A virtual formation train formation control method, system, electronic device and medium

Abstract

The present invention relates to a method, system, electronic device and medium for controlling the formation of virtual formation trains, and particularly relates to the technical field of rail transit. The method includes determining whether a preset event trigger mechanism is triggered according to the control amount of the leading train at the current moment and the state of the unit train; selecting to solve the Tube-MPC problem model or solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment and the optimal nominal state of the target train according to the judgment result, so as to obtain the optimal nominal control amount of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; calculating the optimal control amount of the unit train according to the optimal nominal control amount of the unit train at the current moment, then updating the moment and returning to the judgment step. The present invention can ensure the stability of single trains and queues under the influence of uncertain disturbances and communication delays, and ensure stable formation operation and synchronous operation at small intervals.

Description

Technical Field

[0001] The present invention relates to the technical field of rail transit, and in particular, to a method, a system, an electronic device and a medium for controlling the formation of a virtual formation train. Background Art

[0002] Due to the increasing transportation demands of passenger and freight railways, it is urgent to improve the utilization rate of line and vehicle resources on existing lines. Further shortening the train operation interval is beneficial to improving the utilization of line resources and increasing the number of trains that can operate on existing lines without building new lines; formulating the train formation number and plan according to transportation demands can improve the utilization of vehicle resources, increase the full load rate and avoid empty running. To meet the above demands, the Virtual Coupling (VC) technology, which can further shorten the headway and flexibly adjust the train formation, has been a key concern in the field of rail transit in recent years. The virtual coupling technology can group a certain number of powered unit trains in a certain order and with a small spacing through vehicle-to-vehicle communication to form a train with a stable formation, which is called a Virtually Coupled Train Set (VCTS). In addition, the virtual formation train is an extension of the traditional train formation concept, with the connotation of a train, emphasizing the ability of the units inside the formation to maintain synchronous operation and operation consistent with the traditional train at a small spacing to meet the needs of actual operation scenarios. Without the action of coupler connection, the stability of the small-spacing formation of the virtual formation train directly determines whether it can achieve the form and effect of a train, and the stability is particularly important.

[0003] Considering the interference effects brought by complex factors such as train vehicles and line environment, the virtual formation train may not be able to maintain stable formation operation and synchronous operation at a small spacing, thus reducing the benefits brought by the virtual coupling technology. Therefore, it is of great significance to study how to ensure that the virtual formation train can quickly recover and maintain the formation stability at a small spacing under the influence of interference conditions, so as to improve the utilization rate of line resources and vehicle resources, and provide theoretical support and application exploration for the virtual coupling technology.

[0004] Currently, there are the following four categories of related research on the formation stability control of virtual formation trains:

[0005] 1. Based on the car-following theory, control strategies are designed through car-following models for simulating the formation stability control algorithm of virtual formation trains and designing solutions. Typical researchers include Egidio Quaglietta, Ronghui Liu, etc.

[0006] 2. The feedback control method has the advantages of being easy for theoretical analysis and derivation, having a certain robustness against small disturbances, high algorithm efficiency, and low computational requirements. Many studies focus on the virtual formation train control method based on feedback control. Typical researchers include: Carlo Di Meo, Jaegeun Park, Liu Ling, etc.

[0007] 3. To solve the hard constraint problem of virtual formation control and ensure the optimality of control performance, the optimal control method has been widely studied and applied to the virtual formation control problem. Typical researchers include: Jesus Felez, Su Shuai, etc.

[0008] 4. Considering the dynamic operation characteristics of trains and the complexity of the virtual formation system formed by multiple trains, methods such as deep learning and reinforcement learning provide new research ideas. Typical researchers include: Wang Hongwei, Su Shuai, etc.

[0009] The above four types of methods do not fully consider the influence of uncertain disturbances and communication delays on control performance, lack the analysis of feasibility, local stability, and queue stability, and the actual operation state of the virtual formation train may fluctuate greatly, unable to ensure stable formation operation and synchronous operation at small intervals. Summary of the Invention

[0010] The object of the present invention is to provide a virtual formation train formation control method, system, electronic device, and medium, which can ensure the stability of single trains and queues under the influence of uncertain disturbances and communication delays, and ensure stable formation operation and synchronous operation at small intervals.

[0011] To achieve the above object, the present invention provides the following solutions:

[0012] A virtual formation train formation control method, including:

[0013] Construct the dynamic equations of each unit train in the virtual formation train according to the line gradient and speed limit of each section between each station;

[0014] Construct the state space equations of each unit train according to the dynamic equations of each unit train in the virtual formation train; the state space equations include a nominal state equation and a disturbance state equation;

[0015] Construct a train operation environment model of the virtual formation train according to the state space equations and constraint equations of each unit train; the constraint equations include a state constraint equation and a control variable constraint equation;

[0016] For any unit train in the virtual formation train, judge whether a preset event trigger mechanism is triggered according to the control amount of the leading train at the current moment and the state of the unit train at the current moment;

[0017] If the preset event trigger mechanism is triggered, solve the Tube-MPC problem model based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; the target train is the previous unit train of the unit train;

[0018] If the preset event trigger mechanism is not triggered, solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment;

[0019] According to the uncertain disturbance factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment, calculate the optimal control quantity of the unit train at the current moment, control the unit train according to the optimal control quantity of the unit train at the current moment, then update the current moment and return. For any unit train in the virtual formation train, judge whether the preset event trigger mechanism is triggered according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

[0020] A virtual formation train formation control system, comprising:

[0021] A dynamic equation construction module, configured to construct the dynamic equations of each unit train in the virtual formation train according to the line gradients and speed limits of each section between each station;

[0022] A state space equation construction module, configured to construct the state space equations of each unit train according to the dynamic equations of each unit train in the virtual formation train; the state space equations include a nominal state equation and a disturbance state equation;

[0023] A train operation environment model construction module, configured to construct a train operation environment model of the virtual formation train according to the state space equations and constraint equations of each unit train; the constraint equations include a state constraint equation and a control variable constraint equation;

[0024] A judgment module, configured to judge whether a preset event trigger mechanism is triggered for any unit train in the virtual formation train according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment;

[0025] Tube-MPC problem model solving module, which is used to solve the Tube-MPC problem model based on the train operation environment model, the nominal state of the unit train at the current moment and the optimal nominal state of the target train at the current moment if the preset event triggering mechanism is triggered, so as to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; the target train is the previous unit train of the unit train;

[0026] ELQR controller solving module, which is used to solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment and the optimal nominal state of the target train at the current moment if the preset event triggering mechanism is not triggered, so as to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment;

[0027] Optimal control quantity calculation module, which is used to calculate the optimal control quantity of the unit train at the current moment according to the uncertain disturbance factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment, control the unit train according to the optimal control quantity of the unit train at the current moment, then update the current moment and return For any unit train in the virtual formation train, it is judged whether the preset event triggering mechanism is triggered according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

[0028] An electronic device, comprising:

[0029] A memory and a processor, the memory is used to store a computer program, and the processor runs the computer program to make the electronic device execute the virtual formation train formation control method according to the above.

[0030] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements the virtual formation train formation control method as described above.

[0031] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: The present invention is based on robust invariant sets and model predictive control, adopts the Tube model predictive robust control method, focuses on ensuring the stability of single trains and queues under the influence of uncertain disturbances and communication delays, and ensures stable formation operation and synchronous operation at small spacings. Description of the Drawings

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0033] Figure 1 It is a flowchart of the virtual formation train formation control method provided by the embodiment of the present invention;

[0034] Figure 2 It is a result diagram of the actual state trajectory and the nominal state trajectory in the Tube considering the influence of initial disturbance and uncertain disturbance;

[0035] Figure 3 It is a result diagram of the parameter stability domain considering different communication delays;

[0036] Figure 4 It is a result diagram of the control effect before and after the controller parameters are adjusted considering the influence of uncertain disturbance and communication delay;

[0037] Figure 5 It is a result diagram of the comparison of the calculation time between the traditional model predictive control method and the proposed integrated algorithm;

[0038] Figure 6 It is a flowchart of the idea of the virtual formation train formation control method provided by the embodiment of the present invention. Detailed implementation manners

[0039] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the protection scope of the present invention.

[0040] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0041] As Figure 1 shown, the embodiment of the present invention provides a virtual formation train formation control method, specifically a virtual formation train formation stability robust control method based on Tube, including:

[0042] S1: Construct the dynamic equations of each unit train in the virtual formation train according to the line gradients and speed limits of each section between each station.

[0043] S2: Construct the state - space equations of each unit train according to the dynamic equations of each unit train in the virtual formation train; the state - space equations include a nominal state equation and a perturbation state equation.

[0044] S3: Construct a train operation environment model of the virtual formation train according to the state - space equations and constraint equations of each unit train; the constraint equations include a state constraint equation and a control variable constraint equation.

[0045] S4: For any unit train in the virtual formation train, judge whether a preset event - triggering mechanism is triggered according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

[0046] S5: If the preset event - triggering mechanism is triggered, solve the Tube - MPC problem model based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment.

[0047] S6: If the preset event - triggering mechanism is not triggered, solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment.

[0048] S7: Calculate the optimal control quantity of the unit train at the current moment according to the uncertain perturbation factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment, control the unit train according to the optimal control quantity of the unit train at the current moment, then update the current moment and return to judge whether the preset event - triggering mechanism is triggered for any unit train in the virtual formation train according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

[0049] In practical applications,

[0050] The nominal state equation is specifically

[0051] where represents the nominal state of the \(i\) - th unit train at time \(t\), \(A\) c represents the fifth coefficient matrix, \(B\) c represents the sixth coefficient matrix, represents the nominal control quantity of the \(i\) - th unit train at time \(t\), represents the external input generated by the \(i\) - th unit train receiving the operation state of the leading train at time \(t\).

[0052] The perturbation state equation is specifically:

[0053] in, represents the disturbance state of the i-th unit train at time t, represents the derivative of the perturbed state, represents the disturbance control quantity of the i-th unit train at time t, represents the uncertain disturbance of the i-th unit train at time t.

[0054] The control variable constraint equation is specifically:

[0055] Among them, u i (t k ) indicates t k The control quantity of the i-th unit train at time, represents the set of constraints on the control variables, u i Indicates the actual control quantity per unit mass, represents the set of real numbers, U min Indicates the maximum braking deceleration, U max Indicates the maximum traction acceleration.

[0056] The state constraint equation is specifically:

[0057] Among them, x i (t k ) indicates t k The state of the i-th unit train at time, represents the set of constraints on the state variables, φ z (x i (t k ),x i-1 (t k )) means t k The zth constraint between the i-th unit train and the i-1-th unit train at time, where z represents the sequence number of the constraint.

[0058] In practical applications, the preset event triggering mechanism is specifically:

[0059]

[0060] in, Indicates the preset event trigger mechanism, x i (t k ) indicates t k The state of the i-th unit train at time, denotes the Tube set, u0(t k ) denotes the control quantity of the leading train at the current moment, and σ denotes the threshold value.

[0061] In practical applications, the Tube-MPC problem model is specifically as follows:

[0062]

[0063] Among them,

[0064]

[0065]

[0066] Among them, denotes the first objective function, denotes the nominal control sequence of the i-th unit train at time t k , denotes the (j + 1)-th nominal state of the i-th unit train at time t k , denotes the j-th nominal state of the i-th unit train at time t k , A denotes the seventh coefficient matrix, and B denotes the eighth coefficient matrix. denotes the j-th nominal control quantity of the i-th unit train at time t k , D i (t k+j ∣t k ) denotes the j-th external input generated by the i-th unit train receiving the operating state of the leading train at time t k , x i (t k -τ) denotes the state of the i-th unit train at time t k -τ, denotes the nominal state of the i-th unit train at time t k , denotes the robust invariant set, denotes the Minkowski sum, denotes the state variable improvement constraint set, denotes the state variable constraint set, denotes the Minkowski difference, denotes the control variable improvement constraint set, denotes the control variable constraint set, K tube denotes the feedback gain, denotes the n k -th nominal state of the i-th unit train at time t p , that is, the terminal state, Denote the terminal constraint set, \(Q\) denote the first two-dimensional weight coefficient matrix, \(F\) denote the second two-dimensional weight coefficient matrix, \(P\) denote the third two-dimensional weight coefficient matrix, Denote \(t\) k The nominal state of the \(i\)-th unit train at time \(t\), \(\|\cdot\|_2\) denote the two-norm, Denote \(t\) k The nominal state of the \((i - 1)\)-th unit train at time \(t\), \(R\) denote the one-dimensional weight coefficient, Denote \(t\) k The nominal control quantity of the \(i\)-th unit train at time \(t\), Denote The nominal state of the \(i\)-th unit train at time \(t\), i.e., \(t\) k The terminal state at time \(t\), Denote The nominal state of the \((i - 1)\)-th unit train at time \(t\), i.e., \(t\) k The predicted terminal state at time \(t\), \(n\) p Denote the prediction time domain step. When performing S5 or S6, substitute the optimal nominal state of the target train at time \(t\) k into it for solution. for solution.

[0067] In practical applications,

[0068]

[0069] Among them, Denote \(t\) k The disturbance state of the \(i\)-th unit train at time \(t\), Denote the set of real numbers, \(\eta\) denote the boundary of the uncertain disturbance, \(\delta\) denote the discrete time interval, \(h\) denote the linearization parameter of the dynamic model,

[0070]

[0071] Among them, Denote \(t\) k The nominal control quantity per unit mass of the \(i\)-th unit train at time \(t\).

[0072]

[0073] Among them, Denote \(t\) k The nominal state of the \(i\)-th unit train at time \(t\), Denote \(t\) k The \(z\)-th constraint condition between the \(i\)-th and \((i - 1)\)-th unit trains at time \(t\), \(z\) denote the serial number of the constraint condition.

[0074]

[0075] Among them, \(K\) fDenote the feedback gain of the terminal controller, D i (t k ) represents the external input of the i-th unit train at time t k

[0076] In practical applications, the ELQR controller is specifically:

[0077]

[0078] Among them, Denote the second objective function, Q y Denote the first coefficient matrix, y i (t k+j ∣t k ) represents the j-th integrated state of the i-th unit train at time t k , P y Denote the second coefficient matrix, Denote the n-th integrated state of the i-th unit train at time t k , that is, the integrated terminal state, y p (t i (t k+j+1 ∣t k ) represents the (j + 1)-th integrated state of the i-th unit train at time t k , A y Denote the third coefficient matrix, B y Denote the fourth coefficient matrix, D iy (t k+j ∣t k ) represents the j-th external input of the i-th unit train at time t k , y i (t k ∣t k ) represents the integrated state of the i-th unit train at time t k , T represents taking the transpose, Denote the nominal state of the i-th unit train at time t k -τ, Denote the nominal state of the (i - 1)-th unit train at time t k -τ.

[0079] In practical applications, calculating the optimal control quantity of the unit train at the current moment according to the uncertain disturbance factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment specifically includes:

[0080] According to

[0081]

[0082] ​Calculate the actual control quantity of the unit train at the current moment, where u i (t k ) represents the optimal control quantity of the i-th unit train at time t k . represents the optimal nominal control quantity of the i-th unit train at time t k , K tube represents the feedback gain, represents the uncertain disturbance state of the i-th unit train at time t k .

[0083] As Figure 6 shown, the idea of the virtual formation train formation control method provided by the embodiment of the present invention is specifically as follows:

[0084] A. Virtual formation train model construction. Construction of a virtual formation train model considering uncertain disturbances and minimum spacing constraints:

[0085] 1. Set the train mass, resistance coefficient, and train length according to the train information, set the ramp resistance and line speed limit according to the line information such as slope and speed limit, consider the influence of uncertain air resistance to set the uncertain speed disturbance, and establish a single-particle dynamics model of the virtual formation train, that is, the dynamics equation of each unit train in the virtual formation train, specifically including:

[0086] A.1. The dynamics model of the train is based on Newton's second law, and the running resistance includes the basic resistance r i , the ramp additional resistance g i and the bounded uncertain disturbance w i caused by strong wind, unmodeled air resistance, and other additional resistances, and the disturbance boundary is ||ω i (t)|| ∞ ≤ η. That is, the single-particle dynamics model of the train is:

[0087]

[0088] where s i and v i are the position and speed of the i-th unit train respectively, and the dot above represents the derivative with respect to time; m i represents the mass of the i-th unit train; u i (t) represents the actual control quantity of the i-th unit train at time t; represents the basic resistance, (c0, c1, c2) are Davis coefficients; gi(s i ) is the ramp additional resistance at the position s i of the i-th unit train; Denote the bounded uncertain disturbance caused by strong wind, unmodeled air resistance, and other additional resistances at time \(t\) as \(\eta\), where \(\eta\) is the disturbance boundary.

[0089] A.2. For the convenience of theoretical analysis of the platoon stability, it is necessary to linearize the model. By performing a Taylor expansion around the equilibrium speed \(v\) r , the single-particle dynamics model can be expressed as:

[0090]

[0091] where \(h\) i = \(-(c_1 + 2c_2v\) r ) / m i and are all parameters related to linearization.

[0092] 2. According to the spacing strategy between the internal unit trains of the virtual formation train and the single-particle dynamics model, establish the state-space equation of the unit train, specifically including:

[0093] A.3. Define the state of the \(i\)-th unit train at time \(t\) in the virtual formation as:

[0094]

[0095] where \(\Delta s\) i (t) represents the deviation between the position of the \(i\)-th unit train and the desired position at time \(t\), and \(\Delta v\) i (t) is the speed difference between the \(i\)-th unit train and the leading train at time \(t\); \(s_0(t)\) and \(v_0(t)\) represent the position and speed of the leading train at time \(t\), respectively, and \(s\) i (t) and \(v\) i (t) represent the position and speed of the \(i\)-th unit train at time \(t\), respectively, and \(d\) i = \(i(t\) d v_0 + S\) d + S\) l ) is the desired position of the \(i\)-th unit train considering the fixed time interval \(t\) d , the fixed spacing \(S\) d and the train length \(S\) l .

[0096] A.4. Express the state equation of the \(i\)-th unit train in the virtual formation in discrete form (the discrete time interval is \(\delta\)):

[0097] x\) i (t\) k+1 ) = Ax\) i (t\) k ) + Bu\) i (t\) k ) + D\) i (t\)k ) + W i (t k ) Equation 18

[0098] Among them, the coefficient matrix is

[0099]

[0100] To represent the influence of uncertain disturbances, the nominal state equation and disturbance state equation of the i-th unit train are further defined, represented by and respectively. There are relationships and between the actual state equation, nominal state equation and disturbance state equation. Therefore, the nominal state equation and disturbance state equation can be expressed as Equation 1 and Equation 2.

[0101] 3. According to the traction and braking performance constraints, speed limit constraints and minimum spacing constraints, establish state constraint equations and control variable constraint equations, specifically including:

[0102] A.5. Considering the traction and braking performance constraints, speed limit constraints and minimum spacing constraints, here introduce the constraint conditions on the state x i (t k ) and the control variable u i (t k ), such as Equation 3 and Equation 4. Among them, (U max , U min ) are the maximum traction acceleration and maximum braking deceleration respectively. The specific state constraint conditions φ z {z = 1, 2, 3} are as follows:

[0103] φ l (x i , x i-1 ) = H1(x i - x i - 1) + t d v0 + S d - S m

[0104]

[0105] φ3(x i , x i - 1) = H2x i - v0 + v lim

[0106] Among them, φ1(x i , x i-1 ) represents the first safety spacing that should be maintained between the i-th and the (i - 1)-th unit trains, and φ2(x i , xi-1 ) represents the second safety distance that should be maintained between the $i$-th and the $(i - 1)$-th unit trains, $\varphi_3(x i , x i-1 ) indicates that the speed of the $i$-th and the $(i - 1)$-th unit trains should be less than the speed limit, $H_1 = [1, 0]$ and $H_2 = [0, 1]$ are coefficient matrices, $v lim is the line speed limit value, $S m is the safety distance margin, $S d is the fixed distance.

[0107] B. Design of Tube-based Model Predictive Control (Tube-MPC) algorithm:

[0108] According to the requirements of virtual formation train formation stability control, reducing the spacing error and speed difference between the unit train and the leading train, and between the unit train and its preceding train are taken as control objectives, and the objective function and cost function are set; according to the objective function and the state space equation, the Tube-MPC problem model formula 6 is established, and the optimal controller formula 14 integrating disturbance state feedback is designed, specifically including:

[0109] B.1. Define the stage cost function and the terminal cost function as formulas 7 and 8 respectively, where $n p is the prediction time domain step size, $Q = diag\{q_1, q_2\}$, $F = diag\{f_1, f_2\}$, $P = diag\{p_1, p_2\}$ are weight coefficient matrices, and $R$ is a one-dimensional weight coefficient. According to the cost function, the objective function is defined as:

[0110]

[0111] B.2. In the Tube-MPC framework, introduce and which represent the nominal state trajectory (nominal state sequence) and the nominal control sequence within the prediction time domain respectively. For time $t k $, due to the existence of communication delay $\tau$, the $i$-th unit train can only receive the past state information $x i (t k - \tau)$, which is used to initialize the state initial condition in the model predictive control problem. The specific modeling details of the model predictive control are as formula 6:

[0112] Among them, the first constraint condition is the nominal state equation in A.4; the second constraint condition is the initial state assignment and considers the influence of the delay $\tau$, is a robust invariant set; the third and fourth constraint conditions are the improved constraints of the state variables and control variables, and the robust invariant set is added to cope with the influence of uncertain disturbances, for K tube feedback control gain; and represent the Minkowski sum and difference respectively; the last one is the terminal constraint condition, is the terminal constraint set. In the subsequent step C, the robust invariant set state variable improved constraint set and the control variable improved constraint set will be designed to ensure the feasibility and stability of the above problems.

[0113] B.3. By solving the optimization problem in B.2 at time t k the optimal nominal control sequence and the predicted state trajectory (optimal nominal state sequence) are respectively:

[0114]

[0115]

[0116] where, means, means that for the nominal MPC controller, the optimal nominal control quantity of the i-th unit train at t k is the first term in, that is However, due to the existence of uncertain disturbance factors the actual controller is designed as formula 14, where K tube =[0, k tube is the feedback gain.

[0117] C. Tube set design:

[0118] Considering the influence of uncertain disturbances, calculating the robust invariant set of the perturbed state is C.1, C.2 is to prove and deduce how C.1 is obtained, and based on this invariant set, the Tube set, the state constraint set, and the control variable constraint set are designed, and it is proved that under the influence of uncertain disturbances, the constraint conditions can still be satisfied and the system state is always within the Tube set, specifically including:

[0119] C.1. Propose a theorem: For the virtual formation train system in A.4, if k tube ∈(0, 2 / δ + h), its robust invariant set can be defined as formula 9:

[0120] C.2. Prove that the theorem in C.1 holds: Define the velocity perturbation difference equation as:

[0121]

[0122] wherein, is the speed perturbation. Substituting the boundary constraints of the controller and the perturbation ||ω i (t)|| ∞ ≤η into the above formula, we can obtain:

[0123]

[0124] If |1 + (h - k tube )δ| < 1, that is, k tube ∈(0, 2 / δ + h), the above inequality can be further transformed into:

[0125]

[0126] Similarly, the position error within the prediction horizon can be expressed as:

[0127]

[0128] Therefore, it can be obtained that the perturbation state is within the robust invariant set, that is where the robust invariant set can be obtained by combining the above formulas.

[0129] C.3. According to the optimal predicted state trajectory in B.3 and the robust invariant set in C.1 the Tube set is:

[0130]

[0131] C.4. Propose a theorem: For the virtual formation train system in A.4, under the action of the controller in B.3, there is:

[0132] (i) If the nominal control variable satisfies the constraint conditions in B.2, that is where is defined in the following formula, then the actual control variable u i will satisfy the constraint conditions in A.5, that is Formula 10 can be obtained.

[0133] (ii) If the nominal state variable satisfies the constraint conditions in Formula B.2, that is where is defined in the following formula, then the actual state variable x i will satisfy the constraint conditions in A.5, that is and the actual state variable x i is always in the Tube set we can obtain Equation 11

[0134] wherein,

[0135]

[0136]

[0137]

[0138] C.5. Prove the theorem in C.4: For (i), based on the controller in B.3, by substituting the control variable constraint condition in A.5 and the robust invariant set in C.1 into the nominal control variable can be obtained for the improved constraint set and The relationship between them shows that if under the disturbance there is then it satisfies This means that the control constraints can still be satisfied under the disturbance.

[0139] For (ii), by substituting the state variable constraint condition in A.5 and the robust invariant set in C.1 into the nominal state variable can be obtained for the improved constraint set Due to the relationship in A.4 among the state variables If and then it satisfies Similarly, if using the optimal solution of the optimal problem in B.2 to replace the nominal state we can obtain Therefore, it is proved that the actual state and trajectory of the virtual formation train system in A.4 are always located within the Tube, that is while ensuring that the state variable constraints are satisfied.

[0140] D. Proof of Feasibility and Local Stability:

[0141] To ensure the feasibility and stability of the controller, a terminal controller is constructed to obtain a feasible control sequence, and then a feasible state trajectory is calculated based on this; this state trajectory will satisfy the terminal constraints, ensuring the feasibility of the problem. In addition, a terminal constraint set is designed to ensure the asymptotic stability of the virtual formation train system.

[0142] The proof of feasibility and local stability in Step D includes the following content:

[0143] D.1. To ensure the feasibility of the controller, the following theorem is proposed: For the virtual formation train system in A.4, if the terminal constraint condition formula (12) is satisfied, then the Tube-MPC optimization problem in B.2 is feasible at time t > t k are all feasible, where K f = -(R + B T PB) -1 B T PA is the terminal control gain.

[0144] D.2. Prove the theorem in D.1:

[0145] For time t k+1 , construct a feasible control sequence

[0146]

[0147] where is the terminal controller, which is used to drive the terminal state at the current time to transfer to the next time, and its state transfer equation is:

[0148]

[0149] where A f = (A + BK f ). It should be noted that this terminal controller also needs to satisfy the controller constraint conditions, that is Based on this, the terminal constraint set in D.1 can be obtained by substituting the terminal controller into the nominal control constraint in C.4. In addition, the controller gain parameter K in the terminal constraint set f needs to be further designed to ensure the feasibility of the controller.

[0150] Based on the terminal controller, a feasible predicted state trajectory at time t k+1 can be constructed:

[0151]

[0152] To ensure the feasibility at time t k+1 , the terminal state needs to be within the terminal constraint set . This can be achieved by making the terminal state asymptotically converge to zero. By constructing the terminal state transfer equation into a linear quadratic regulation problem to ensure convergence, so K f = -(R + B T PB) -1 B TPA. It means that if then will also hold. Therefore, it can be proved that if the Tube-MPC problem in B.2 is feasible at time t k then, by recursive induction, it is feasible at all times t > t k .

[0153] D.3. To ensure the asymptotic stability of the controller, the theorem is proposed: for the virtual formation train system in A.4, if the following constraint conditions are satisfied:

[0154]

[0155] then the Tube-MPC in B.2 is asymptotically stable and input-to-state stable.

[0156] D.4. Prove the theorem in D.3: According to the feasible control sequence and state trajectory in D.2, the non-optimal cost at time t k+1 can be calculated for comparison with the optimal cost. Select the optimal cost as the Lyapunov function Therefore, it only needs to prove that the relationship holds to prove the asymptotic stability. Subtract the Lyapunov function at time t k from that at t k+1 , and we can get:

[0157]

[0158] To obtain V J (t k+1 ) - V J (t k ) < 0, substitute K f = -(R + B T PB) -1 B T PA into the above, and the following inequality can be obtained:

[0159]

[0160] By the Schur Complement, the above inequality can be expressed by the linear matrix inequality in D.3, and can be solved using the LMI toolbox in MATLAB.

[0161] From this, we can get V J (t k+1 ) - V J (t k ) < 0, indicating that the optimal state of the nominal virtual formation train system asymptotically converges to the equilibrium state. Therefore, there exists a The function β(·, ·) satisfies that:

[0162]

[0163] In addition, the perturbation boundary is given by C.1, which means that there exists a class function γ(·) such that:

[0164]

[0165] According to the relationship and the initial perturbation condition Combining the above formulas, we can obtain:

[0166]

[0167] Thus, it is proved that the virtual formation train system in A.4 is input-to-state stable, and the solution obtained by the proposed algorithm is asymptotically bounded.

[0168] E. Proof of queue stability:

[0169] Since the Tube-MPC problem requires a numerical algorithm and it is impossible to further explicitly analyze the queue stability of the controller. Considering the case where the constraints are not violated and the perturbation is small, the control problem can be transformed into the following Extended-linear quadratic regulator (ELQR) problem to obtain an approximate optimal feedback control rate; based on this, the sufficient conditions for queue stability are derived using the frequency domain analysis method.

[0170] The proof of queue stability in step E includes the following content:

[0171] E.1. Considering the case where the constraints are not violated and the perturbation is small, the control problem in B.2 can be transformed into the following ELQR problem, namely formula 13, to obtain an approximate optimal solution:

[0172] where is the integrated state, represents the external input, Q y = diag{Q, F}, P y = diag{P, P}, A y = diag{A, A} and B y = [B T , B T T are coefficient matrices.

[0173] ​E.2. To derive the optimal control law for this ELQR problem, a batch algorithm (Batch Solution) is used to solve it, and the following form of the linear feedback controller can be obtained:

[0174]

[0175] where, represents the control gain of the state offset, is the external input control gain due to the traction and braking of the leading train and the preceding unit train.

[0176] E.3. To describe the speed response of the i-th unit train to the leading train and the preceding train in the frequency domain, the derivative of the feedback control law in E.2 is taken and the Laplace transform is performed, and the following can be obtained:

[0177]

[0178] where,

[0179]

[0180] Here, the coefficients are expressed in a simplified form, that is and

[0181] E.4. Theorem is proposed: For the virtual formation train system in A.4, under the control of the controller in E.2, if the following conditions are satisfied

[0182]

[0183] where, Λ = {l, p},

[0184]

[0185] then the system is queue stable.

[0186] E.5. Prove the theorem in E.4: Queue stability holds if

[0187]

[0188] Therefore, first perform the modulo operation on Substitute s = jω, e τjω = cos(τω) + j sin(τω), τ ≥ 0, ω > 0, sin(τω) ≤ τω, cos(τω) ≤ 1, and k s + hk v ≥ 0 into the formula in E.3 to obtain

[0189]

[0190] Queue stability requires 4|NM Λ | 2 -|DM| 2 ≤0 holds, that is, it satisfies and Thus, the sufficient conditions shown in the theorem in E.4 can be obtained.

[0191] F. Integrated control algorithm design:

[0192] To integrate the Tube-MPC and ELQR controllers, an event-triggering mechanism is designed to describe the actual operating state of the unit train to cope with sections with large disturbances and speed limit changes along the line and cruise sections with small disturbances and constant speed limits, and to improve the solution efficiency of the algorithm.

[0193] The integrated control algorithm design in step F includes the following:

[0194] F.1. To integrate the Tube-MPC and ELQR controllers, an event-triggering mechanism is designed as shown in Equation 5, where u0(·∣t k )={u0(t k+j ∣t k ):j = 0,…,n p -1}, σ∈[0,U max . Specifically, the first event in the above formula represents the state leaving the Tube, and the other two events represent the continuous traction or braking of the leading train due to speed limit changes. A threshold σ is set here to distinguish between the traction condition and the cruise condition. This event-triggering mechanism is to describe the actual operating state of the unit train to cope with sections with large disturbances and speed limit changes along the line and cruise sections with small disturbances and constant speed limits. Therefore, introducing the event set into the algorithm can improve the efficiency without having to solve the complex constrained optimization problem in B.2 at each moment, that is, using the ELQR feedback controller in E.2 for control when there is no triggered event set .

[0195] The virtual formation train formation control method described in the embodiments of the present invention is specifically as follows in practical applications:[[]]

[0196] 101. Line information input:

[0197] Determine the inter-station length according to the actual line information, input the line gradient, speed limit and other information of each section of the station, set the train mass, resistance coefficient, train length, traction and braking performance constraints according to the train information; set the desired spacing and minimum spacing constraints according to the spacing strategy between the unit trains inside the virtual formation to realize the modeling of the virtual formation train operation environment model.

[0198] 102. Initialize the status information of all unit trains in the virtual formation:

[0199] At time t k = t0, the leading train (i = 0) loads the recommended speed curve and transmits the current status information through vehicle-to-vehicle communication. Each unit train will receive the information from the leading train and obtain its own current status.

[0200] 103. At time t k , calculate the optimal nominal control quantity and the optimal nominal state Optimal nominal control sequence and the predicted state trajectory

[0201] 103.1. The i-th unit train receives the status of the leading train and the preceding unit train i - 1.

[0202] 103.2. According to whether the actual running state of the i-th unit train is still in the Tube and whether it is in the cruising state, judge whether Event Formula 5 is triggered. If triggered, go to Step 103.3; otherwise, go to Step 103.4.

[0203] 103.3. Based on the virtual formation train operation environment model in Step 101 and the status of the preceding vehicle in Step 103.1, solve the Tube-MPC problem model, i.e., Formula 6, and calculate the optimal nominal control sequence and the predicted state trajectory and transmit the above status and control information to the following vehicle i + 1.

[0204] 103.4. Based on the virtual formation train operation model in Step 101 and the status of the preceding vehicle in Step 103.1, solve the ELQR controller, i.e., Formula 13, solve the ELQR problem, and calculate the feedback control quantity Let and transmit this control quantity information to the following vehicle i + 1.

[0205] 103.5. Due to the uncertain disturbance factors Combined with the nominal control quantity in 103.3 or 103.4, calculate the actual control quantity according to Formula 14, and update the time step t k = t k+1 ; if t k is less than the total simulation duration, then go to Step 103; otherwise, terminate the algorithm.

[0206] The above algorithm can be implemented using MATLAB, Python, C#, or other languages. In this example, MATLAB is used for implementation.

[0207] In this implementation example, the CRH high-speed EMU is taken as the research object, and the Beijing-Shanghai line data is used as an example for simulation experiments.

[0208] Figure 2 It is the actual state trajectory and the nominal state trajectory in the Tube considering the influence of initial disturbance and uncertain disturbance. In the experiment, the virtual formation train consists of a leading train and four subsequent unit trains, cruising at a speed of 300 km / h. An initial disturbance of Δv1 = 2 m / s and Δs1 = 12 m is applied to the first unit train, accounting for approximately 2.4% and 8% of the running speed and spacing, respectively. Figure 2 It shows that the initial disturbance is eliminated on the unit train, and under the influence of uncertain disturbance, the actual operating state is constrained within the Tube and always remains near the optimal nominal state trajectory. This result proves that the virtual formation train system is asymptotically stable under the current controller. At the same time, it can be found from Figure 2 that the fluctuation range of the state deviation and the size of the Tube (about ±0.1 m / s in speed difference and about ±0.2 m in spacing error) are both smaller than the boundary of the uncertain disturbance η = 0.5.

[0209] Figure 3 are the controller parameters under different communication delays τ = {0, 0.2, 0.4, 0.6} s (corresponding to Figure 3 (a), Figure 3 (b), Figure 3 (c), and Figure 3 (d) respectively) of the stability domain (the color bar is the value range of the parameter ). According to the sufficient condition for queue stability, the influence of communication delay on queue stability can be analyzed, as shown in Figure 3 . With the other parameters fixed, the stability domain is plotted within the domain of the three main influencing parameters . It can be seen from Figure 3 (a), Figure 3 (b), Figure 3 (c), and Figure 3 (d) that the stability domain shrinks sharply with the increase of communication delay. This result provides a strategy and direction for controller parameter adjustment and control performance improvement under communication delay conditions. Figure 4 is a comparison chart of the effects before and after adjusting the controller parameters based on the Figure 3 stability domain considering the influence of communication delay. Figure 4 (a) is before adjustment: control variable, Figure 4 (b) is after adjustment: control variable,Figure 4 (c) Before adjustment: speed difference, Figure 4 (d) After adjustment: speed difference, Figure 4 (e) Before adjustment: spacing deviation, Figure 4 (f) After adjustment: spacing deviation. Comparing Figure 4 the results in, it can be seen that communication delay has an obvious negative impact on control performance. Figure 4 In the left column, before parameter adjustment, even though the initial disturbance amplitude decreases and the controller attempts to cancel the disturbance, there are still large fluctuations in the running speed. At the same time, the speed fluctuation of the 4th unit train exceeds that of its preceding unit train, so the single - vehicle stability and the queue stability are not guaranteed. Compared with Figure 4 the results given in the left column, Figure 4 the fluctuation amplitudes of the states and control variables in the right column are significantly improved, and it can be seen that the single - vehicle asymptotic stability is guaranteed, where the disturbance is weakened and the speed difference and spacing deviation asymptotically converge to the equilibrium state.

[0210] Figure 5 This is a comparative experiment on the calculation time between the traditional model predictive control method and the proposed integrated algorithm. Since the prediction horizon is the main parameter related to the calculation time of the model predictive controller, the prediction horizon is selected as the independent variable, and its range is set from 2 s to 22 s. In Figure 5 although the calculation times of both methods show a parabolic upward trend, the integrated control algorithm is more efficient than the traditional model predictive control algorithm. It can be found that the integrated control algorithm better meets the real - time requirements of practical applications, and its calculation time is lower than 0.2 s in most cases.

[0211] The embodiment of the present invention also provides a virtual formation train formation control system corresponding to the above - mentioned method, including:

[0212] A dynamic equation construction module, configured to construct the dynamic equations of each unit train in the virtual formation train according to the line gradient and speed limit of each section between each station.

[0213] A state - space equation construction module, configured to construct the state - space equations of each unit train according to the dynamic equations of each unit train in the virtual formation train; the state - space equations include a nominal state equation and a disturbance state equation.

[0214] A train operation environment model construction module, configured to construct a train operation environment model of the virtual formation train according to the state - space equations and constraint equations of each unit train; the constraint equations include state constraint equations and control variable constraint equations.

[0215] A judgment module, configured to, for any unit train in the virtual formation train, determine whether a preset event triggering mechanism is triggered according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

[0216] A Tube-MPC problem model solving module, configured to, if the preset event triggering mechanism is triggered, solve the Tube-MPC problem model based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment.

[0217] An ELQR controller solving module, configured to, if the preset event triggering mechanism is not triggered, solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment.

[0218] An optimal control quantity calculation module, configured to calculate the optimal control quantity of the unit train at the current moment according to the uncertain disturbance factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment, control the unit train according to the optimal control quantity of the unit train at the current moment, then update the current moment and return to determine whether the preset event triggering mechanism is triggered for any unit train in the virtual formation train according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

[0219] An embodiment of the present invention further provides an electronic device, including:

[0220] A memory and a processor, where the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the virtual formation train formation control method according to the above.

[0221] An embodiment of the present invention further provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the virtual formation train formation control method as described above is implemented.

[0222] The present invention realizes a stable and robust control method for the virtual formation train formation based on Tube, and has the following advantages:

[0223] It has strong anti-interference ability. Based on the robust invariant set and model predictive control, it focuses on ensuring the stability of single trains and platoons under the influence of uncertain disturbances and communication delays. Considering the influence of uncertain disturbances during the train operation, the Tube model predictive robust control method can confine the perturbed system state within the Tube set smaller than the disturbance fluctuation range, and can adapt to complex operating conditions, such as strong wind weather or scenarios of entering and exiting tunnels. The sufficient conditions for platoon stability are derived through frequency domain analysis, enabling the virtual formation to quickly recover to a stable operating state after being disturbed, and ensuring the feasibility and asymptotic stability of the algorithm.

[0224] It has platoon stability. Based on the Extended-linear quadratic regulator (ELQR) and frequency domain analysis, the stable domain of the controller parameters under the influence of communication delay is solved. By selecting the controller parameters within the obtained stable domain of parameters, the propagation of disturbances within the virtual formation trains can be effectively avoided, ensuring that the uncertain disturbances gradually decay during the propagation within the virtual formation trains under the influence of communication delay, and enabling the virtual formation trains to quickly recover and maintain a stable formation, thus ensuring the platoon stability of the algorithm.

[0225] It has high computational efficiency. Through the integrated control strategy, feedback control can be directly carried out when the disturbance is small without additional optimization calculations.

[0226] Considering the uncertain speed disturbance, a robust control algorithm is designed using the Tube-based Model Predictive Control (Tube-MPC). On the premise of meeting the minimum spacing constraint, the influence of uncertain disturbances is reduced, so that the fluctuation range of the system state is always within the Tube constraint set smaller than the disturbance boundary.

[0227] Based on the robust invariant set theory, the constraint sets of state variables and control inputs are improved and designed, ensuring the feasibility and local stability of the proposed algorithm.

[0228] Based on the event-triggered mechanism, an integrated control strategy combining Tube-MPC and ELQR is designed, reducing the computational complexity and improving the algorithm efficiency.

[0229] An integrated control algorithm is designed, improving the solution efficiency and having good real-time performance.

[0230] In this specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0231] In this article, specific examples are used to elaborate on the principles and implementation manners of the present invention. The descriptions of the above embodiments are only used to help understand the method of the present invention and its core idea. At the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation on the present invention.

Claims

1. A method for controlling the formation of a virtual formation train, characterized in that, Including: Construct the dynamic equations of each unit train in the virtual formation train according to the line gradient and speed limit of each section between each station; Construct the state space equations of each unit train according to the dynamic equations of each unit train in the virtual formation train; the state space equations include a nominal state equation and a perturbation state equation; Construct a train operation environment model of the virtual formation train according to the state space equations and constraint equations of each unit train; the constraint equations include a state constraint equation and a control variable constraint equation; For any unit train in the virtual formation train, judge whether a preset event trigger mechanism is triggered according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment; If the preset event trigger mechanism is triggered, solve the Tube-MPC problem model based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; the target train is the previous unit train of the unit train; If the preset event trigger mechanism is not triggered, solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment, and the optimal nominal state of the target train at the current moment, to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; Calculate the optimal control quantity of the unit train at the current moment according to the uncertain perturbation factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment, control the unit train according to the optimal control quantity of the unit train at the current moment, then update the current moment and return to judge whether the preset event trigger mechanism is triggered according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment for any unit train in the virtual formation train.

2. The virtual formation train formation control method according to claim 1, wherein, The preset event trigger mechanism is specifically: Among them, represents a preset event trigger mechanism, x i (t k ) represents the state of the i-th unit train at time t k , represents the Tube set, u0(t k ) represents the control quantity of the leading train at the current moment, and σ represents the threshold value.

3. The virtual formation train formation control method according to claim 2, characterized in that The Tube-MPC problem model is specifically: Among them, represents the first objective function, represents t k the nominal control sequence of the i-th unit train at time t, represents t k the (j + 1)-th nominal state of the i-th unit train at time t, represents t k the j-th nominal state of the i-th unit train at time t, A represents the seventh coefficient matrix, B represents the eighth coefficient matrix, represents t k the j-th nominal control quantity of the i-th unit train at time t, D i (t k+j ∣t k ) represents t k the j-th external input generated by the i-th unit train receiving the operating state of the leading train at time t, x i (t k -τ) represents t k the state of the i-th unit train at time t - τ, represents t k the nominal state of the i-th unit train at time t, represents the robust invariant set, represents the Minkowski sum, represents the state variable improved constraint set, represents the state variable constraint set, represents the Minkowski difference, represents the control variable improved constraint set, represents the control variable constraint set, K tube represents the feedback gain, represents t k the n p -th nominal state of the i-th unit train at time t, i.e., the terminal state, represents the terminal constraint set, Q represents the first two-dimensional weight coefficient matrix, F represents the second two-dimensional weight coefficient matrix, P represents the third two-dimensional weight coefficient matrix, represents t k the nominal state of the i-th unit train at time t, || ||2 represents the two-norm, represents t k the nominal state of the (i - 1)-th unit train at time t, R represents the one-dimensional weight coefficient, represents t k the nominal control quantity of the i-th unit train at time t, represents the nominal state of the i-th unit train at time t, represents the nominal state of the (i - 1)-th unit train at time t, n p Indicates the prediction time domain step size.

4. A method for controlling the formation of a virtual formation train according to claim 3, characterized in that The ELQR controller is specifically: Among them, represents the second objective function, Q y represents the first coefficient matrix, y i (t k+j ∣t k ) represents t k the j-th integrated state of the i-th unit train at time t, P y represents the second coefficient matrix, represents t k the n-th integrated state of the i-th unit train at time t p th integrated state, y i (t k+j+1 ∣t k ) represents t k the (j + 1)-th integrated state of the i-th unit train at time t, A y represents the third coefficient matrix, B y represents the fourth coefficient matrix, D iy (t k+j ∣t k ) represents t k the j-th external input of the i-th unit train at time t, y i (t k ∣t k ) represents t k the integrated state of the i-th unit train at time t, T represents taking the transpose, represents t k the nominal state of the i-th unit train at time t - τ, represents t k the nominal state of the (i - 1)-th unit train at time t - τ.

5. A method for controlling the formation of a virtual formation train according to claim 1, characterized in that The calculating the optimal control quantity of the unit train at the current moment according to the uncertain perturbation factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment specifically includes: According to the formula calculate the actual control quantity of the unit train at the current moment, where u i (t k ) represents the actual control quantity of the i-th unit train at time t k , represents the optimal nominal control quantity of the i-th unit train at time t k , K tube represents the feedback gain, represents the uncertain disturbance state of the i-th unit train at time t k .

6. A method for controlling the formation of a virtual formation train according to claim 4, characterized in that Among them, represents the disturbance state of the i-th unit train at time t k moment, represents the set of real numbers, η represents the boundary of the uncertain disturbance, δ represents the discrete time interval, and h represents the linearization parameter of the dynamic model. Among them, represents the nominal control quantity per unit mass of the i-th unit train at time t, k U min represents the maximum braking deceleration, max U represents the maximum traction acceleration; in, Indicates t k The nominal state of the i-th unit train at time, Indicates t k The zth constraint between the i-th and i-1-th unit trains at time, where z represents the sequence number of the constraint. Among them, K f represents the feedback gain of the terminal controller, D i (t k ) represents the external input of the i-th unit train at time t k .

7. A method for controlling the formation of a virtual formation train according to claim 6, characterized in that The specific nominal state equation is where represents the nominal state of the i-th unit train at time t, represents the derivative of the nominal state, A c represents the fifth coefficient matrix, B c represents the sixth coefficient matrix, represents the nominal control quantity of the i-th unit train at time t, represents the external input generated by the i-th unit train receiving the operating state of the leading train at time t; The specific disturbance state equation is as follows where represents the disturbance state of the i-th unit train at time t, represents the derivative of the disturbance state, represents the disturbance control quantity of the i-th unit train at time t, represents the uncertain disturbance of the i-th unit train at time t; The specific control variable constraint equation is where u i (t k ) represents the control quantity of the i-th unit train at time t k , represents the constraint set of the control variable, represents the set of real numbers, U min represents the maximum braking deceleration, U max represents the maximum traction acceleration; The specific state constraint equation is as follows where x i (t k ) represents the state of the i-th unit train at time t k , represents the set of constraints of the state variables, and φ z (x i (t k ), x i-1 (t k )) represents the z-th constraint condition between the i-th unit train and the (i - 1)-th unit train at time t k , where z represents the serial number of the constraint condition.

8. A virtual formation train formation control system, characterized in that, Including: A dynamic equation construction module, configured to construct the dynamic equations of each unit train in the virtual formation train according to the line gradient and speed limit of each section between each station; A state space equation construction module, configured to construct the state space equations of each unit train according to the dynamic equations of each unit train in the virtual formation train; the state space equations include a nominal state equation and a perturbation state equation; A train operation environment model construction module, which is used to construct a train operation environment model of a virtual formation train according to the state space equations and constraint equations of each unit train; the constraint equations include state constraint equations and control variable constraint equations; A judgment module, which is used to judge whether a preset event triggering mechanism is triggered for any unit train in the virtual formation train according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment; A Tube-MPC problem model solving module, which is used to solve the Tube-MPC problem model based on the train operation environment model, the nominal state of the unit train at the current moment and the optimal nominal state of the target train at the current moment if the preset event triggering mechanism is triggered, so as to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; the target train is the previous unit train of the unit train; An ELQR controller solving module, which is used to solve the ELQR controller based on the train operation environment model, the nominal state of the unit train at the current moment and the optimal nominal state of the target train at the current moment if the preset event triggering mechanism is not triggered, so as to obtain the optimal nominal control quantity of the unit train at the current moment and the optimal nominal state of the unit train at the current moment; An optimal control quantity calculation module, which is used to calculate the optimal control quantity of the unit train at the current moment according to the uncertain disturbance factors of the unit train at the current moment and the optimal nominal control quantity of the unit train at the current moment, control the unit train according to the optimal control quantity of the unit train at the current moment, then update the current moment and return to judge whether the preset event triggering mechanism is triggered for any unit train in the virtual formation train according to the control quantity of the leading train at the current moment and the state of the unit train at the current moment.

9. An electronic device, characterized in that, It includes: A memory and a processor, the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to execute the virtual formation train formation control method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores a computer program, and when the computer program is executed by the processor, it realizes the virtual formation train formation control method according to any one of claims 1 to 7.

Images