An event-triggered multi-train cooperative fault-tolerant control method

Abstract

The application relates to an event-triggered multi-train cooperative fault-tolerant control method, which comprises the following steps: constructing a multi-train operation dynamics model; calculating a position tracking error of the train and a speed tracking error of the train, and obtaining a position preset performance control signal and a speed preset performance control signal; respectively designing a fault rate estimation function of the train and a disturbance compensation function caused by the fault, and designing a virtual control signal and a fault-tolerant control input signal; designing a distributed event-triggered condition of the train; and when the distributed event-triggered condition of the train is met, updating the fault-tolerant control input signal of the train and simultaneously sending the speed tracking error of the train and the speed preset performance control signal of the train to the next train which is adjacent to the train, so that the cooperative operation of the train is effectively ensured under the condition that the performance of the train executor is reduced and the communication resource is limited.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-speed train operation control, and particularly relates to a multi-train cooperative fault-tolerant control method based on event triggering. BACKGROUND

[0002] As an important part of building high-quality comprehensive three-dimensional traffic network, high-speed railway has been rapidly developed. In order to enhance the reaction speed, safety and improve the carrying capacity of high-speed railway system to the emergency, the high-speed train cooperative control has been paid great attention. Compared with single train control, adjacent trains can directly communicate in train cooperative operation mode, and real-time access to the position, speed, acceleration, control strategy and other information of adjacent trains, according to the line conditions, the running state of adjacent trains is estimated, and the multi-train cooperative control strategy is formulated and the command issued by the dispatch is quickly executed.

[0003] However, the complex operating environment leads to the communication network inevitably existing communication delay, and it is difficult for the car-to-car to realize real-time and high-frequency information transmission. Therefore, the problem of limited communication network resources needs to be considered in the design of multi-train cooperative control. SUMMARY

[0004] (I) Technical problems to be solved

[0005] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present application provides a multi-train cooperative fault-tolerant control method based on event triggering, which solves the technical problems of high communication cost of the control method in the prior art, and the introduction of discontinuous signal leads to unstable system closed-loop performance.

[0006] (II) Technical solutions

[0007] In order to achieve the above-mentioned purposes, the main technical solutions adopted by the present application include:

[0008] The embodiment of the application provides a kind of based on event trigger's multi-train cooperative fault-tolerant control method, which includes: in the case where the actuator of train is considered to fail, based on the running resistance of each train, multi-train running dynamics model is constructed;Wherein, multi-train running dynamics model includes the position of this train, the speed of this train and the actual control input of this train when the actuator of this train fails, and the actual control input is determined based on the fault-tolerant control input signal corresponding to this train;Based on the given cooperative target position curve and the position of this train, the position tracking error of this train is calculated, and based on the given cooperative target speed curve, the virtual control signal of this train and the speed of this train, the speed tracking error of this train is calculated, and the position tracking error is nonlinearly transformed to obtain the position preset performance control signal, and the speed tracking error of this train is also nonlinearly transformed to obtain the speed preset performance control signal;Based on the speed tracking error and the speed preset performance control signal of this train, fault rate estimation function and disturbance function caused by compensation failure are designed respectively, and based on the position tracking error and the position preset performance control signal, virtual control signal is designed, and also based on fault rate estimation function, disturbance function, the speed tracking error of this train, the speed preset performance control signal, the speed tracking error of another train when event triggers and the speed preset performance control signal of another train when event triggers, fault-tolerant control input signal is designed;Based on the speed tracking error and the speed preset performance control signal, the distributed event trigger condition of this train is designed, and when the distributed event trigger condition of this train is satisfied, the fault-tolerant control input signal of this train is updated and the speed tracking error of this train and the speed preset performance control signal of this train are sent to the next train as the adjacent vehicle of this train.

[0009] In one possible embodiment, the multi-train cooperative fault-tolerant control method further includes: when the distributed event trigger condition of this train is not satisfied, the speed tracking error of this train and the speed preset performance control signal of this train are re-collected until the distributed event trigger condition is satisfied.

[0010] In one possible embodiment, the expression of the multi-train running dynamics model is:

[0011]

[0012] Wherein, i represents the train number of this train;x i (t) represents the position of this train at time t; represents the derivative of the position of the i th train;v i (t) represents the speed of this train at time t; represents the derivative of the speed of the i th train;u i R(t) represents the actual control input of this train at time t when the actuator malfunctions; f i (t) represents the train's running resistance.

[0013] In one possible embodiment, The expression is:

[0014]

[0015] Where, θ i This represents the failure rate of the train, and θ i satisfy conditions, θ This represents the minimum failure rate. This represents the maximum failure rate, and when θ i A value of 0 indicates that the actuators of this train are not faulty; u i D (t) represents the fault-tolerant control input signal.

[0016] In one possible embodiment, the speed tracking error is designed based on a backstepping control method, and the expression for the speed tracking error is:

[0017] e vi (t)=v i (t)-v di (t)-a i (t);

[0018] Among them, e vi (t) represents the speed tracking error; v di (t) represents the given cooperative target velocity curve; a i (t) represents the virtual control signal for this train.

[0019] In one possible embodiment, the failure rate estimation function is expressed as follows:

[0020]

[0021]

[0022] in, This represents the failure rate θ of the train. i The estimated value; Represents θ i The update law; d1, k 2i and σ i All are positive gain parameters; ρ vi (t) represents the speed preset performance control signal; s pi (t) represents the position tracking error e pi(t) the normalized position error signal after transformation; w vi (t) the desired smooth bounded tracking performance function set as velocity; a di represents the given cooperative target acceleration profile.

[0023] In one possible embodiment, the expression of the disturbance function is:

[0024]

[0025] wherein, represents the estimation of γ i , and γ i satisfies and λ i satisfies λ i ≤1-θ i ; d2 represents a positive gain parameter; represents the update law of γ i .

[0026] In one possible embodiment, the expression of the virtual control signal is:

[0027] α i (t) = -k 1i (ρ pi (t) + e pi (t));

[0028] wherein, a i (t) represents the virtual control signal; k 1i represents a control parameter to be designed; ρ pi (t) represents the position pre-set performance control signal.

[0029] In one possible embodiment, the expression of the fault-tolerant control input signal is:

[0030]

[0031] wherein, u i D represents the fault-tolerant control input signal; k 2i and k 3i both represent a control parameter to be designed; j represents the train number of the other train; if the train and the other train can communicate, a ij is equal to 1, otherwise a ij is equal to 0; t kj j represents the k j th triggering time of the other train; represents the k jthe speed preset performance control signal at the time of the (k-1)th triggering; the (k-1)th triggering time of the other train; j the speed tracking error at the time of the (k-1)th triggering.

[0032] In one possible embodiment, the distributed event triggering condition is:

[0033]

[0034]

[0035]

[0036] wherein, k i represents the number of event triggering of the train; represents the (k-1)th triggering time of the train; i represents the (k-1)th triggering time of the other train; i +1th triggering time of the other train; represents the value of p vi (t) at the triggering time represents the value of e vi (t) at the triggering time i represents the triggering threshold constant of the i-th train designed.

[0037] (III) Beneficial Effects

[0038] The beneficial effects of the present application are:

[0039] The embodiments of the present application provide a multi-train cooperative fault-tolerant control method based on event triggering, which introduces the mechanism of event triggering, consumes less communication resources through less information transmission times, and can achieve a control performance similar to the widely used time triggering mechanism, thereby effectively ensuring the cooperative operation of the trains under the condition of performance degradation of the train actuators and limited communication resources, reducing the number of event triggering while meeting the control performance required by the formation.

[0040] In order to make the above-mentioned purposes, features and advantages of the embodiments of the present application more obvious and easy to understand, the following preferred embodiments are described in detail below, and the accompanying drawings are described as follows. BRIEF DESCRIPTION OF DRAWINGS

[0041] ​​​In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments of the present application. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation to the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0042] Figure 1 A flow chart of a multi-train cooperative fault-tolerant control method based on event triggering provided by the embodiments of the present application is shown;

[0043] Figure 2 A schematic diagram of a multi-train cooperative fault-tolerant control method based on event triggering provided by the embodiments of the present application is shown;

[0044] Figure 3 A schematic diagram of a reference target speed curve provided by the embodiments of the present application is shown;

[0045] Figure 4 A schematic diagram of a designed control input of each train provided by the embodiments of the present application is shown;

[0046] Figure 5 A schematic diagram of a position tracking error of a multi-train provided by the embodiments of the present application is shown;

[0047] Figure 6 A schematic diagram of a speed tracking error of a multi-train provided by the embodiments of the present application is shown;

[0048] Figure 7A A fault degree estimation schematic diagram of a train provided by the embodiments of the present application is shown;

[0049] Figure 7B A fault degree estimation schematic diagram of another train provided by the embodiments of the present application is shown;

[0050] Figure 7C A fault degree estimation schematic diagram of still another train provided by the embodiments of the present application is shown;

[0051] Figure 7D A fault degree estimation schematic diagram of yet another train provided by the embodiments of the present application is shown;

[0052] Figure 8 A schematic diagram of the number of event triggering provided by the embodiments of the present application is shown. DETAILED DESCRIPTION

[0053] In order to better explain the present application, in order to facilitate understanding, the following will be described in detail by specific embodiments, combined with the drawings.

[0054] The existing train cooperative control does not consider the communication constraint in actual train operation, needs real-time state data of adjacent trains for formulating a cooperative control strategy, has high communication cost, and introduces discontinuous signals, thereby causing unstable closed-loop performance of the system.

[0055] In addition, the train operation environment has the characteristics of high density, long operation mileage, and harsh operation environment, and with the occurrence of component aging or decline in performance of traction / braking motors, the running performance of the high-speed train is reduced, and even a safety accident can be caused. Therefore, it is necessary to ensure that the train still achieves ideal performance under the condition of failure of the actuator. That is, the performance of the actuator of the high-speed train is reduced, which reduces the tracking performance, so that the train cannot efficiently complete the scheduling task, and even causes the entire system to be unstable.

[0056] Based on this, the embodiment of the present application provides a multi-train cooperative fault-tolerant control method based on event triggering, introduces an event triggering mechanism, reduces the number of information transmission times and the consumption of communication resources, and can achieve control performance similar to the widely used time triggering mechanism, thereby effectively ensuring cooperative operation of the train under the condition of performance reduction of the train actuator and limited communication resources, while meeting the control performance required by the formation and reducing the number of event triggers.

[0057] In order to better understand the above technical solutions, the exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided to enable a clearer, more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0058] Please refer to Figure 1 , Figure 1 A flowchart of a multi-train cooperative fault-tolerant control method based on event triggering provided by the embodiment of the present application is shown. As shown in the multi-train cooperative fault-tolerant control method can be executed by an electronic device, and the specific device of the electronic device can be set according to actual needs, and the embodiment of the present application is not limited thereto. Specifically, the multi-train cooperative fault-tolerant control method includes: Figure 1

[0059] Step S110, under the condition of failure of the actuator of the train, a multi-train operation dynamics model is constructed based on the running resistance of each train. The multi-train operation dynamics model includes the position of the train, the speed of the train, and the actual control input of the train when the actuator of the train fails, and the actual control input is determined based on the fault-tolerant control input signal corresponding to the train. ​

[0060] It should be understood that the dynamics model of multi-train operation can also be called the nonlinear dynamics model of a single mass point.

[0061] It should also be understood that the specific model of the multi-train operation dynamics model can be set according to actual needs, and the embodiments of this application are not limited thereto.

[0062] Optionally, considering N trains running on the line, the following multi-train operation dynamics model is established:

[0063]

[0064] In the formula, i represents the train number of this train, and i is any positive integer from 1 to N; t represents the time; x i (t) represents the position of the train at time t; The derivative representing the position of the i-th train; v i (t) represents the speed of the train at time t; The derivative of the speed of the i-th train; u i R (t) represents the actual control input of this train at time t when the actuator malfunctions; f i (t) represents the unknown train running resistance of this train.

[0065] as well as, The expression (or calculation formula) is:

[0066]

[0067] In the formula, θ i This represents the failure rate of the train, and θ i satisfy conditions, θ This represents the minimum failure rate. This represents the maximum failure rate, and when θ i A value of 0 indicates that the actuators of this train are not faulty; u i D (t) represents the designed fault-tolerant control input signal (or the designed control input).

[0068] And, f i The expression for (t) is:

[0069] f i (t)=c0+c1v i (t)+c2v i 2 (t);

[0070] wherein c0, c1 and c2 each represent a known basic drag coefficient.

[0071] In step S120, a position tracking error of the train is calculated based on the given cooperative target position curve and the position of the train, a speed tracking error of the train is calculated based on the given cooperative target speed curve, the virtual control signal of the train and the speed of the train, the position tracking error is nonlinearly transformed to obtain a position preset performance control signal, and the speed tracking error of the train is nonlinearly transformed to obtain a speed preset performance control signal.

[0072] It should be understood that the specific process of calculating the position tracking error of the train based on the given cooperative target position curve and the position of the train can be set according to actual requirements, and the embodiments of the present application are not limited thereto.

[0073] Optionally, the position tracking error is expressed as follows:

[0074] e pi (t)=x i (t)-x di (t);

[0075] wherein e pi (t) represents the position tracking error; x i (t) represents the position of the train given in step S110; x di (t) represents the given cooperative target position curve, and the specific curve of the cooperative target position curve can be set according to actual requirements.

[0076] It should also be understood that the specific process of calculating the speed tracking error of the train based on the given cooperative target speed curve, the virtual control signal of the train and the speed of the train can also be set according to actual requirements, and the embodiments of the present application are not limited thereto.

[0077] Optionally, the speed tracking error is designed according to a backstepping control method, and the speed tracking error is expressed as follows:

[0078] e vi (t)=v i (t)-v di (t)-α i (t);

[0079] wherein e vi (t) represents the speed tracking error; v di (t) represents the given cooperative target speed curve, and the specific curve of the cooperative target speed curve can also be set according to actual requirements; a i (t) represents the virtual control signal of the train to be designed.

[0080] It should also be understood that the specific process of performing nonlinear transformation on the position tracking error to obtain the position preset performance control signal is also set according to actual needs, and the embodiments of the present application are not limited thereto.

[0081] Optionally, in order to constrain the position tracking error within a preset range, the position tracking error can be transformed to obtain a normalized position error signal s pi (t). And, based on the normalized position error signal s pi (t), nonlinear transformation is performed to obtain a position preset performance control signal p pi (t) that is monotonically increasing in the interval (-1, 1).

[0082] Wherein, the expression of s pi (t) is as follows:

[0083]

[0084] In the formula, w pi (t) represents the expected smooth bounded tracking performance function set for the position.

[0085] And, the expression of p pi (t) is as follows:

[0086]

[0087] It should also be understood that the specific process of performing nonlinear transformation on the speed tracking error of the train to obtain the speed preset performance control signal is also set according to actual needs, and the embodiments of the present application are not limited thereto.

[0088] Optionally, in order to constrain the speed tracking error within a preset range, the speed tracking error can be transformed to obtain a speed preset performance control signal s vi (t). And, based on the speed preset performance control signal s vi (t), nonlinear transformation is performed to obtain a speed preset performance control signal p vi (t) that is monotonically increasing in the interval (-1, 1).

[0089] Wherein, the expression of s vi (t) is as follows:

[0090]

[0091] In the formula, w vi (t) represents the expected smooth bounded tracking performance function set for the speed.

[0092] And, the expression of p vi (t) is as follows:

[0093]

[0094] Step S130, based on the speed tracking error of the current train and the speed preset performance control signal, respectively design the fault rate estimation function of the current train and the disturbance function caused by the fault compensation, and based on the position tracking error and the position preset performance control signal, design the virtual control signal, and also based on the fault rate estimation function, the disturbance function, the speed tracking error of the current train, the speed preset performance control signal, the speed tracking error of another train at the event trigger and the speed preset performance control signal of another train at the event trigger, design the fault-tolerant control input signal.

[0095] It should be understood that the specific function of the fault rate estimation function can be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0096] Optionally, in order to enable the train to maintain the preset tracking performance when the performance of the train is degraded due to the failure of the actuator, the fault rate estimation function of the current train (i.e. the ith train) is designed as follows:

[0097]

[0098] In the formula, represents the estimated value of the fault rate θ i of the current train in the multi-train running dynamics model in step S110; represents the update law of θ i .

[0099] And the expression of q i is as follows:

[0100]

[0101] Wherein, d1, k 2i and σ i are positive gain parameters; a di represents a given cooperative target acceleration curve, and the specific curve of the cooperative target acceleration curve can be set according to actual needs.

[0102] It should also be understood that the specific function of the disturbance function can be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0103] Optionally, in order to eliminate the disturbance caused by the fault, the expression of the disturbance function used to estimate it is as follows:

[0104]

[0105] In the formula, represents the disturbance caused by the fault.i an estimate of the value of γ i satisfies and λ i satisfies λ i ≤1-θ i ; denotes the update law of γ i ; d2 denotes a positive gain parameter.

[0106] It should also be understood that the specific form of the virtual control signal can also be set according to actual requirements, and the embodiments of the present application are not limited thereto.

[0107] Optionally, the expression of the virtual control signal is as follows:

[0108] α i (t) = -k 1i (ρ pi (t) + e pi (t));

[0109] In the formula, a i (t) denotes the virtual control signal; k 1i denotes a control parameter to be designed (or also referred to as a control parameter to be set), and it can be set according to actual requirements.

[0110] It should also be understood that the specific form of the fault-tolerant control input signal can also be set according to actual requirements, and the embodiments of the present application are not limited thereto.

[0111] Optionally, the expression of the fault-tolerant control input signal is as follows:

[0112]

[0113] In the formula, u i D denotes the fault-tolerant control input signal; k 2i and k 3i both denote control parameters to be designed, and they can be set according to actual requirements; j denotes the train number of another train, and j is also a positive integer less than or equal to N and not equal to i; if the present train and another train can communicate and transmit, it is determined that the jth train is the neighboring train of the ith train, and a ij is equal to 1, otherwise a ij is equal to 0; denotes the k j th triggering time of another train; denotes the speed preset performance control signal of another train at the k j th triggering time; denotes the speed tracking error of another train at the k j th triggering time.

[0114] And, in order to reduce the number of information transmission between trains, the state information (i.e. speed tracking error e vi and speed preset performance control signal p vj ) transmitted by each train to the adjacent train is transmitted at the triggering time of the train, and when the state information is not transmitted to the adjacent train, the state information of the adjacent train is discontinuous based on events, which can reduce the number of transmissions compared to the time-triggered mode.

[0115] Step S140, based on the speed tracking error and the speed preset performance control signal, the distributed event triggering condition of the train is designed, and when the distributed event triggering condition of the train is met, the fault-tolerant control input signal of the train is updated and the speed tracking error of the train and the speed preset performance control signal of the train are sent to the next train as the adjacent train of the train.

[0116] It should be understood that the specific form of the distributed event triggering condition can be set according to actual needs, and the embodiments of the present application are not limited thereto.

[0117] Optionally, the expression of the distributed event triggering condition of the train is as follows:

[0118]

[0119]

[0120]

[0121] Wherein, k i represents the number of event triggering of the train, and k i ∈N; represents the k i th triggering time of the train; represents the k vi i+1th triggering time of the other train; represents the measurement error of the speed preset performance control signal p vi (t) in step S120; represents the value of p vi (t) at the triggering time ; represents the measurement error of the speed tracking error e vi (t) in step S120; represents the value of e vi (t) at the triggering time ; r i represents the triggering threshold constant of the designed i th train.

[0122] and the fault-tolerant control input signal u in step S130 i D (t) the neighboring vehicle information e vj and p vj Only when the trigger condition is met, the update is performed. And when the trigger condition indicates that when the trigger condition of the ith train is met, the fault-tolerant control input signal (or control input) of the train is updated and the state information (i.e. the speed tracking error e vi (t) of the train and the speed preset performance control signal p vi (t) of the train are sent to the neighboring train; when the trigger condition of the ith train is not met, the state information (i.e. the speed tracking error e -5 (t) of the train and the speed preset performance control signal p pi (t) of the train are re-collected for calculation until the trigger condition is met, so as to effectively reduce the number of information transmission between trains. For details, please refer to Figure 2 .

[0123] Therefore, by means of the above technical solutions, the embodiments of the present application realize the safe operation of multiple trains under the failure of the actuator, while ensuring the tracking performance of the multiple trains and reducing the number of communications between the trains.

[0124] In order to facilitate understanding of the embodiments of the present application, the following will be described through specific embodiments.

[0125] Specifically, in the simulation experiment, the cooperative operation of 4 trains is considered, the reference target speed curve is as shown in Figure 3 , the sampling time is set to 0.01s; the high-speed train parameters are selected as: c0=0.1176, c1=0.00077616, c2=1.6x10 -5 ; and considering the maximum running speed of the high-speed train, the position deviation and speed deviation within the sampling time interval are set as the expected tracking performance, which is set to W pi (t)=1, W vi (t)=1, under such conditions, the control method can obtain better tracking performance; the control parameters are set as: k 1i =0.5, k 2i =0.5, k 3i =0.05, r i =0.01, d1=0.02, d2=0.1, s i =0.025+0.02e -0.005t. And, considering the fault degree of the actuators in the queue is θ1=0.25, θ2=0.3, θ3=0.2, θ4=0.15 respectively. And, through the event-triggered multi-train preset performance fault-tolerant control method for each train, the control input, position and speed tracking error, fault degree estimation value, and event-triggering times of each train are as shown in Figures 3 to 8 .

[0126] And, Figure 4 The control input of each train of the embodiment of the present application is shown in the following table. Figure 5 And Figure 6 It can be seen that the position and speed tracking errors of the multi-trains can always remain within the set expected tracking performance in the case of train actuator failure; from Figures 7A to 7D It can be seen that each train can accurately estimate the fault degree; Figure 8 It can be seen that the triggering times of the time-triggered mode is 150000 times, and the triggering times of each train is reduced by about 97.5%, so the embodiment of the present application can effectively reduce the communication times between trains.

[0127] It should be understood that the above-mentioned event-triggered multi-train cooperative fault-tolerant control method is only exemplary, and those skilled in the art can make various modifications according to the above-mentioned method, and the modified scheme also belongs to the protection scope of the present application.

[0128] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program code.

[0129] The present application is described with reference to flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions.

[0130] It should be noted that the word "a" or "an" located before a component does not exclude the presence of multiple such components. The present application can be implemented by means of hardware including several distinct components, and by means of a suitably programmed computer. In the case of several devices, several of these devices can be implemented by the same item of hardware. The use of the words first, second and third, etc. does not imply any order. These words can be understood as being part of the component name.

[0131] Furthermore, it is to be understood that the use of "a" or "an", "the" or "said" employed throughout the present description denotes a non-limiting inclusion of one or more of the referenced features or steps. Any reference to prior art in this description is not to be understood as an admission that it was widely known or formed part of the common general knowledge in any jurisdiction as at the priority date of the application.

[0132] Although the preferred embodiments of the application have been described, those skilled in the art will understand that they can be subject to many changes and modifications without departing from the spirit and scope of the application. Accordingly, the technical solutions should be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the application.

[0133] Obviously, many modifications and variations of the present application are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the technical solutions and equivalent technologies thereof, the present application can embrace all such modifications and variations as legal equivalents.

Claims

1. A multi-train cooperative fault-tolerant control method based on event triggering, characterized in that, include: Considering the failure of the actuators of the trains, a multi-train operation dynamics model is constructed based on the running resistance of each train. The multi-train operation dynamics model includes the position of the train, the speed of the train, and the actual control input of the train when the actuator fails. The actual control input is determined based on the fault-tolerant control input signal corresponding to the train. Based on the given cooperative target position curve and the position of the train, the position tracking error of the train is calculated, and based on the given cooperative target speed curve, the virtual control signal of the train and the speed of the train, the speed tracking error of the train is calculated. The position tracking error is then subjected to a nonlinear transformation to obtain a position preset performance control signal, and the speed tracking error of the train is also subjected to a nonlinear transformation to obtain a speed preset performance control signal. Based on the speed tracking error of this train and the speed preset performance control signal, the fault rate estimation function and the disturbance function for compensating for faults of this train are designed respectively. Based on the position tracking error and the position preset performance control signal, the virtual control signal is designed. Furthermore, based on the fault rate estimation function, the disturbance function, the speed tracking error of this train, the speed preset performance control signal, the speed tracking error of another train when the event is triggered, and the speed preset performance control signal of another train when the event is triggered, the fault-tolerant control input signal is designed. Based on the speed tracking error and the speed preset performance control signal, the distributed event triggering conditions of the train are designed, and when the distributed event triggering conditions of the train are met, the fault-tolerant control input signal of the train is updated and the speed tracking error and the speed preset performance control signal of the train are sent to the next train, which is the adjacent vehicle of the train.

2. The multi-train cooperative fault-tolerant control method according to claim 1, characterized in that, The multi-train cooperative fault-tolerant control method also includes: If the distributed event triggering conditions of this train are not met, the speed tracking error and the speed preset performance control signal of this train will be re-acquired until the distributed event triggering conditions are met.

3. The multi-train cooperative fault-tolerant control method according to claim 1 or 2, characterized in that, The expression for the multi-train operation dynamics model is as follows: Where i represents the train number of the train in question; x i (t) represents the position of the train at time t; The derivative representing the position of the i-th train; v i (t) represents the speed of the train at time t; The derivative of the speed of the i-th train; u i R (t) represents the actual control input of the train at time t when the actuator malfunctions; f i (t) represents the train's running resistance.

4. The multi-train cooperative fault-tolerant control method according to claim 3, characterized in that, The The expression is: Where, θ i This represents the failure rate of the train, and θ i satisfy conditions, θ This represents the minimum failure rate. This represents the maximum failure rate, and when θ i A value of 0 indicates that the actuator of this train is not faulty; u i D (t) represents the fault-tolerant control input signal.

5. The multi-train cooperative fault-tolerant control method according to claim 3, characterized in that, The speed tracking error is designed based on the backstepping control method, and the expression for the speed tracking error is: e vi (t)=v i (t)-v di (t)-a i (t); Among them, e vi (t) represents the speed tracking error; v di (t) represents the given cooperative target velocity curve; a i (t) represents the virtual control signal of this train.

6. The multi-train cooperative fault-tolerant control method according to claim 5, characterized in that, The expression for the failure rate estimation function is: in, The failure rate θ of this train is indicated. i The estimated value; Represents θ i The update law; d1, k 2i and σ i All are positive gain parameters; ρ vi (t) represents the speed preset performance control signal; s pi (t) represents the position tracking error e pi (t) is the normalized position error signal obtained after transformation; w vi (t) represents the desired smooth and bounded tracking performance function set for the velocity; a di This represents the acceleration curve of a given cooperative objective.

7. The multi-train cooperative fault-tolerant control method according to claim 6, characterized in that, The expression for the disturbance function is: in, Indicates the relationship with γ i The estimated value of γ, and γ i satisfy and λ i Satisfying λ i ≤1-θ i d2 represents a positive gain parameter; Indicates γ i The renewal law.

8. The multi-train cooperative fault-tolerant control method according to claim 7, characterized in that, The expression for the virtual control signal is: a i (t)=-k 1i (r pi (t)+e pi (t)); Among them, a i (t) represents the virtual control signal; k 1i Indicates the control parameters to be designed; ρ pi (t) represents the position preset performance control signal.

9. The multi-train cooperative fault-tolerant control method according to claim 8, characterized in that, The expression for the fault-tolerant control input signal is: Among them, u i D Indicates the fault-tolerant control input signal; k 2i and k 3i All represent the control parameters to be designed; j represents the train number of the other train; if the current train and the other train can communicate, then a ij If it equals 1, otherwise a ij equals 0; t kj j Indicates the kth term of the other train j The next trigger moment; Indicates the kth term of the other train j The speed preset performance control signal at the next trigger moment; Indicates the kth term of the other train j Speed ​​tracking error at the next trigger moment.

10. The multi-train cooperative fault-tolerant control method according to claim 9, characterized in that, The conditions for triggering the distributed event are as follows: Where, k i This indicates the number of times the event was triggered on this train; Represents the kth term of this train. i The next trigger moment; Indicates the kth term of the other train i +1 trigger time; Represents ρ vi (t) at the trigger time The value; e vi (t) at the trigger time The value of r; i This represents the trigger threshold constant for the i-th train in the design.

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