the number of vehicles and the spatial average traffic flow can be approximately expressed by a multi-term function with a unique maximum point. At the same time, there is a certain proportional relationship between the traffic flow through the road network and the traffic flow leaving the road network.

[0146] By collecting and fitting the data of spatial average traffic flow and traffic flow leaving the road network in three areas with different numbers of vehicles in the VISSIM platform, we can get the following results: Figure 6(a) to Figure 6(d) The MFD image shown. The data relationship of region i is shown below:

[0147]

[0148]

[0149] Where N i (k d ) represents region i k d The average number of vehicles in the space within the step, in veh, represents the average traffic volume in area i, in veh / s, D i Indicates the traffic volume leaving the road network, in veh / s, d i is the highest exponent of the polynomial, are polynomial coefficients, κi is the proportionality coefficient. From Figure 6(a) and Figure 6(b), we can get: i =5,a5=-2.404914×10 -17 ,a4=2.070999×10 -13 ,a3=-6.163690×10 -10 ,a2=5.037646×10 -7 ,a1=4.214855×10 -4 ,a0=-3.211271×10 -2 ,1 / κ i =0.068786, when the spatial average traffic flow is the largest, the corresponding number of vehicles is 1431.

[0150] Similarly, the j and l regions can be obtained

[0151]

[0152] d j =5,a'5=2.784146×10 -17 ,a'4=-1.276308×10 -13 ,a'3=2.304215×10 -10 , a'2=-3.8293×10 -7 ,a'1=3.901908×10 -4 ,a'0=-2.17964×10 -2 ,1 / κ j = 0.024461, when the spatial average traffic volume is the largest, the corresponding number of vehicles is 843. As shown in Figure 6(c) and Figure 6(d).

[0153]

[0154] d l =5,a'5'=2.784146×10 -17 ,a'4'=-1.276308×10 -13 ,a'3'=2.304215×10 -10 , a'2'=-3.8293×10 -7 ,a'1'=3.901908×10 -4 ,a'0'=-2.17964×10 -2 ,1 / κ l =0.024461, when the spatial average traffic flow is the largest, the corresponding number of vehicles is 843.

[0155] Step 3.1 Choose whether to trigger the hierarchical distributed MPC controller

[0156] The conditions and process for triggering the hierarchical distributed MPC controller are as follows: Figure 7 shown.

[0157] Step 3.2 Perform hierarchical control and design the upper controller

[0158] The hierarchical control framework is shown as follows Figure 8 As shown, the upper controller adopts centralized control, and its main purpose is to combine the MFD properties in the area and control the inflow and outflow of vehicles in the area to maintain the number of vehicles in the area at the number of vehicles corresponding to the maximum traffic flow. From step 2.1, we can see that N i,critical =1431,N j,critical =843,N l,critical = 843. When the vehicle is oversaturated in the road network, the model predictive control method used in the invention can be used to adjust the number of vehicles to achieve optimal traffic flow.

[0159] The upper controller performs inter-regional traffic exchange and outflow traffic control for the three regions, using centralized control. The optimization problem is constructed as follows:

[0160] J upper =J TTS +αJ pen

[0161] in

[0162]

[0163] Where α is the coefficient of the penalty term, M is the set of divided regions, that is, M = {i, j, l}, T u is the actual time corresponding to the step control duration. In this example, the target expected value is α=0.25, T u =30s. The equality constraints corresponding to the optimization problem can be composed of the following parts.

[0164] The equality constraints formed by the prediction equation for the number of vehicles in the area are:

[0165] N i (k d +p+1|k d )=N i (k d +p|k d )+T u ·{[Q i,in (k d +p|k d )-Q i,out (k d +p|k d )]

[0166] +[Qji (k d +p|k d )-Q ij (k d +p|k d )]+[Q il (k d +p|k d )-Q li (k d +p|k d )]}

[0167] N j (k d +p+1|k d )=N j (k d +p|k d )+T u ·{[Q j,in (k d +p|k d )-Q j,out (k d +p|k d )]

[0168] +[Q ij (k d +p|k d )-Q ji (k d +p|k d )]+[Q lj (k d +p|k d )-Q jl (k d +p|k d )]}

[0169] N l (k d +p+1|k d )=N l (k d +p|k d )+T u ·{[Q l,in (k d +p|k d )-Q l,out (k d +p|k d )]

[0170] +[Q il (k d +p|k d )-Q li (k d +p|kd )]+[Q jl (k d +p|k d )-Q lj (k d +p|k d )]}

[0171] The equality constraints of the road network properties obtained from the MFD image are:

[0172]

[0173] D i (k d +p|k d )=Q i,out (k d +p|k d )+Q ij (k d +p|k d )+Q il (k d +p|k d )

[0174]

[0175] D j (k d +p|k d )=Q j,out (k d +p|k d )+Q ji (k d +p|k d )+Q jl (k d +p|k d )

[0176]

[0177] D l (k d +p|k d )=Q l,out (k d +p|k d )+Q li (k d +p|k d )+Q lj (k d +p|k d )

[0178] The inequality constraints of the optimization problem are composed of the intervals of traffic flow in the region. Take the inequality constraint of the traffic exchange volume in the i→j region as an example:

[0179] 0≤Q ij (k d +p|k d )≤m ij ·q s,ij

[0180] Where m ij is the number of lanes for vehicles traveling from i to j, q s,ij is the maximum traffic flow that a lane can carry for vehicles traveling from i to j. Figure 1 and Figure 2 The road network diagram shown is m ij =m il =m ji =m li =m jl =4,m lj =2,m i,out =14,m j,out =6,m l,out =8, q is obtained from the simulation data s,ij =q s,il =q s,i,out =0.6veh / s,q s,ji =q s,jl =q s,j,out =q s,li =q s,lj =q s,l,out =0.14veh / s. Similarly, the present invention can obtain the inequality constraints of the exchange directions of vehicle flows between other areas and the outflow of vehicle flows outside the road network.

[0181] Step 3.3 Solve the optimization problem required by the upper-level controller

[0182] The upper controller uses the number of vehicles N in the area in the current simulation step i (k d ),N j (k d ),N l (k d ) is the system state quantity, and the control sequence Q of the vehicle flow is obtained by solving i,out (k d +p|k d ),Q ij (k d +p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d+p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d );in The invention obtains a set of control sequences at time p in the future, and each control sequence at a time is composed of 9 vehicle flows. The control sequence at p=0 is passed to the lower controller.

[0183] Step 4.1 Classify the road segments within the subsystems that each agent of the lower-level controller is responsible for

[0184] For the lower-level controller, the subsystems are further divided into three regions: i, j, and l, and then the distributed MPC control is used to achieve optimization. The distributed MPC control is as follows: Fig. 9 shown.

[0185] There are multiple road sections in a large-scale urban road network. In a subsystem of the road network, each road section can be divided into two categories: (1) The road section that connects the area with the outside world and exchanges vehicles. The outside world here includes the external environment of the entire road network and the adjacent area according to the location of the area. The road section that is connected to the external environment of the entire road network and exchanges vehicles is controlled by controlling the green light duration of the signal light to control Q i,out ,Q j,out and Q l,out The realization of the road section connecting adjacent areas and exchanging vehicles is to control the green light duration of the traffic light to control Q ij ,Q il ,Q ji ,Q jl ,Q lj and Q li (2) The remaining sections connecting the various intersections in the subsystem. This type of section controls the passage of vehicles in the subsystem by controlling the green light duration of the signal, thereby improving the passage efficiency of vehicles in the subsystem, such as the passage time and average speed. Figure 1 The white dashed area Figure 2The road network shown is taken as a subsystem. For example, the road sections of category (1) are 1, 12, 13, 14, 17, 30, 31, 32, and the road sections of category (2) are 4, 5, 6, 7, 8, 9, 10, 11, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36. In this way, the road sections in all subsystems of the three regions are classified.

[0186] Step 4.2 Establish a store-and-forward model for the road sections in each subsystem

[0187] The store-and-forward model of road segment z can be described as:

[0188]

[0189] n z (k d ) represents the segment z at step k d Average number of vehicles in is the lower layer prediction time domain; w, z are both road segments within the subsystem and the two road segments are connected to each other. represents w as an upstream segment of z; is the set of upstream sections of z; r wz represents the turning rate of lane w leading to the downstream section z, which is a constant value; q w and q z represents the departure flow of the two road segments, which is calculated as the average number of vehicles leaving the road segment within the simulation step in the actual time interval. The model also needs to meet the following constraints:

[0190] 1) The outgoing flow q converted from the green light time z The equality constraints are:

[0191] q z (k d +p|k d )=S z ·g z (k d +p|k d )

[0192]

[0193] Among them, S z is the saturated traffic flow of section z, which can be obtained from historical data, in units of veh / s. At an intersection, the traffic light cycle is divided into multiple phases, and the traffic lights of each section in each phase have different colors and times, so as to determine the traffic rules that will not cause traffic conflicts. z Represents the green light time allocated to section z, which is the sum of the green light times of section z in different phases within a traffic light cycle. Contains the phase when the downstream traffic light color of section z is green, g P Indicates the green light time corresponding to the P phase.

[0194] 2) To ensure that the green light time of road section z is fully utilized, it is necessary to wait for enough vehicles to pass through, so the inequality constraint must be satisfied:

[0195] q z (k d +p|k d )≤n z (k d +p|k d )

[0196] 3) To ensure that the vehicle meets the traffic conditions, the following inequality constraints exist:

[0197]

[0198] is the maximum number of vehicles that road section z can accommodate, which is a known constant.

[0199] 4) Inequality constraints on the range of green light duration:

[0200]

[0201] The maximum time that the green light at the downstream intersection can be set when vehicles pass through section z.

[0202] Step 4.3 Design the objective function for the (1) type of road section in the subsystem

[0203] The first type of road section in the subsystem is responsible for connecting the area with the outside world and exchanging vehicles. The outside world here includes the external environment of the entire road network and adjacent areas according to the location of the area. Traffic flow is controlled by traffic lights to achieve the control sequence obtained by the upper controller. Taking subsystem i1 in area i as an example, if there is a road section responsible for connecting areas i and j, its objective function is designed as:

[0204]

[0205] is the set of road segments connecting areas i and j in subsystem i1; Q ij The value of is the first item obtained from the corresponding upper layer, that is, Q ij (k d |k d );m ij Take the number of road sections connecting areas i and j in this subsystem, that is, The number of road segments.

[0206] By adding Q ij and m ij By replacing the corresponding values ​​of other (1)-type road sections, we can obtain the corresponding objective functions of all (1)-type road sections in each area and subsystem of the road network.

[0207]

[0208] represents the corresponding objective function of the road section connecting the two areas i and l in the subsystem i1. The present invention can thus design the objective function for each road section of type (1). In each subsystem, by adding the objective functions of all the road sections of type (1), the first term in the objective function of the distributed MPC optimization problem can be obtained, that is,

[0209] Ψ(k d )=Ψ (1) (k d )+Ψ (2) (k d )+...

[0210] Step 4.4 Design the objective function for the (2) type of road section in the subsystem

[0211] The second type of road section in the subsystem belongs to all other road sections except the first type. It is responsible for connecting various intersections and controlling the passage of vehicles in the subsystem by controlling the green light duration of signals, thereby improving the passage efficiency of vehicles in it. For the second type of road section in one of the subsystems, its objective function is designed as:

[0212]

[0213] The objective function consists of the following items:

[0214]

[0215] is the set of the (2)th type of road sections in the subsystem, n z is the maximum number of vehicles on road section z. Function Φ (1) (k d ) represents the occupancy rate of vehicles in the road section, Φ (2) (k d ) represents the travel time of vehicles in the road section, Φ (3) (k d ) represents the number of redundant vehicles (without driving action) in the road section, and the three are related by the coefficient α z,p , β z,p , γ z,p After transformation and superposition, they together form the objective function of the second type of road section, namely Φ(k d) is shown in the form. According to the weights of different items, in this example, α z,p =1,β z,p =0.5,γ z,p =0.3.

[0216] Step 4.5 Construct the distributed MPC optimization problem of the subsystem

[0217] The objective functions of the (1st) and (2nd) road sections in the subsystem are obtained from steps 4.3 and 4.4, so the DMPC optimization problem of the subsystem constructed by the present invention is:

[0218] J lower =Ψ(k d )+Φ(k d )

[0219] The constraints of this optimization problem are the constraints that all road sections of type (2) need to satisfy for the storage-and-forward model established in step 4.2.

[0220] Step 4.6 Improve the ADMM algorithm and apply it to solve the distributed MPC optimization problem in each region

[0221] In distributed MPC, since there are multiple subsystems in each area, there is a coupling problem between subsystems in the optimization solution. The ADMM algorithm is used to perform collaborative processing between subsystems on each solution result to solve the coupling problem between systems, where λ is the Lagrange multiplier.

[0222] Step 4.7: The obtained control sequence is designed to satisfy Figure 3 The phase-distributed signal light timing scheme is applied to each intersection of the road network.

[0223] In step 4.6, the ADMM algorithm is used to call the relevant solver tool in MATLAB to solve the green light duration control sequence of the traffic lights corresponding to each intersection:

[0224]

[0225] in, is the lower layer prediction time domain, and Z is the last item of all road segments z. Take the first column and get k d The predicted green light duration at each moment is designed to meet the traffic order, i.e. Figure 3 A set of signal light schemes with non-conflicting phases is shown and applied to each intersection. Figure 3 The green light phases of four intersections in a subsystem are shown. The green lights of all intersections in the road network need to be set accordingly, which can be achieved by directly adjusting the signal light settings.

[0226] Step 5: Continue the vehicle traffic on the road network, starting from the current kd Time advances to k d At time +1, each sensor collects data, let k d +1→k d , repeat steps 3.1 to 4.7 to achieve rolling optimization.

[0227] In order to better demonstrate the effectiveness of the present invention, the traffic flow control results of the hierarchical and distributed model predictive control (hereinafter referred to as hierarchical distributed MPC) method in the present invention are compared with the other two control methods:

[0228] 1) Use only distributed MPC: For large-scale urban road networks, directly divide them into multiple Figure 2 After the subsystem is shown, distributed MPC is used to solve the distributed MPC optimization problem shown in steps 4.1 to 4.7. That is, without using hierarchical MPC and MFD properties, the following optimization problem is solved directly:

[0229] J lower =Ψ(k d )+Φ(k d )

[0230] Constraints:

[0231]

[0232] q z (k d +p|k d )=S z ·g z (k d +p|k d )

[0233]

[0234] q z (k d +p|k d )≤n z (k d +p|k d )

[0235]

[0236] Where z is the road section within the subsystem, and all constraints are z represents the constraint set of each road section in the subsystem.

[0237] 2) Fixed-time traffic light control: that is, no control scheme is used to change the traffic light timing during the road network traffic, and only one set of timing scheme is used to control the traffic of vehicles at each intersection, which is in line with traditional road network traffic control in most cases.

[0238] Figure 10(a) is a schematic diagram of the change of the number of vehicles in area i under different control strategies in the example verification; Figure 10(b) is a schematic diagram of the change of the number of vehicles in area j under different control strategies in the example verification; Figure 10(c) is a schematic diagram of the change of the number of vehicles in area l under different control strategies in the example verification. It can be seen from the changes of vehicles in the three areas that in the state of vehicle oversaturation, the hierarchical distributed MPC can effectively control the number of vehicles to fluctuate around the number of vehicles corresponding to the maximum traffic flow obtained from the MFD image. Only using distributed MPC through traffic lights can also control the number of vehicles to decrease to alleviate congestion, while fixed-time traffic light control cannot control the road network system after oversaturation occurs, and the number of vehicles will remain in the oversaturated state.

[0239] Figure 11(a) is a schematic diagram of the weighted traffic flow of area i under different control strategies in the example verification; Figure 11(b) is a schematic diagram of the weighted traffic flow of area j under different control strategies in the example verification; Figure 11(c) is a schematic diagram of the weighted traffic flow of area l under different control strategies in the example verification. It can be seen from the weighted traffic flow that before the vehicle oversaturation occurs, the traffic flow has experienced an increase and then a decrease, which is consistent with the road network properties revealed by MFD. After that, the weighted traffic flow can be effectively maintained at the maximum value by using hierarchical distributed MPC to control the road network traffic flow; while only using distributed MPC will excessively reduce the number of vehicles. Although congestion is reduced, the traffic flow carrying capacity of the road network is also wasted; the weighted traffic flow change controlled by fixed-time traffic lights is similar to Figure 11, both of which are stable and have no increase.

[0240] Fig.12 The diagram is a schematic diagram of the average speed of vehicles in the road network changing over time under different control strategies in the example verification. Both the layered + distributed MPC and the single distributed MPC effectively increase the average speed of vehicles after oversaturation, and the speed of vehicles in their traffic flow is significantly higher than that of the strategy without control lights.

[0241] In addition, the following table shows the average road occupancy rate of the road network using three control strategies after oversaturation:

[0242]

[0243] It can be seen from the table that the road occupancy rate decreases after using hierarchical distributed MPC.

[0244] Combined with the test results, when the road network is oversaturated with traffic, the use of hierarchical distributed MPC can maintain the number of vehicles in the road network near the optimal value, which can maximize the traffic efficiency of the road network while alleviating congestion.

[0245] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A hierarchical and distributed model predictive control method for large-scale urban road network traffic flow, characterized in that: The road network includes a group of intersections connected by roads. If the number of connected intersections is greater than 4, it is a large-scale urban road network. The method specifically includes the following steps: Step 1: Divide the urban road network into three areas: I, J, and L; Step 2: Collect data on the area divided by the road network to obtain the MFD image and properties of the regional road network; Step 3: Optimize and solve the upper controller in the hierarchical MPC, specifically: the three regions I, J, and L together constitute the control object of the upper controller of the hierarchical MPC, with the number of vehicles in the three regions as the state quantity, and the traffic exchange volume between regions and the road network outflow as the control quantity; the goal of the optimization problem is to improve the vehicle traffic efficiency in each region by utilizing the characteristics of MFD, and to maximize the spatial average traffic flow; the designed objective function consists of two parts: 1) minimize the number of vehicles in the region; 2) maintain the number of vehicles in each region at the critical value of MFD to maximize the spatial average traffic flow; Step 4: Combine distributed MPC to optimize the lower-level MPC of the hierarchical strategy; Each subsystem in each area is the control object of the lower controller of the hierarchical MPC, and the distributed MPC is used for optimization and solution, with the number of vehicles on each road in the subsystem as the state quantity and the length of the green light time of each intersection in the subsystem as the control quantity; Step 5: Vehicles continue to pass through the road network, and from the current moment to the next moment, each sensor continues to collect data, and steps 3 to 4 are repeated to achieve rolling optimization.

2. The hierarchical and distributed model predictive control method for large-scale urban road network traffic flow as claimed in claim 1, characterized in that: The step 1: dividing the urban road network into regions, specifically: The urban road network is divided into three areas, I, J, and L. The three areas are divided based on the same road network structure, and the division method is not unique; on this basis, the road network is further divided into multiple subsystems with the same structure in each area, and the number of intersections in each subsystem and the distribution method of each intersection are the same.

3. The hierarchical and distributed model predictive control method for large-scale urban road network traffic flow as claimed in claim 1, characterized in that: Step 2: Collect data on the area divided by the road network to obtain the MFD image and properties of the regional road network, specifically: In each road section, sensors are used to obtain the d The number of vehicles on each road section n z (k d ), z=1,2,3..., and the traffic volume q of each road section z (k d ), and use this to calculate at time k d The average number of vehicles N in the three areas i (k d ),N j (k d ),N l (k d ), the turning rate r of each lane w leading to the downstream section z wz ,w=1,2,3...Use sensors at the entrances and exits and connections of the area to obtain the traffic exchange volume Q of each area ij (k d ),Q ji (k d ),Q il (k d ),Q li (k d ),Q jl (k d ),Q lj (k d ) and the traffic volume Q flowing into and out of the road network i,in (k d ),Q i,out (k d ),Q j,in (k d ),Q j,out (k d ),Q l,in (k d ),Q l.out (k d ); Where Q ij (k d ) is the time k d The traffic exchange volume from inner area I to area J, Q ji (k d ) is the time k d The traffic exchange volume from inner J area to I area, Q il (k d ) is the time k d The traffic exchange volume from the inner I area to the L area, Q li (k d ) is the traffic exchange volume from area L to area I, Q jl (k d ) is the traffic exchange volume from area J to area L, Q lj (k d ) is the traffic exchange volume from area L to area J; Q i,in (k d ) is the traffic volume flowing into area I, Q i,out (k d ) is the traffic volume outflowing from area I, Q j,in (k d ) is the traffic volume flowing into area J, Q j,out (k d ) is the traffic volume outflowing from area J, Q l,in (k d ) is the traffic volume flowing into area L, Q l.out (k d ) is the traffic flow out of area L; Set the value Q of the traffic flow in the road network in the three areas i,in ,Q j,in ,Q l,in A constant value known at all times; For the three areas I, J, and L divided by the road network, each has a corresponding MFD image and a functional relationship corresponding to the image. The MFD image represents two properties of the traffic flow in the road network. One is the fitting functional relationship between the number of existing vehicles and the passing traffic flow, and the other is the proportional relationship between the passing traffic flow and the traffic flow leaving the road network. The corresponding MFD image is obtained by collecting the relevant quantities of the road network and correspondingly fitting the curve on the coordinate axis. The number of vehicles N corresponding to the maximum passing traffic flow in the road network is further obtained from the functional relationship between the number of vehicles and the passing traffic flow. i,critical , it is known from the existing research on road network MFD that this value is unique.

4. The hierarchical and distributed model predictive control method for large-scale urban road network traffic flow as claimed in claim 3, characterized in that: The step 3: optimizing and solving the upper controller in the hierarchical MPC is as follows: In the case of oversaturated road network, the upper controller uses the number of vehicles N in the current area as the i (k d ),N j (k d ),N l (k d ) is the system state quantity, the regional vehicle flow exchange quantity and the road network outflow vehicle flow are the control quantities, and the optimization problem design is carried out according to the properties obtained from the MFD images of the three regions; The goal of this optimization problem is to improve the vehicle traffic efficiency in each area by utilizing the characteristics of MFD, by maximizing the spatial average traffic flow; the designed objective function consists of two parts: 1) minimizing the number of vehicles in the area; 2) maintaining the number of vehicles in each area at the critical value of MFD to maximize the spatial average traffic flow; the objective function contains the target term of optimizing the number of vehicles and tracking N i,critical , N j,critical and N l,critical The penalty term; the optimization problem is solved by the fmincon solver in MATLAB, and the control sequence Q of the traffic flow is obtained i,out (k d +p|k d ),Q ij (k d +p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d );in is the upper layer prediction time domain, symbol (k d +p|k d ) represents the k-based d Step to k d + prediction of the system state in p steps; A set of control sequences within the future p steps is obtained. The control sequence at each moment consists of 9 vehicle flows. The control sequence when p=0 is taken and passed to the lower-level controller.

5. The hierarchical and distributed model predictive control method for large-scale urban road network traffic flow as claimed in claim 4, characterized in that: The basis for judging the oversaturation of the road network is k d In the step, whether the average number of vehicles in any of the three areas I, J, and L exceeds the number of vehicles corresponding to the maximum traffic flow.

6. The hierarchical and distributed model predictive control method for large-scale urban road network traffic flow according to claim 1, characterized in that: The step 4: combining distributed MPC to optimize and solve the lower-level MPC of the hierarchical strategy, specifically: For the three areas I, J, and L, the upper-level controller obtains the optimized control sequence and passes it to the lower-level controller for implementation. At the same time, the lower-level controller needs to optimize the green light time length of the traffic lights in each direction of the intersection and coordinate the traffic capacity of each road in the road network. Distributed MPC is used to design the lower-level controller, and the store-and-forward model is selected to establish the mathematical model of each road section; For each area, it is further divided into multiple subsystems according to the structure of the road network, and the number and distribution of intersections in each subsystem are required to be the same; a distributed MPC controller is designed in each subsystem; The lower-level controller completes the following tasks at specific intersections through the control of traffic light signals: (1) the realization of the traffic flow control sequence obtained by the upper-level controller; (2) the optimization of vehicle traffic on each road section; therefore, the objective function of the optimization problem solved by the distributed MPC of each subsystem in the lower-level controller needs to consist of two items; After the subsystems are divided in each area, the road sections contained in each subsystem are divided into two categories: The first type of road section is a road section that connects the area with the outside world and exchanges vehicles. The outside world here includes the external environment of the entire road network and the adjacent area according to the location of the area. The road section connected to the external environment of the entire road network and exchanges vehicles is controlled by controlling the green light duration of the traffic light to control Q i,out ,Q j,out and Q l,out The realization of the road section connecting adjacent areas and exchanging vehicles is to control the green light duration of the traffic light to control Q ij ,Q il ,Q ji ,Q jl ,Q lj and Q li Implementation of The second type of road section is the other road sections connecting various intersections in the subsystem. This type of road section controls the passage of vehicles in the subsystem by controlling the green light duration of the signal, thereby improving the passage efficiency of vehicles in the subsystem. In the optimization problem solved by distributed MPC, the cost function designed for the (1) type of road section is to achieve the solution result of the upper-level controller. i,out (k d +p|k d ),Q ij (k d +p|k d ),Q il (k d +p|k d ),Q j,out (k d +p|k d ),Q ji (k d +p|k d ),Q jl (k d +p|k d ),Q l,out (k d +p|k d ),Q lj (k d +p|k d ),Q li (k d +p|k d ), take the control sequence at time p = 0, and the number of vehicles n in each road section z (k d ) is the state quantity, n z (k d ) represents the segment z at step k d The average number of vehicles in the intersection corresponds to the length of time g that the traffic light is green z (k d ) is the control quantity, and the objective function of this part is designed; where z represents the road section, which is the (1) type road section in each subsystem; In the optimization problem solved by distributed MPC, the cost function designed for the (2) type of road section is to optimize the control to improve the traffic efficiency of vehicles in the area, with the number of vehicles n in each road section as the goal. z (k d ) is the state quantity, corresponding to the length of the green light time g at the intersection z (k d ) is the control quantity, and the objective function of this part is designed; Where z represents the road section, which is the (2) type road section in each subsystem; Through the design of the objective functions corresponding to the two types of road sections, each road section in a subsystem has its corresponding objective function, and the objective function of the distributed MPC optimization problem that the subsystem needs to solve is obtained by adding the objective functions of each road section; In each area, the alternating direction multiplier method ADMM is used to perform collaborative processing between subsystems on each solution result; Decompose the global optimization problem into multiple sub-problems, allow local variables and global variables to be updated alternately, and gradually converge to the global optimum; The alternating direction multiplier method ADMM is modified as follows: 1) Local optimization: Take the green time of each link as an independent optimization variable, solve the objective function of each link, and obtain the local variable g z ; 2) Global coordination: Introduce the average green time of all links in the region as the global variable g to ensure coordination and balance between different links; 3) Variable update: Update the Lagrange multiplier to gradually correct the difference between individual green time and the global average time to ensure the coordination of the entire network; Solve and obtain the green light duration control sequence of the traffic lights corresponding to each intersection: in, is the lower layer prediction time domain, Z is the last item of all road sections z; take the first column and get k d The green light duration at the +1 moment is designed to meet the traffic order, that is, a set of signal light schemes with non-conflicting phases are applied to each intersection. This method is manually designed and directly controls the setting of the signal lights for application.

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