Heavy-load group train cross-layer control system based on random game

Abstract

The invention discloses a heavy-load group train cross-layer control system based on a random game, and the system comprises a data collection module which is used for collecting the parameter information of trains in a heavy-load train group and the communication state between the trains; the game algorithm construction module is used for constructing a random game algorithm based on the parameter information of the trains and the communication state between the trains; the control strategy generation module is used for inputting an H-infinity optimal control algorithm based on a game strategy generated by a random game algorithm, and updating the running state of the train in real time; and the state feedback module is used for receiving the train running state updated in real time and carrying out information interaction. According to the invention, for a heavy-load freight scene with a large ramp of 30 per mill or more and more than 200 marshalling vehicles, through a random cross-layer control architecture and a dynamic resistance compensation algorithm, technical objectives of reducing brake instruction transmission delay time, control unit fault switching time and ramp constant-speed control errors are realized; and the running safety and the braking efficiency of the train under complex working conditions are improved.

Description

Technical Field

[0001] This invention relates to the field of heavy-load train control technology in rail transit, specifically to a cross-level control system for heavy-load group trains based on random game theory. Background Technology

[0002] In recent years, with the growth in energy demand, heavy-haul railway coal transportation has faced a severe shortage of transport capacity. To improve transportation efficiency, the industry has generally adopted the methods of lengthening train formations and increasing axle load. However, such measures complicate the longitudinal dynamic characteristics of trains, which can easily lead to problems such as uneven force on couplers and insufficient coordination of braking systems. This results in frequent acceleration or deceleration during operation, which not only reduces energy efficiency but also exacerbates equipment wear and safety risks.

[0003] Against this backdrop, the heavy-haul train group operation mode has emerged, enhancing overall transport capacity through the coordinated formation of multiple trains. However, the strong dynamic coupling between trains within the group and the numerous environmental disturbances (such as gradient changes and wind resistance fluctuations) make it difficult for traditional control systems, which rely on fixed models or single Kalman filter estimations, to accurately track train states. This results in control command lags, frequent speed adjustments, and impacts the stability and safety of group operation. Specifically, this manifests as follows:

[0004] 1. Delayed Coordination Control: The existing system is slow to respond to the dynamic distribution of traction / braking force among trains in the train group, which aggravates longitudinal impact and is prone to coupler breakage or derailment accidents.

[0005] 2. Difficulty in longitudinal dynamics modeling of heavy-haul train groups: During operation, heavy-haul train groups are affected by many factors such as track gradient, track curve radius, wheel hub friction and the load of heavy-haul trains. In addition, they are more susceptible to communication interference. These uncertain interferences are difficult to model and cannot be accurately modeled, resulting in high nonlinearity and complexity in the longitudinal dynamics modeling of heavy-haul train groups.

[0006] 3. The contradiction between energy consumption and efficiency: Frequent speed adjustments can lead to safety hazards during the operation of heavy-load train groups, and result in serious energy waste, while also restricting further improvement in transportation efficiency.

[0007] Based on the aforementioned problems, a control system for heavy-haul train group operations is urgently needed. This invention combines stochastic game theory with complex system modeling, and takes into account the characteristics of heavy-haul train group operations to construct a cross-layer architecture, which serves as the foundation for a collaborative control system. Furthermore, based on stochastic game theory, the interference and the payoffs of both sides are defined within the game system, and a cross-layer optimization control system is designed to achieve a balance between the global stability and local response rate of the train group operation, providing technical support for the efficient and safe operation of heavy-haul railways. Summary of the Invention

[0008] To address the above technical problems, this invention proposes a cross-level control system for heavy-load group trains based on random game theory. The system specifically includes:

[0009] The data acquisition module is used to collect parameter information of trains in the heavy-haul train group and the communication status between trains;

[0010] The game algorithm construction module is used to construct a random game algorithm based on the parameter information of the train and the communication status between the trains;

[0011] The control strategy generation module is used to generate the game strategy input H based on the random game algorithm. ∞ Domain optimization algorithms are used to update the train's operating status in real time.

[0012] The status feedback module is used to receive real-time updates on train operation status and exchange information.

[0013] Optionally, in the data acquisition module, the train parameter information includes the number of train groups, the traction force matrix of the train groups, the braking force matrix of the train groups, the status matrix of the train groups, the control matrix of the train groups, the noise matrix of the train groups, and the control rate of the train groups.

[0014] Optionally, in the data acquisition module, the communication status between the trains specifically includes:

[0015]

[0016] in, For t k+1 Estimated train operation status at any time The state matrix, For the control matrix, u c (t k ) for t k The actual control input at any given time, u(t) k ) for t k Timing control input, L θ For observation gain, Let β be the observation matrix. θ Indicates the communication status; a value of 1 indicates that the transmission of vehicle status information has failed due to interference, while a value of 0 indicates that the transmission has succeeded. K θ To control the gain, For t k Estimated train operation status at any time.

[0017] Optionally, the random game algorithm includes interference actions. and defensive actions

[0018]

[0019] Among them, f n (k) and g m (k) represent defensive actions (def) n and interference actions jam m The probability of occurrence, where n is the probability of the nth interference attempt. t represents the total number of times interference is initiated. k Let m be the time interval, and m be the number of times the m-th defensive action is initiated.

[0020] Optionally, the control strategy generation module includes a closed-loop controller and an H... ∞ Domain closed-loop control algorithm and operation status calculation submodule;

[0021] The closed-loop controller is used to calculate the actual speed parameters of the train group;

[0022] The H ∞ The domain optimization algorithm is used to characterize the interaction between decision-making actions and uncertain disturbances between the train group's operating state and the game strategy generated by the random game algorithm based on the actual speed parameters.

[0023] The operation status calculation submodule is used to calculate the operation status of the train group based on the decision action interaction.

[0024] Optionally, the closed-loop controller specifically comprises:

[0025] Based on uncertain interference and the vehicle-to-vehicle communication channel status, the desired speed parameters of the train are input into the closed-loop controller, and the actual speed parameters of the train group are output within the scope of the closed-loop controller:

[0026] u i (t): = μ i (t,x i (t); θ(t)), t∈[t0, t n ),

[0027] w i，e (t): = v i (t,x i (t); θ(t)), t∈[t0, t n ),

[0028] Among them, u i (t) represents the control input for train i, μ i (t,x i (t); θ(t)) represents the closed-loop control strategy, t is the time variable, t0 is the time when the disturbance occurs, and t n w represents the time when the interference behavior ends. i,e (t) represents the interference noise at time vi (t,x i (t); θ(t)) represents the state space of train i's game behavior, x i θ(t) represents the running state of train i, and θ(t) represents the communication state of train-to-train communication at time t.

[0029] Optionally, the closed-loop controller is a minimum-maximum closed-loop controller;

[0030] Minimum value calculation:

[0031]

[0032] Where V(·) is the cost function, and θ is the communication state. Let t be the expected function. h For the communication period, u i To control the input, w i,e For interference and noise, Let λ be the total number of game-related actions. nm Here is the transition matrix;

[0033] Maximum value calculation:

[0034]

[0035] in, For the closed-loop perturbation algorithm, μ * is a closed-loop controller, and v is the game state space.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] This invention aims to solve key problems in existing technologies, such as braking response delay, insufficient redundancy, and low speed control accuracy on slopes. Specifically designed for long slopes of 30‰ or higher and heavy-haul freight train formations of 200 cars or more, it employs an innovative stochastic cross-layer control architecture and dynamic resistance compensation algorithm to reduce braking command transmission delay, control unit fault switching time, and slope constant speed control error, thereby significantly improving train operational safety and braking efficiency under complex conditions. Attached Figure Description

[0038] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a structural diagram of a cross-layer control system based on random game theory provided in an embodiment of the present invention;

[0040] Figure 2 This is a design diagram of the input and output module of the cross-layer control system provided in an embodiment of the present invention;

[0041] Figure 3 This is a block diagram of the cross-layer controller input / output of a heavy-haul train group cross-layer control system based on random game theory provided in an embodiment of the present invention.

[0042] Figure 4 This is a block diagram of the input / output module design for the physical domain closed-loop controller provided in an embodiment of the present invention;

[0043] Figure 5 This is the H based on the information domain provided in the embodiments of the present invention. ∞ Optimal controller input / output module design block diagram;

[0044] Figure 6 This is a block diagram of the input / output module design for a cross-layer controller feedback control model based on random game theory, provided in an embodiment of the present invention. Detailed Implementation

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] Example:

[0047] A cross-level control system for heavy-load group trains based on random game theory, such as Figure 1 As shown, the system includes:

[0048] The data acquisition module is used to collect parameter information of trains in heavy-haul train groups and the communication status between trains.

[0049] To ensure the safe and reliable operation of each train in a heavy-haul train group under uncertain disturbances and to improve the robustness of complex control systems, this invention comprises two parts in a multi-layer control system.

[0050] First, the behavior between communication interference and defense algorithms is modeled as a stochastic game, and the interests of both parties are maximized by solving the saddle point equilibrium.

[0051] Secondly, by designing H based on random game theory... ∞ Control algorithms are used to ensure the robustness of the control system for heavy-haul train groups under disturbance conditions.

[0052] like Figures 2-3 As shown, the cross-level control system for heavy-haul train groups ensures stable operation of the heavy-haul train groups within the control system by designing closed-loop control and state feedback mechanisms for the controller and mapping them to the domain. In t kAt time 1, due to uncertain interference, the measured train state information of train i has a random delay, the mathematical expression of which is as follows:

[0053]

[0054] Among them, y i (t k ) represents the output of the cross-layer controller, y i,e (t k ) represents the measurement output of the cross-layer controller. Due to interference, y i (t k The delay information of y cannot be observed by adjacent trains. Therefore, this invention uses y i,e (t k ) represents y i (t k The prediction results of the communication process in ). Represents the state space set for vehicle-to-vehicle communication, with random variable δ. θ It is disturbed and follows a Bernoulli distribution, as shown in the following expression:

[0055]

[0056] Due to uncertain interference, the transmission of status information for each train in the cross-level control system of heavy-haul train groups will experience uncertain delays. In this embodiment, the status information of train i is defined as follows:

[0057]

[0058] Where, δ θ =0 indicates that the status information of train i in the heavy-load train group was successfully transmitted; otherwise, it indicates that the status information of train i in the heavy-load train group failed to be transmitted due to uncertain interference.

[0059] The game theory algorithm construction module is used to construct a random game theory algorithm based on the parameter information of the train and the communication status between the trains.

[0060] This invention maps the information interaction between the physical and information domains in the dynamic operation of heavy-haul train groups using stochastic game theory. The implementation of the control system in this invention will consist of the following steps.

[0061] ① Design of a closed-loop controller based on the physical domain

[0062] To mitigate the impact of interference on the operation of heavy-haul train group systems, this invention proposes a cross-layer control design based on stochastic game theory. This algorithm employs a hybrid zero-sum game to map the actions between uncertain interference and defense algorithms, thereby preventing the heavy-haul train group system from becoming inoperable due to communication interruptions. The cross-layer control based on stochastic game theory estimates the probability of an interfering agent initiating an interfering action in the time dimension through measurement. In its specific implementation, this is achieved by mapping it to a domain, through H... ∞ Closed-loop control and state feedback control in the domain are used to solve the stability of the physical domain control system, thereby ensuring that the heavy-haul train group system can operate reliably even in the face of malicious interference.

[0063] like Figure 4 As shown, x i θ(t) and θ(t) represent the operation and car-to-car communication states of train i in a heavy-haul train group, respectively. Therefore, the state formula for train i in a heavy-haul train group under long communication delay scenarios can be obtained as follows:

[0064]

[0065] Where, x i,0 u represents the fixed initial state of the heavy-load train group convoy i at the start time t0. i (t) is the control input, w i,e Used to characterize the impact of interference, θ(t) represents the state of vehicle-to-vehicle communication. The value of θ(t) varies depending on the defensive action (def) and the interfering action (jam), and θ(t) is a function of time t. For ease of writing, θ(t) is defined here as the abbreviation θ(t, def, jam).

[0066] ② H based on information domain ∞ Optimal control:

[0067] The purpose of the stochastic game theory algorithm proposed in this invention is to solve security problems caused by uncertainty through stochastic game theory. For example... Figure 5 As shown, in a random game between two parties, there is a conflict between uncertain disturbances and defensive algorithms. This primarily refers to the fact that the disturber aims to maximize the impact of its disruptive behavior on the performance of the heavy-haul train group control system, while the defensive algorithm seeks to minimize the impact of the disturbance on system performance through defensive actions. Therefore, the cross-layer control system achieves H through mapping of the physical domain. ∞ The stability of the system within the domain is ultimately achieved through optimized control, which balances the minimization of control system performance consumption with the maximization of disturbances.

[0068] Furthermore, due to the randomness of uncertain interference during operation, a large amount of random information streams are ultimately transmitted into the vehicle-to-vehicle communication channel. To further model the uncertainty of interference behavior, this invention models the vehicle-to-vehicle communication state affected by interference as a Markov jump process with an initial distribution of π0. Additionally, λ = λ nm This is the transition rate matrix, used to characterize the uncertainty of interference. It is important to emphasize that this matrix defines the transition rate of the vehicle-to-vehicle communication channel state from n to m, such that for λ = λ... nm , λ nm ≥0, have

[0069] In order to achieve H ∞ In terms of domain optimization control, this invention defines the interference algorithm and defense algorithm in the random game algorithm as follows, from the perspective of uncertain interference characteristics and ensuring the stability of heavy-load train groups: and Its specific expression is as follows:

[0070]

[0071] Among them, f n (k) and g m (k) represent defensive actions (def) n and interference actions jam m The probability of occurrence. Indicates interference action from interference space Choose one interference action, the interference space is composed of This embodiment defines the possible action components. The defensive mechanisms that the Vehicle Onboard Based Controller (VOBC) can employ through vehicle-to-vehicle communication are defined as follows: in It is the set of all possible defensive actions.

[0072] The control strategy generation module is used to generate the game strategy input H based on the random game algorithm. ∞ The domain optimization algorithm updates the train's operating status in real time.

[0073] like Figure 6 As shown, the closed-loop controller in a heavy-haul train group is designed to ensure the efficient operation of train i in the cross-level control system. The input to the closed-loop controller is the desired speed parameter r of the train. i (t), the output is the actual velocity parameter v. i(t). As can be seen from the above analysis, the control inputs of the closed-loop controller defined in this embodiment are all affected by uncertain disturbances and the vehicle-to-vehicle communication channel state. Therefore, for the convenience of control optimization, they are defined as follows:

[0074] u i (t): = μ i (t,x i (t); θ(t)), t∈[t0, t n ),

[0075] w i，e (t): = v i (t,x i (t); θ(t)), t∈[t0, t n ),

[0076] Where μ is the controller.

[0077] Furthermore, in this embodiment, the heavy-haul train group operation control system is defined as a nonlinear control system, and the expected benefit under state θ is shown in the following formula:

[0078]

[0079] The cost function L can be expressed as:

[0080]

[0081] This embodiment transforms the system stability control problem under uncertain disturbances into a H-squared problem based on random game theory. ∞ The optimization control problem is solved using stochastic game theory, aiming to maximize the disturbance action while minimizing the cost function of the control system. To achieve this goal, this embodiment transforms the control problem into a minimax optimization problem and studies cross-layer control as a zero-sum game. Therefore, the implementation of this embodiment is based on designing a minimax closed-loop controller. It is also a closed-loop perturbation algorithm. If the upper limit is , then its mathematical description is as follows:

[0082]

[0083] Furthermore, this embodiment transforms the game process into a partial differential equation, and lets represent the cost function related to the differential game. On the other hand, from H ∞ From the perspective of domain optimization, in the initial state of the cross-level control system for heavy-haul train groups, when the communication state is θ, the communication interval [t, t] is... n Within a given range, the function V(t,x,i) approximates the upper bound of the random game. The set of minimum values ​​based on function V is then given by the following equation:

[0084]

[0085] Furthermore, let's begin with the H-level control of random game across layers. ∞ Optimized design of the controller.

[0086] The above analysis shows that the uncertainty of the decision-making behavior of both parties in a zero-sum game affects the state transition rate in real time, and also impacts the cost function. The effective boundary is affected. The cost function of the cross-layer control system of this invention can be mapped to two parts, namely in H ∞ Domain closed-loop control algorithm for (μ) f v f The algorithm and its application to the operation status of heavy-load train groups in a cross-layer control system ultimately manifest in the physical domain as operational safety and efficiency of the train train fleet. Therefore, to better characterize the real-time interaction between the train group's operational status and uncertain disturbances, this invention introduces an important index into the zero-sum random game of the minimax optimization function, called the discounted return. Typically, the discounted return v... β (n, f, g) represents the performance loss of the cross-layer control system under the vehicle-to-vehicle communication state θ and the algorithm (f, g). Furthermore, the discounted return is only limited by v. β (n-1, f, g), then the discounted return v β (n, f, g) is shown in the following formula:

[0087]

[0088] Where β is the discount factor, For expectation operators.

[0089] Based on the above analysis, this embodiment will solve for the optimal defense algorithm based on cross-layer design. In order to solve the algorithm more effectively, the definition of saddle point equilibrium is given first, as shown in the following formula:

[0090] (Saddle point equilibrium) is expressed by the following formula:

[0091] v β =[v β (θ1), …, v β (θ n )] T

[0092] Among them, v β This is a discounted zero-sum random game, and a unique solution can be obtained from the following formula:

[0093]

[0094] Here, val is a function that generates the game value of a random matrix game.

[0095] The saddle point equalization algorithm obtains the value through the following equation:

[0096] {f * (θ),g * (θ)}∈arg val{Γ(θ)},

[0097] Here, arg val represents the hybrid algorithm that generates the game value.

[0098] random variable δ θ and β θ Used to characterize the QoS performance of vehicle-to-vehicle communication channels, its value is affected by interference actions and defense algorithms. This embodiment defines four sets, namely: and Mapping δ using these four sets θ and β θ The relationship is as follows:

[0099]

[0100] ③ H under disturbance in cross-layer control system ∞ Robust controller optimization design:

[0101] This invention describes the dynamic control model of the system and defines it as a nonlinear control system. Based on this, a hybrid model is proposed for a known vehicle-to-vehicle communication system with state θ. This invention maps the expectation to H when the stochastic game algorithms are f(θ) and g(θ). ∞ The system's indicators When the initial condition is zero, define H ∞ Domain Indicators The following inequalities must be satisfied:

[0102]

[0103] The objective of this embodiment is to combine H ∞ Domain optimal control and cross-level control design are used to optimize the cross-level control method based on stochastic game theory. To enable the use of existing tools for subsequent solutions, the aforementioned H... ∞ The conditions for exponential control are converted into LMI inequalities to achieve robust control of the nonlinear control system. Therefore, this embodiment derives the process and finally obtains the following formula, the specific content of which is shown below.

[0104] For all θ∈Θ, if there exists a positive definite matrix and and real matrix and If the following linear matrix inequality holds, then there exists a hybrid algorithm pair (f) θ g θ ) and the given scalar For all non-zero values, the mixture model w k It is exponentially stable and can achieve H ∞ - Norm constraint.

[0105] The LMI formula is shown below:

[0106]

[0107] in, and And satisfy the following conditions:

[0108]

[0109] also, This represents the eigenvalues ​​of matrix B2.

[0110] K θ =VΣ -1 P 11 ΣV T M θ ,L θ =S1N θ ,

[0111]

[0112] in,

[0113]

[0114] The status feedback module is used to receive real-time updates on the train's operating status and to exchange information.

[0115] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A multi-level control system for heavy-load group trains based on random game theory, characterized in that, The system includes: The data acquisition module is used to collect parameter information of trains in the heavy-haul train group and the communication status between trains; The game algorithm construction module is used to construct a random game algorithm based on the parameter information of the train and the communication status between the trains; The control strategy generation module is used to generate the game strategy input H based on the random game algorithm. ∞ Domain optimization algorithms are used to update the train's operating status in real time. The status feedback module is used to receive real-time updates on train operation status and exchange information.

2. The heavy-load group train cross-level control system based on random game theory according to claim 1, characterized in that, In the data acquisition module, the train parameter information includes the number of train groups, the traction force matrix of the train groups, the braking force matrix of the train groups, the status matrix of the train groups, the control matrix of the train groups, the noise matrix of the train groups, and the control rate of the train groups.

3. The heavy-load group train cross-level control system based on random game theory according to claim 1, characterized in that, In the data acquisition module, the communication status between trains is specifically as follows: in, For t k+1 Estimated train operation status at any time The state matrix, For the control matrix, u c (t k ) for t k The actual control input at any given time, u(t) k ) for t k Timing control input, L θ For observation gain, Let β be the observation matrix. θ Indicates the communication status; a value of 1 indicates that the transmission of vehicle status information has failed due to interference, while a value of 0 indicates that the transmission has succeeded. K θ To control the gain, For t k Estimated train operation status at any time.

4. The heavy-load group train cross-level control system based on random game theory according to claim 1, characterized in that, The random game algorithm includes interference actions. and defensive actions Among them, f n (k) and g m (k) represent defensive actions (def) n and interference actions jam m The probability of occurrence, where n is the probability of the nth interference attempt. t represents the total number of times interference is initiated. k Let m be the time interval, and m be the number of times the m-th defensive action is initiated.

5. The heavy-load group train cross-level control system based on random game theory according to claim 1, characterized in that, The control strategy generation module includes a closed-loop controller and an H... ∞ Domain closed-loop control algorithm and operation status calculation submodule; The closed-loop controller is used to calculate the actual speed parameters of the train group; The H ∞ The domain optimization algorithm is used to characterize the interaction between decision-making actions and uncertain disturbances between the train group's operating state and the game strategy generated by the random game algorithm based on the actual speed parameters. The operation status calculation submodule is used to calculate the operation status of the train group based on the decision action interaction.

6. The heavy-load group train cross-level control system based on random game theory according to claim 5, characterized in that, The closed-loop controller is specifically: Based on uncertain interference and the vehicle-to-vehicle communication channel status, the desired speed parameters of the train are input into the closed-loop controller, and the actual speed parameters of the train group are output within the scope of the closed-loop controller: u i (t):=μ i (t,x i (t); θ(t)),t∈[t0,t n ), w i，e (t):=v i (t,x i (t); θ(t)),t∈[t0,t n ), Among them, u i (t) represents the control input for train i, μ i (t,x i (t); θ(t)) represents the closed-loop control strategy, t is the time variable, t0 is the time when the disturbance occurs, and t n w represents the time when the interference behavior ends. i,e (t) represents the interference noise at time v i (t,x i (t); θ(t)) represents the state space of train i's game behavior, x i θ(t) represents the running state of train i, and θ(t) represents the communication state of train-to-train communication at time t.

7. The heavy-load group train cross-level control system based on random game theory according to claim 6, characterized in that, The closed-loop controller is a minimum-maximum closed-loop controller. Minimum value calculation: Where V(·) is the cost function, and θ is the communication state. Let t be the expected function. h For the communication period, u i To control the input, w i,e For interference and noise, Let λ be the total number of game-related actions. nm Here is the transition matrix; Maximum value calculation: in, For the closed-loop perturbation algorithm, μ * is a closed-loop controller, and v is the game state space.

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