Train formation distributed cooperative control method based on model predictive control

Abstract

The invention discloses a model predictive control-based train formation distributed cooperative control method, which comprises the following steps of: acquiring a train tracking speed running curve, train speed limiting information and a train running resistance coefficient, and establishing a train formation model; according to a preset model predictive control algorithm, in a set predictive control time domain, according to a train formation model, a control target and constraint conditions, state variables of positions and running speeds of all trains in a train formation and control variables of control forces of all the trains in the train formation are used to predict the train formation according to state variables of the positions and running speeds of all the trains in the train formation. Respectively generating optimization control problems of the leading train and the following train in the train formation; and based on a synchronization theory, solving an optimization control problem of each train to obtain a control force of each train in the formation, and inputting the control force into a train operation control system to realize distributed control of each train in the train formation. The method is based on a model predictive control algorithm, uses a synchronization theory, and reduces the use of computing resources and communication resources in practice.

Description

Technical Field

[0001] The present invention relates to the field of urban rail transit train control, and more specifically, to a distributed cooperative control method for train formations based on model predictive control. Background Art

[0002] In recent years, urban rail transit systems have been facing increasingly serious imbalances in passenger flow distribution. The capacity of existing lines has reached its limit, which has limited the ability to transfer large-scale passenger flows by increasing the density of trains in local areas. In order to achieve dynamic matching of passenger and vehicle flows, train formation technology has emerged. This technology can further shorten the interval between train runs, posing new challenges to existing train operation control methods.

[0003] The operation phases of train formations can be divided into, for example, dynamic formation, speed convergence operation, dynamic disorganization, etc. The control objectives and constraints of train formation operation in each phase are different. Among them, the control objective of the speed convergence operation phase is to make the formation vehicles accurately track the desired cruising speed. At present, there is no conclusion on the research on train formations, and there is still little research on the collaborative control method of train formations. Therefore, how to realize the distributed collaborative control of train formations in the speed convergence phase has become a problem that needs to be solved at present.

[0004] The first train in the direction of the train formation is the leader or leading train, and the remaining trains in the formation are following trains. In the train formation, the leading train in the formation follows the ATO curve; the following train, under the action of the vehicle-to-vehicle communication system, establishes a communication link with the adjacent train, and obtains the speed, position and other status information sent by the leading train in real time. Each following train regards the leading train as the leader, and uses the ATO curve tracked by the leading train as the reference trajectory. According to the line information stored in the database and the status information of the vehicle, it calculates and controls each train to track the reference trajectory, and controls the tracking distance between adjacent trains to achieve the following overall control goals of the formation: there is no collision during the operation of each train in the formation, and finally the entire formation reaches a state where it runs together at the same speed. Each train in the formation has higher autonomy and can realize distributed control.

[0005] There are many constraints in the operation process of urban rail transit trains, and the control objectives of train formations are clear. Research usually uses the control architecture of Model Predictive Control (MPC) to control urban rail transit train formations. In the model predictive control problem of train formations, although the trains in the formation are decoupled in their own dynamics, in the finite time constrained optimization problem to be solved at each sampling time, due to the existence of factors such as spacing constraints, adjacent trains have an inseparable coupling relationship in the cost function and constraints. In order to deal with the coupling cost and coupled physical constraints, existing studies usually assume that each train in the formation updates its own state in sequence. However, due to the limited computing resources and communication resources in practice, in order to reduce the computing time, the use of synchronization strategy can achieve the real-time requirements of train formation control. Summary of the invention

[0006] The object of the present invention is to provide a distributed cooperative control method for train formation based on model predictive control to solve at least one of the problems existing in the prior art.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A first aspect of the present invention provides a distributed cooperative control method for a train formation based on model predictive control, comprising:

[0009] S1. Obtain the train tracking speed operation curve, train speed limit information and train operation resistance coefficient, and establish a train formation model;

[0010] S2. According to the preset model predictive control algorithm, in the set predictive control time domain, according to the train formation model, control objectives and constraints, with the state variables of the position and running speed of each train in the train formation, with the control variables of the control force of each train in the train formation, respectively generate the optimization control problems of the leading train and the following train in the train formation;

[0011] S3. Based on synchronization theory, solve the optimization control problem of each train, obtain the control force of each train in the formation, and input the control force into the train operation control system to realize distributed control of each train in the train formation.

[0012] Optionally, the train formation model is

[0013]

[0014] Among them, x i (t) is the position of the i-th train in the train formation at sampling time t; v i (t) is the speed of the i-th train in the train formation at sampling time t; For xi The derivative of (t); v i The derivative of (t); u i (t) is the difference between the traction force and the additional resistance of the i-th train in the train formation at the sampling time t or the difference between the braking force and the additional resistance of the i-th train in the train formation at the sampling time t; M i is the mass of the i-th train in the train formation; c i0 is the friction resistance of the i-th train in the train formation, c i1 is the resistance coefficient of the i-th train in the train formation, c i2 is the aerodynamic drag coefficient of the i-th train in the train formation; d i (ω) is the unit unknown disturbance that the i-th train in the train formation is subjected to during its operation, and t is the sampling time.

[0015] Optionally, the model predictive control algorithm adopts a discrete dynamics model of urban rail transit train formation.

[0016] The model predictive control algorithm is

[0017]

[0018] in, v k|t The derivative of; (·k|t) is the state predicted at time point k at sampling time t, x k|t To predict the position of the train at time point k at sampling time t, v k|t is to predict the speed of the train at time point k at sampling time t; x k+1|t v is the position of the train at time point k+1 obtained by dynamically updating the state variables at time point k predicted at sampling time t; k+1|t is the speed of the train at time point k+1 obtained by dynamically updating the state variables at time point k predicted at sampling time t; Δt is the sampling period.

[0019] Optionally, the constraint conditions of the leading train include a control force constraint of the leading train, a speed limit constraint of the leading train and a terminal speed constraint of the leading train;

[0020] The control force constraint of the leading train is

[0021] -Ma br ≤u k|t ≤Ma dr

[0022] Among them, u k|t is the control force predicted by the leading train at time point k at sampling time t; Ma brThe maximum braking force of the leading train; Ma dr The maximum traction power for leading trains;

[0023] The speed limit constraint of the leading train is

[0024] 0≤v k|t ≤v lim (x k|t )

[0025] Among them, v k|t To predict the speed of the leading train at time k at sampling time t, v lim v is the line speed limit that the leading train of the train formation is subject to during operation and is known before operation; lim (x k|t ) is the predicted speed limit of the leading train at the location of time point k at sampling time t;

[0026] The terminal speed constraint of the leading train is

[0027]

[0028] Among them, N p For the prediction time domain; is the speed of the leading train at the end of the prediction time domain at sampling time t; It is the speed limit of the leading train at its location when predicting the end of the time domain.

[0029] Optionally, the constraint conditions of the following train include a control force constraint of the following train, a speed limit constraint of the following train, a spacing safety constraint of the following train, a compatibility constraint of the following train, and a terminal constraint of the following train;

[0030] The control force constraint of the following train is:

[0031] -M i a i,b ≤u i,k|t ≤M i a i,d

[0032] Among them, u i,k|t is the control force predicted for the following train i at time point k at sampling time t; M i a i,b is the maximum braking force of the following train; M i a i,d The maximum traction power for the following train;

[0033] The speed limit constraint of the following train is:

[0034] 0≤v i,k|t ≤vlim (x i,k|t )

[0035] Among them, v i,k|t is the speed of the following train i at time point k predicted at sampling time t; v lim (x i,k|t ) is the speed limit of the following train i at the location of time point k predicted at sampling time t;

[0036] The safety constraint of the following train spacing is:

[0037] d i-1,i,k|t ≥d min

[0038] Among them, d min is the minimum safe distance between adjacent following trains; d i-1,i =x i-1 -x i -L i-1 is the distance between the following train i and the following train i-1; L i-1 is the length of the following train i-1;

[0039] The compatibility constraint of the following train is

[0040]

[0041] Where X = [xv] T is the state vector of the train, X i,k|t is the state vector predicted at time point k for the following train i at sampling time t; The upper bound of the deviation of the compatibility constraint is the deviation limit between the actual state of each train in the train formation and the assumed predicted state;

[0042] The terminal constraint of the following train is

[0043]

[0044] in, is the extended state vector including the distance between adjacent trains, x represents position, v represents speed, and d represents distance; f is the terminal constraint set; is the predicted time domain endpoint t+N of the following train i at sampling time t p The extended state vector at .

[0045] Optionally, the terminal constraint set X f include

[0046]

[0047]

[0048] Among them, a Emax is the emergency braking acceleration; a Smin is the minimum braking acceleration; γ i is the constraint to control the error term; To predict the time domain endpoint t+N of the following train i at sampling time t p Speed; S i is the constraint set related to the distance between following train i; T i is the set of time-related constraints for following train i; To predict the distance between the following train i and the following train i-1 at the end point in the time domain at sampling time t; It is the speed limit of the following train i at the sampling time t predicted by the following train at the location of the following train at the end point of the time domain.

[0049] Optionally, the leading train control target is

[0050] The control target of the leading train is

[0051]

[0052] Wherein, Q is the first weighting matrix in model predictive control, and R is the second weighting matrix in model predictive control; v r,k is the speed of the leading train at time point k; the first term represents the error between the predicted speed of the leading train at time point k at sampling time t and the speed of the leading train at time point k; the second term It indicates the control power of the leading train;

[0053] The following train control target is

[0054]

[0055] Among them, d des represents the expected spacing between adjacent trains in the formation; is the terminal cost; ||·||P represents the weighted norm; the first term It represents the speed deviation between the following train i and the preceding train i-1. The second term represents the control force of the following train i; the third term A spacing maintenance term added to the cost function of following train i;

[0056] Item 4 represents the terminal cost. Optionally,

[0057] The optimal control model of the leading train is

[0058]

[0059] x t|t =x t

[0060] v t|t =v t

[0061] -Ma br ≤u k|t ≤Ma dr

[0062] 0≤v k|t ≤v lim (x k|t )

[0063]

[0064] The optimal control model of the following train is:

[0065]

[0066] v i,t|t =v i,t

[0067] x i,t|t =x i,t

[0068] 0≤v i,k|t ≤v lim (x i,k|t )

[0069] -M i a i,b ≤u i,k|t ≤M i a i,d

[0070] d i-1,i,k|t >=d min

[0071]

[0072] Optionally, S3 further includes

[0073] S31. At sampling time t, measure the state X of train i i,t ;

[0074] S32, according to the state X of the train i i,t , calculate the hypothetical control input and hypothetical state sequence of train i Assume that the trajectory and compatibility constraints have upper bounds on the deviations The maximum error between the assumed trajectory of train i and the assumed trajectory of neighboring trains and the minimum error between the assumed trajectory of train i and the assumed trajectory of neighboring trains;

[0075] S33, solving the optimization control model of each train in the train formation to obtain the first control input sequence The first control input sequence The first element Apply it to the train operation control system, wait until the next sampling time t+1, update the train operation control system state, and repeat steps S31-S33 until the control process ends.

[0076] Optionally, the calculation assumes that the control input formula is

[0077]

[0078] in, is the hypothetical control input of train i at time k at sampling time t, κ i,k|t It is a terminal auxiliary controller, and the prediction time domain range is [t,t+N p ], In the prediction time domain [t,t+N p ] is the hypothetical control input sequence for train i, In the prediction time domain [t,t+N p ] the first control input sequence of train i, [] T Represents matrix transpose;

[0079] The hypothesized trajectory

[0080]

[0081] The maximum error and minimum error between the assumed trajectory of train i and the assumed trajectory of neighboring trains are:

[0082]

[0083] in, and e i,t are respectively in the time interval [t,t+N p ], where the maximum and minimum errors between the hypothetical trajectory of train i and its neighboring train hypothetical trajectory; j is a neighboring train, and is the set of neighbor trains j corresponding to train i;

[0084] The upper bound of the deviation of the compatibility constraint The formula for the value range of is

[0085]

[0086] in, N p is the prediction time domain; ε∈(0,N p ] is the control sampling period; μi∈(0,1); a ij Represents the coupling relationship of train state variables; and e j,t are the neighbor train j in the time interval [t,t+N p ] with the maximum and minimum errors of the hypothesized trajectory of train i.

[0087] The beneficial effects of the present invention are as follows:

[0088] The present invention can decouple the calculation of the coupling relationship caused by various constraints in the actual operation of the train formation by using synchronization theory, aiming at the limited computing and communication resources in practice, and reduce the use of computing resources and communication resources in practice, and reduce the calculation time, thereby simplifying the calculation process of the control quantity. The present invention can improve the efficiency of train operation and realize the safe and efficient operation of the train formation in the speed convergence stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0090] Figure 1 A flow chart of a distributed cooperative control method for train formations based on model predictive control in one embodiment of the present invention is shown.

[0091] Figure 2 A schematic diagram showing the stress conditions of a train in an embodiment of the present invention.

[0092] Figure 3 A specific flow chart of a distributed cooperative control method for train formations based on model predictive control in one embodiment of the present invention is shown. DETAILED DESCRIPTION

[0093] In order to explain the present invention more clearly, the present invention is further described below in conjunction with embodiments and drawings. Similar components in the drawings are represented by the same reference numerals. It should be understood by those skilled in the art that the content specifically described below is illustrative rather than restrictive, and the protection scope of the present invention should not be limited thereto.

[0094] The distributed collaborative control method of train formation based on model predictive control provided by the present invention uses a model predictive control algorithm to describe the distributed control problem of train formation, considers various constraints existing in the actual operation process of the train formation in the problem, and uses synchronization theory to decouple the coupling relationship brought by the coupling constraints, which makes the distributed control problem difficult to solve.

[0095] like Figure 1 As shown, a distributed cooperative control method for train formation based on model predictive control includes:

[0096] S1. Obtain the train tracking speed operation curve, train speed limit information and train operation resistance coefficient, and establish a train formation model;

[0097] S2. According to the preset model predictive control algorithm, in the set predictive control time domain, according to the train formation model, control objectives and constraints, with the state variables of the position and running speed of each train in the train formation, with the control variables of the control force of each train in the train formation, respectively generate the optimization control problems of the leading train and the following train in the train formation;

[0098] S3. Based on synchronization theory, solve the optimization control problem of each train, obtain the control force of each train in the formation, and input the control force into the train operation control system to realize distributed control of each train in the train formation.

[0099] In one embodiment, a train formation model is established, and the specific process is as follows:

[0100] according to Figure 2 A single-vehicle operation model is established based on the longitudinal train dynamics (LTD) model. The train is taken as a mass point to analyze the force of the train and establish the dynamic equation of the train as follows:

[0101]

[0102] Among them, x(t) is the position of the train at sampling time t, in m; v(t) is the speed of the train at sampling time t, in m / s; is the derivative of x(t); is the derivative of v(t); F is the traction or braking force of the train, F tra Indicates the traction force, F bra Indicates braking force; M is the mass of the train, in kg; c0, c1, c2 are used to calculate the basic resistance W B The Davis equation coefficients are usually obtained through empirical statistics, where c0 (N / kg) is composed of rolling friction resistance and bearing friction resistance, c1 (Ns / m / kg) is the resistance coefficient, which is usually positive, and c2 (Ns 2 / m 2 / kg) is the aerodynamic drag coefficient; D(ω) is the unknown disturbance during the train operation; W E is the additional resistance of the train, which is caused by the additional resistance of the ramp W i And the curve additional resistance W r Composition, unit curve additional resistance wr =600 / R, where R represents the curve radius. The additional resistance of the tunnel is not considered here.

[0103] According to the above single-vehicle model, the train formation operation model is established as follows:

[0104]

[0105] Among them, x i (t) is the position of the i-th train in the train formation at sampling time t; v i (t) is the speed of the i-th train in the train formation at sampling time t; For x i The derivative of (t); v i The derivative of (t); u i (t) is the difference between the traction force and the additional resistance of the i-th train in the train formation at the sampling time t or the difference between the braking force and the additional resistance of the i-th train in the train formation at the sampling time t; M i is the mass of the i-th train in the train formation; c i0 is the friction resistance of the i-th train in the train formation, c i1 is the resistance coefficient of the i-th train in the train formation, c i2 is the aerodynamic drag coefficient of the i-th train in the train formation; d i (ω) is the unit unknown disturbance that the i-th train in the train formation is subjected to during its operation, and t is the sampling time.

[0106] In one embodiment, step S2 "designs a model predictive control algorithm, given a prediction time domain, in the given prediction time domain, based on the train formation model, constraints and control objectives, takes the position and running speed of each train in the formation as state variables, takes the control force of each train in the formation as control variables, and generates distributed optimization control problems for the leading train and the following train in the formation respectively". For the urban rail transit train operation control system, the control process is discrete, sampling at each sampling time, and control is performed, and the sampling period △t is usually selected as 0.1 seconds. Then step S2 further includes the following sub-steps:

[0107] S21. Use the discrete dynamics model of urban rail transit train formation for control design. The specific process is as follows:

[0108] At sampling time t, the discrete form of the urban rail transit train formation model is established as follows:

[0109]

[0110] Among them, (·k|t) is the state predicted at time point k at sampling time t, v k|t The derivative of x k|t To predict the position of the train at time point k at sampling time t, v k|t is to predict the speed of the train at time point k at sampling time t; x k+1|t v is the position of the train at time point k+1 obtained by dynamically updating the state variables at time point k predicted at sampling time t; k+1|t is the speed of the train at time point k+1 obtained by dynamically updating the state variables at time point k predicted at sampling time t; Δt is the sampling period.

[0111] S22. Given the prediction time domain, according to the train formation model, constraints and control objectives, the distributed optimization control problems of the leading train and the following train in the formation are generated respectively. The specific process is as follows:

[0112] Given the prediction time domain is N p ,Since the control objectives of the leading train and the following train in the train formation are different, the control objectives and constraints of the leading train and the following train in the formation are considered separately:

[0113] The control goal of the leading train is to follow the reference trajectory as much as possible while satisfying the constraints of state and input, while making the input as small as possible, thereby minimizing the energy exhaustion.

[0114]

[0115] Among them, among them, To minimize the cost function of the control input sequence; represents the control input sequence with solution; Q is the first weighting matrix in model predictive control, R is the second weighting matrix in model predictive control; the first term represents the error between the predicted speed of the leading train at time point k at sampling time t and the speed of the leading train at time point k, v r,k is the speed of the leading train at time point k; by minimizing the train speed error, the leading train can track the set reference trajectory. It represents the control force of the leading train, which is used to make the control force input as small as possible, thereby making the energy consumption as small as possible.

[0116] The constraint conditions of the leading train include the control force constraint of the leading train, the speed limit constraint of the leading train and the terminal speed constraint of the leading train;

[0117] The control force constraint of the leading train is

[0118] -Ma br ≤uk|t ≤Ma dr

[0119] Among them, u k|t is the control force predicted by the leading train at time point k at sampling time t; Ma br The maximum braking force of the leading train; Ma dr The maximum traction power for leading trains;

[0120] The speed limit constraint of the leading train is

[0121] 0≤v k|t ≤v lim (x k|t )

[0122] Among them, v k|t To predict the speed of the leading train at time k at sampling time t, v lim v is the line speed limit that the leading train of the train formation is subject to during operation and is known before operation; lim (x k|t ) is the predicted speed limit of the leading train at the location of time point k at sampling time t;

[0123] The terminal speed constraint of the leading train is

[0124]

[0125] Among them, N p For the prediction time domain; is the speed of the leading train at the end of the prediction time domain at sampling time t; The terminal speed constraint indicates that the train speed cannot exceed the line speed limit at future times outside the current prediction time domain.

[0126] The control goal of the following train is to follow the speed of the preceding vehicle as quickly as possible while satisfying various constraints such as state and input, and to stabilize the distance between the preceding vehicle and the preceding vehicle to the ideal distance as much as possible while maintaining a safe distance from the preceding vehicle without collision.

[0127]

[0128] Among them, d des represents the expected spacing between adjacent trains in the formation; represents the terminal cost; ||·||P represents the weighted norm; the first item in the control objective of the following train It is used to enable any following train i in the formation to run at the speed of the preceding train i-1. The second term It is used to make the input as small as possible to achieve energy saving. Unlike the leading train, the cost function of the following train adds a distance maintenance term, i.e. the third term. It is used to ensure that the distance between any following train i and the preceding train i-1 in the formation is as stable as possible at the ideal distance. Indicates the terminal cost.

[0129] The constraint conditions of the following train include the control force constraint of the following train, the speed limit constraint of the following train, the spacing safety constraint of the following train, the compatibility constraint of the following train and the terminal constraint of the following train;

[0130] The control force constraint of the following train is:

[0131] -M i a i,b ≤u i,k|t ≤M i a i,d

[0132] Among them, u i,k|t is the control force predicted for the following train i at time point k at sampling time t; M i a i,b is the maximum braking force of the following train; M i a i,d The maximum traction power for the following train;

[0133] The speed limit constraint of the following train is:

[0134] 0≤v i,k|t ≤v lim (x i,k|t )

[0135] Among them, v i,k|t is the speed of the following train i at time point k predicted at sampling time t; v lim (x i,k|t ) is the speed limit of the following train i at the location of time point k predicted at sampling time t;

[0136] The safety constraint of the following train spacing is:

[0137] d i-1,i,k|t ≥d min

[0138] Among them, d min is the minimum safe distance between adjacent following trains; d i-1,i =x i-1 -x i -L i-1 is the distance between the following train i and the following train i-1; L i-1 is the length of the following train i-1;

[0139] The compatibility constraint of the following train is

[0140]

[0141] Where X = [xv] T is the state vector of the train, X i,k|t is the state vector predicted at time point k for the following train i at sampling time t; The upper bound of the deviation of the compatibility constraint is the deviation limit between the actual state of each train in the train formation and the assumed predicted state;

[0142] The terminal constraint of the following train is

[0143]

[0144] in, is the extended state vector including the distance between adjacent trains, x represents position, v represents speed, and d represents distance; f is the terminal constraint set; is the predicted time domain endpoint t+N of the following train i at sampling time t p The extended state vector at .

[0145] Terminal constraint set X f include

[0146]

[0147] Among them, a Emax is the emergency braking acceleration; a Smin is the minimum braking acceleration; γ i is the constraint to control the error term; To predict the time domain endpoint t+N of the following train i at sampling time t p Speed; S i is the constraint set related to the distance between following train i; T i is the set of time-related constraints for following train i; To predict the distance between the following train i and the following train i-1 at the end point in the time domain at sampling time t; It is the speed limit of the following train i at the sampling time t predicted by the following train at the location of the following train at the end point of the time domain.

[0148] The optimal control model of the leading train is

[0149]

[0150] x t|t =x t

[0151] v t|t =v t

[0152] -Ma br ≤u k|t ≤Ma dr

[0153] 0≤v k|t ≤v lim (x k|t )

[0154]

[0155] The optimal control model of the following train is:

[0156]

[0157] v i,t|t =v i,t

[0158] x i,t|t =x i,t

[0159] 0≤v i,k|t ≤v lim (x i,k|t )

[0160] -M i a i,b ≤u i,k|t ≤M i a i,d

[0161] d i-1,i,k|t >=d min

[0162]

[0163] In one embodiment, Figure 3 As shown, step S3 further includes:

[0164] S31 measures the vehicle state X at sampling time t i,t , receiving the state X of the preceding vehicle transmitted by the preceding vehicle i-1,t , and also pass the state of the vehicle to the following vehicle i+1;

[0165] S32 calculates and passes hypothetical state sequences to other trains Assume that the trajectory and compatibility constraints have upper bounds on the deviations The maximum and minimum errors between the assumed trajectory of the vehicle and the assumed trajectory of the neighbor;

[0166] S33, solving the optimization control model of each train in the train formation to obtain the first control input sequence The first control input sequence The first element Apply to the train operation control system, wait until the next sampling time t+1, update the train operation control system state, and repeat steps S31-S33 until the control process ends;

[0167] Step S32 calculates and transmits the assumed state sequence of the vehicle to other trains The maximum and minimum errors between the hypothesis trajectory and its neighbor train hypothesis trajectory, and the upper bound of the deviation for compatibility constraints In order to meet the needs of limited communication resources and computing resources, all trains in the formation solve the optimization problem of their own trains synchronously, that is, each train i solves the finite time constraint optimization problem of its own train at the current moment at each sampling time k under the same system clock to obtain the optimal control input sequence from the current moment to a limited time domain in the future. According to the above discussion, it can be known that the neighbor train j of each train i, The future state trajectory and predicted trajectory of i are unknown. Each train in the formation needs to additionally calculate the assumed state sequence (trajectory) of the train in the future prediction time domain and pass it to its neighboring trains. To ensure the control effect, the actual state of the train in the formation needs to be as consistent as possible with the assumed predicted state. Step S32 further includes the following sub-steps:

[0168] S321 calculates the assumed control input,

[0169] The assumed control input of the i-th train in the platoon at sampling time t at time k is

[0170]

[0171] Among them, κ i,k|t It is a terminal auxiliary controller, and the prediction time domain range is [t,t+N p ], In the prediction time domain [t,t+N p ] is the hypothetical control input sequence for each train i in the train formation, In the prediction time domain [t,t+N p ] is the first control input sequence of each train i in the train formation, [] T Represents matrix transpose;

[0172] S322 assumes that a hypothetical control input sequence is applied to each train in the train formation, and the resulting hypothetical predicted state trajectory is:

[0173]

[0174] S323 receives the assumed trajectory from the preceding vehicle, calculates the maximum and minimum errors between the assumed trajectory of the vehicle and the assumed trajectory of the preceding vehicle, transmits the calculation result to the following vehicle, and receives the calculation result transmitted by the preceding vehicle. The specific process is as follows:

[0175]

[0176] in, and e i,t are respectively in the time interval [t,t+N p ], where the maximum and minimum errors between the hypothetical trajectory of train i and its neighboring train hypothetical trajectory; j is a neighboring train, and is the set of neighbor trains j corresponding to train i;

[0177] S324 Calculate the upper bound of the deviation of the compatibility constraint The formula for the value range of is

[0178] The upper bound of the deviation of the compatibility constraint The formula for the value range of is

[0179]

[0180] in, N p is the prediction time domain; ε∈(0,N p ] is the control sampling period; μi∈(0,1); a ij Represents the coupling relationship of train state variables; and e j,t are the neighbor train j in the time interval [t,t+N p ] with the maximum and minimum errors of the hypothesized trajectory of train i.

[0181] In particular, according to this embodiment, the process described in the flowchart above can be implemented as a computer software program. For example, this embodiment includes a computer program product, which includes a computer program tangibly contained on a computer-readable medium, and the computer program includes program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication part, and / or installed from a removable medium.

[0182] The flow chart and schematic diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product of the present embodiment. In this regard, each square box in the flow chart or schematic diagram can represent a part of a module, program segment or code, and a part of the above-mentioned module, program segment or code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the schematic diagram and / or flow chart, and the combination of the square boxes in the schematic diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0183] The modules involved in the description of this embodiment may be implemented by software or hardware.

[0184] As another aspect, this embodiment further provides a non-volatile computer storage medium, which may be the non-volatile computer storage medium included in the above-mentioned device in the above-mentioned embodiment, or may be a non-volatile computer storage medium that exists independently and is not installed in the terminal.

[0185] In the description of the present invention, it should be noted that the terms "upper", "lower", etc. indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific position, be constructed and operated in a specific position, and therefore cannot be understood as a limitation on the present invention. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a connection between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0186] It should also be noted that, in the description of the present invention, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the statement "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0187] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not limitations on the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the embodiments here. All obvious changes or modifications derived from the technical solution of the present invention are still within the protection scope of the present invention.

Claims

1. A distributed cooperative control method for train formation based on model predictive control, characterized in that: include: S1. Obtain the train tracking speed operation curve, train speed limit information and train operation resistance coefficient, and establish a train formation model; S2. According to the preset model predictive control algorithm, in the set predictive control time domain, according to the train formation model, control objectives and constraints, with the state variables of the position and running speed of each train in the train formation, with the control variables of the control force of each train in the train formation, respectively generate the optimization control problems of the leading train and the following train in the train formation; S3. Based on synchronization theory, solve the optimization control problem of each train, obtain the control force of each train in the formation, and input the control force into the train operation control system to realize distributed control of each train in the train formation.

2. The method according to claim 1, characterized in that The train formation model is Among them, x i (t) is the position of the i-th train in the train formation at sampling time t; v i (t) is the speed of the i-th train in the train formation at sampling time t; For x i The derivative of (t); v i The derivative of (t); u i (t) is the difference between the traction force and the additional resistance of the i-th train in the train formation at the sampling time t or the difference between the braking force and the additional resistance of the i-th train in the train formation at the sampling time t; M i is the mass of the i-th train in the train formation; c i0 is the friction resistance of the i-th train in the train formation, c i1 is the resistance coefficient of the i-th train in the train formation, c i2 is the aerodynamic drag coefficient of the i-th train in the train formation; d i (ω) is the unit unknown disturbance that the i-th train in the train formation is subjected to during its operation, and t is the sampling time.

3. The method according to claim 2, characterized in that The model predictive control algorithm adopts the discrete dynamics model of urban rail transit train formation. The model predictive control algorithm is Among them, (·k|t) is the state predicted at time point k at sampling time t, v k|t The derivative of x k|t To predict the position of the train at time point k at sampling time t, v k|t is to predict the speed of the train at time point k at sampling time t; x k+1|t v is the position of the train at time point k+1 obtained by dynamically updating the state variables at time point k predicted at sampling time t; k+1|t is the speed of the train at time point k+1 obtained by dynamically updating the state variables at time point k predicted at sampling time t; Δt is the sampling period.

4. The method according to claim 3, characterized in that: The constraint conditions of the leading train include the control force constraint of the leading train, the speed limit constraint of the leading train and the terminal speed constraint of the leading train; The control force constraint of the leading train is -And br ≤u k|t ≤And dr Among them, u k|t is the control force predicted by the leading train at time point k at sampling time t; Ma br The maximum braking force of the leading train; Ma dr The maximum traction power for leading trains; The speed limit constraint of the leading train is 0≤v k|t ≤v lim (x k|i ) Among them, v k|t To predict the speed of the leading train at time k at sampling time t, v lim v is the line speed limit that the leading train of the train formation is subject to during operation and is known before operation; lim (x k|t ) is the predicted speed limit of the leading train at the location of time point k at sampling time t; The terminal speed constraint of the leading train is Among them, N p For the prediction time domain; is the speed of the leading train at the end of the prediction time domain at sampling time t; It is the speed limit of the leading train at its location when predicting the end of the time domain.

5. The method according to claim 4, characterized in that The constraint conditions of the following train include the control force constraint of the following train, the speed limit constraint of the following train, the spacing safety constraint of the following train, the compatibility constraint of the following train and the terminal constraint of the following train; The control force constraint of the following train is: -M i a i，b ≤u i，k|t ≤M i a i,d Among them, u i，k|t is the control force predicted for the following train i at time point k at sampling time t; M i a i,b is the maximum braking force of the following train; M i a i，d The maximum traction power for the following train; The speed limit constraint of the following train is: 0≤v i，k|t ≤v lim (x i,k|t ) Among them, v i，k|t is the speed of the following train i at time point k predicted at sampling time t; v lim (x i,k|t ) is the speed limit of the following train i at the location of time point k predicted at sampling time t; The safety constraint of the following train spacing is: d i-1,i,k|t ≥d min Among them, d min is the minimum safe distance between adjacent following trains; d i-1,i =x i-1 -x i -L i-1 is the distance between the following train i and the following train i-1; L i-1 is the length of the following train i-1; The compatibility constraint of the following train is Where X = [xv] T is the state vector of the train, X i,k|t is the state vector predicted at time point k for the following train i at sampling time t; The upper bound of the deviation of the compatibility constraint is the deviation limit between the actual state of each train in the train formation and the assumed predicted state; The terminal constraint of the following train is in, is the extended state vector including the distance between adjacent trains, x represents position, v represents speed, and d represents distance; f is the terminal constraint set; is the predicted time domain endpoint t+N of the following train i at sampling time t p The extended state vector at .

6. The method according to claim 5, characterized in that The terminal constraint set X f include Among them, a Emax is the emergency braking acceleration; a Smin is the minimum braking acceleration; γ i is the constraint to control the error term; To predict the time domain endpoint t+N of the following train i at sampling time t p Speed; S i is the constraint set related to the distance between following train i; T i is the set of time-related constraints for following train i; To predict the distance between the following train i and the following train i-1 at the end point in the time domain at sampling time t; It is the speed limit of the following train i at the sampling time t predicted by the following train at the location of the following train at the end point of the time domain.

7. The method according to claim 6, characterized in that The control target of the leading train is Where Q is the first weighting matrix in model predictive control, and R is the second weighting matrix in model predictive control; v r,k is the speed of the leading train at time point k; the first term represents the error between the predicted speed of the leading train at time point k at sampling time t and the speed of the leading train at time point k; the second term It indicates the control power of the leading train; The following train control target is Among them, d des represents the expected spacing between adjacent trains in the formation; is the terminal cost; ||·||P represents the weighted norm; the first term It represents the speed deviation between the following train i and the preceding train i-1. The second term represents the control force of the following train i; the third term A spacing maintenance term added to the cost function of following train i; Item 4 Indicates the terminal cost.

8. The method according to claim 7, characterized in that The optimal control model of the leading train is x t|t =x t v t|t =v t -And br ≤u k|t ≤And dr 0≤v k|t ≤v lim (x k|t ) The optimal control model of the following train is: v i,t|t =v i,t x i,t|t =x i,t 0≤v i,k|t ≤v lim (x i,k|t ) -M i a i,b ≤u i,k|t ≤M i a i,d d i-1,i,k|t >=d min 9. The method according to claim 8, characterized in that The S3 further comprises S31. At sampling time t, measure the state X of train i i,t ; S32, according to the state X of the train i i,t , calculate the hypothetical control input and hypothetical state sequence of train i Assume that the trajectory and compatibility constraints have upper bounds on the deviations The maximum error between the assumed trajectory of train i and the assumed trajectory of neighboring trains and the minimum error between the assumed trajectory of train i and the assumed trajectory of neighboring trains; S33, solving the optimization control model of each train in the train formation to obtain the first control input sequence The first control input sequence The first element Apply it to the train operation control system, wait until the next sampling time t+1, update the train operation control system state, and repeat steps S31-S33 until the control process ends.

10. The method according to claim 9, characterized in that The calculations assume that the control input formula is in, is the hypothetical control input of train i at time k at sampling time t, κ i,k|t It is a terminal auxiliary controller, and the prediction time domain range is [t,t+N p ], In the prediction time domain [t, t+N p ] is the hypothetical control input sequence for train i, In the prediction time domain [t,t+N p ] the first control input sequence of train i, [] T Represents matrix transpose; The hypothesized trajectory The maximum error and minimum error between the assumed trajectory of train i and the assumed trajectory of neighboring trains are: in, and e i,t are respectively in the time interval [t,t+N p ], where the maximum and minimum errors between the hypothetical trajectory of train i and its neighboring train hypothetical trajectory; j is a neighboring train, and is the set of neighbor trains j corresponding to train i; The upper bound of the deviation of the compatibility constraint The formula for the value range of is in, N p is the prediction time domain; ε∈(0,N p ] is the control sampling period; μ i ∈(0,1); a ij Represents the coupling relationship of train state variables; and e j,t are the neighbor train j in the time interval [t,t+N p ] with the maximum and minimum errors of the hypothesized trajectory of train i.

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