CN112537340A - Multi-train scattered event trigger control method based on discrete communication data - Google Patents
Multi-train scattered event trigger control method based on discrete communication data Download PDFInfo
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Abstract
The invention provides a multi-train dispersion event trigger control method based on discrete communication data, which comprises the following steps of: aiming at a plurality of trains running on the same line, carrying out longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train; analyzing the communication topology of multi-train cooperative control based on a graph theory to obtain a multi-train communication topology structure; defining a tracking target of a plurality of trains based on a single substance point model of the high-speed train and a multi-train communication topological structure, and converting the single substance point model of the high-speed train into a multi-train error kinetic equation; establishing a multi-train scattered event trigger cooperative control condition model based on a multi-train communication topological structure and the multi-train error kinetic equation; and establishing a multi-train low-gain anti-saturation cooperative controller based on a multi-train communication topological structure and a multi-train dispersion event trigger cooperative control condition model. The method provided by the invention can realize multi-train cooperative control, and can reduce communication frequency and controller switching times.
Description
Technical Field
The invention relates to the technical field of high-speed train operation control, in particular to a multi-train dispersion event trigger control method based on discrete communication data.
Background
Compared with a manual driving mode, an Automatic Train Operation (ATO) system can realize accurate parking, improve the train operation efficiency, improve the operation comfort level and save the operation energy consumption through train positioning and speed control. At present, a fixed blocking system or a quasi-mobile blocking system is still adopted for a high-speed railway, the distance between trains is large, the running efficiency is low, and the necessary trend in the future is to research the multi-train cooperative running in a mobile blocking mode under the background of intellectualization, networking and digitization of the high-speed railway.
At present, for the research of multi-train cooperative control, the condition information such as the position, the speed and the like of a train is not considered mostly according to periodic sampling, and the multi-train cooperative control has a discrete characteristic, if the discrete characteristic of the information is not considered in the design process of a controller, the performance index of the controller can be reduced, the stability of a train control system can be seriously influenced, the train deviates from a tracked target curve, the train shakes, the stability of train operation is reduced, the energy consumption is increased, and even the safety of train operation is influenced. In the running process of the train, due to the limitation of communication resources, information transmission between the trains and real-time reliable and large-capacity information transmission are not practical, and high-frequency updating at a sampling period cannot be realized due to the mechanical characteristics of an on-board controller. The above difficulties can be overcome using event-triggered mechanisms. The existing time triggering mode is to drive the collection, transmission and processing of the system information at a fixed time interval, and the event triggering control mode is driven by an event, so that the communication times and the controller switching times between the systems can be reduced on the premise of ensuring that the control performance is not reduced.
In addition, due to the actual traction/braking characteristics of the train, in the design process of the controller, the saturation phenomenon of the controller of the train needs to be considered so as to avoid influencing the reduction of the control performance, the problem can be effectively solved through a low-gain anti-saturation controller design method, and the convergence speed of the system can be improved.
Disclosure of Invention
The embodiment of the invention provides a multi-train dispersion event trigger control method based on discrete communication data, which is used for solving the problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme.
A method for multi-train scatter event trigger control based on discrete communication data, comprising:
aiming at a plurality of trains running on the same line, carrying out longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train;
analyzing the communication topology of multi-train cooperative control based on a graph theory to obtain a multi-train communication topology structure;
defining a tracking target of a plurality of trains based on a single substance point model of the high-speed train and a multi-train communication topological structure, and converting the single substance point model of the high-speed train into a multi-train error kinetic equation;
establishing a multi-train scattered event trigger cooperative control condition model based on a multi-train communication topological structure and a multi-train error kinetic equation;
and establishing a multi-train low-gain anti-saturation cooperative controller based on a multi-train communication topological structure and a multi-train dispersion event trigger cooperative control condition model.
Preferably, for a plurality of trains running on the same line, performing longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train comprises:
aiming at n trains running on the same line, establishing a train longitudinal dynamics model:
wherein x isi(t)、vi(t) and mi(T) position, speed and mass of the ith train, Ti(t) is the control action, i.e. traction/braking force, of the ith train, f (v)i) Unit mass received by the i-th trainIs expressed as f (v)i)＝c1+c2vi+c3vi 2Wherein c is1、c2And c3Are davis equation coefficients;
designing traction/braking force T of train based on longitudinal dynamic model of traini(t) in the form of
Ti(t)＝miui(t)+mif(vi) (2)，
Wherein u isi(t) is an anti-saturation cooperative control item to be designed for enabling the train to operate in accordance with the state of the adjacent train; m isiui(t) is a cooperative control item for controlling the train to cooperatively operate in conformity with the state of the adjacent train, mif(vi) The resistance suffered by the train in operation is compensated;
substituting equation (2) into equation (1) to obtain
Let the target position and the target cruising speed of the ith train be respectively
And vdIn the formula IdThe minimum safe distance between trains;
defining a tracking interval n of adjacent trainsi＝xi-xi+1,i∈I[1,n-1]。
Preferably, based on the graph theory, analyzing the communication topology of the multi-train cooperative control, and obtaining the multi-train communication topology structure includes:
the method comprises the steps that bidirectional information transmission is carried out among all trains through a communication network, a multi-train cooperative control communication topology is converted into a weighted undirected graph form, and a multi-train communication topology structure G is obtained as (V, W, A);
wherein V ═ { V ═ V1,v2,…,vnIs the set of nodes that the train makes up,
represents a set of edges, A ═ aij]∈Zn×nFor the adjacency matrix, if train i can communicate with train j, then aij>0, otherwise aij1 is equal to 0, and let aiiD is 0, and is the in-degree matrix of the weighted undirected graph G, denoted D ═ diag { deg. }in(vi),i∈I[1,n]Therein of
The laplacian matrix of the weighted undirected graph G is defined as L ═ D-a; definition of NiIs a topological-adjacency set of trains, denoted Ni＝{vj:(vj,vi),j∈I[1,n]}; if the train i can obtain the information of the radio block center,
a target velocity distance curve, h, can be obtainedi1, otherwise, hi＝0；
Let H be diag { H1,h2,…,hnJ, define Q ═ L + H, λmaxMax { λ (Q) } denotes the maximum characteristic value of Q, λminMin { λ (Q) } represents the minimum eigenvalue of Q.
Preferably, the method for tracking multiple trains is defined based on the single particle point model of the high-speed train and the multi-train communication topological structure, and the step of converting the single particle point model of the high-speed train into the multi-train error kinetic equation comprises the following steps:
let yi＝[xi-xid,vi-vd]TAnd representing the tracking error, the error kinetic equation of the ith train is as follows:
definition of y (t) ═ y1(t)y2(t)…yn(t)]T，U(t)＝[u1(t)u2(t)…un(t)]TObtaining the multi-train error kinetic equation
Wherein the content of the first and second substances,
the target expressing the Kronecker product and the multi-row vehicle cooperative control is expressed as
Wherein, | | · | | represents L2And (4) norm.
Preferably, the multi-train dispersion event triggering cooperative control condition model includes:
wherein the content of the first and second substances,
indicating the kth trainiUpdate time of the secondary controller, yi(k tau) represents discrete sample state information for the train,
representing the state of the train when the last event triggered,
is the state information sent by the oncoming vehicle for the last time, and the parameters
Satisfy the requirement of
Mu is a range undetermined normal number, theta ═ P (omega) BBTP (omega), P (omega) satisfies the Riccati equation ATP(ω)+P(ω)A-P(ω)BBTP (ω) — (ω) a solution of P (ω), inf { · } represents the infimum of the set.
Preferably, the multi-train low-gain anti-saturation cooperative controller comprises:
wherein, β is a parameter to be designed, and ω satisfies the following relationship:
wherein
Mu satisfies
As can be seen from the technical solutions provided by the embodiments of the present invention, the method for triggering control of multiple train dispersion events based on discrete communication data, provided by the present invention, includes the following steps: aiming at a plurality of trains running on the same line, carrying out longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train; analyzing the communication topology of multi-train cooperative control based on a graph theory to obtain a multi-train communication topology structure; defining a tracking target of a plurality of trains based on a single substance point model of the high-speed train and a multi-train communication topological structure, and converting the single substance point model of the high-speed train into a multi-train error kinetic equation; establishing a multi-train scattered event trigger cooperative control condition model based on a multi-train communication topological structure and the multi-train error kinetic equation; and establishing a multi-train low-gain anti-saturation cooperative controller based on a multi-train communication topological structure and a multi-train dispersion event trigger cooperative control condition model. The method provided by the invention has the following beneficial effects:
firstly, in the process of multi-train cooperative control, the periodic discrete characteristic of information in the actual acquisition, transmission and processing processes is considered, an event trigger control method is used, the vehicle control signal is updated only when the trigger event is met, and updated train state information is sent to the adjacent trains, so that the updating times of a controller and the communication times between the trains are reduced.
Secondly, due to the saturation phenomenon of the train controller, the output of the controller is bounded, and the low-gain anti-saturation cooperative controller is used in the design process of the controller, so that the effective cooperative operation of the train can be ensured, and the convergence speed of the system adjusting process is improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a process flow diagram of a method for triggering control of multiple train dispersion events based on discrete communication data according to the present invention;
FIG. 2 is a process flow diagram of a preferred embodiment of a method for split event triggered control of multiple trains based on discrete communicated data in accordance with the present invention;
fig. 3 is a schematic diagram of the coordinated operation of multiple trains in the method for triggering control of multiple train dispersion events based on discrete communication data according to the present invention;
fig. 4 is a schematic diagram illustrating a multi-train dispersion event trigger control principle in the method for controlling the multi-train dispersion event trigger based on the discrete communication data according to the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
The invention provides a multi-train scattered event triggering control new technical method based on discrete communication data aiming at the discreteness of information sampling and traction/brake boundedness of a high-speed train, realizes multi-train cooperative control, and can reduce communication frequency and controller switching times.
Referring to fig. 1 and 2, the present invention provides a method for triggering control of multiple train dispersion events based on discrete communication data, comprising the following steps:
aiming at a plurality of trains running on the same line, carrying out longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train;
analyzing the communication topology of multi-train cooperative control based on a graph theory to obtain a multi-train communication topology structure;
defining a tracking target of a plurality of trains based on the high-speed train single substance point model and the multi-train communication topological structure, and converting the high-speed train single substance point model into a multi-train error dynamic equation;
establishing a multi-train scattered event trigger cooperative control condition model based on the multi-train communication topological structure and the multi-train error kinetic equation;
and establishing a multi-train low-gain anti-saturation cooperative controller based on the multi-train communication topological structure and the multi-train decentralized event trigger cooperative control condition model.
Further, in some preferred embodiments, the first step specifically includes:
as shown in fig. 3, considering n trains traveling on one route, the first train is train 1, and the remaining trains are train 2, train 3, …, and train n in this order along the traveling direction. Taking a train I belonging to I [1, n ] as an example, establishing a train longitudinal dynamics model:
wherein x isi(t)、vi(t) and mi(t) the position, speed and mass of the ith train, respectively; t isi(t) is the control action, i.e. traction/braking force, of the ith train; f (v)i) The running resistance per unit mass of the ith train is expressed as: f (v)i)＝c1+c2vi+c3vi 2Wherein c is1、c2And c3Are davis equation coefficients.
The traction/braking force T of the train can be designedi(t) is of the form:
Ti(t)＝miui(t)+mif(vi) (2)
wherein u isi(t) is the cooperative control term to be designed for anti-saturation, the first term miui(t) is a cooperative control item for controlling the train to cooperatively run consistently with the adjacent train state and to run at the same speed with the designed distance as the running interval; second term mif(vi) The resistance to the train during operation is compensated. Since the state of the vehicle and the adjacent vehicle are transmitted to the controller of the train in the form of discrete data, the first item can be written as ui(t)＝ui(k τ), t ∈ [ k τ, (k +1) τ), k ∈ N, τ denotes the sampling period of the signal.
When this is taken into formula (1) according to formula (2), it is possible to obtain:
let the target position and the target cruising speed of the ith train be respectively
And vd，ldThe minimum safe distance between trains.
Defining a tracking interval ni＝xi-xi+1,i∈I[1,n-1]。
Further, the second step specifically includes:
assuming two-way information transmission between all trains in the system through the communication network, the train communication topology can be described as weighted undirected graph G ═ (V, W, a), where V ═ V1,v2,…,vnIs the set of nodes that the train makes up;
representing a set of edges; a ═ aij]∈Zn×nFor the adjacency matrix, if train i can communicate with train j, then aij>0, if not, aij1 is equal to 0, and let aii0. D is the in-degree matrix of the weighted undirected graph G, denoted D ═ diag { deg. }in(vi),i∈I[1,n]Therein of
The laplacian matrix of the weighted undirected graph G is defined as L ═ D-a. Definition of NiIs a "topology-adjacency" set of trains, denoted Ni＝{vj:(vj,vi),j∈I[1,n]}. If the train i can obtain the information of the radio block center and can obtain the target speed distance curve, hi1, otherwise, hi0. Let H be diag { H1,h2,…,hnJ, define Q ═ L + H, λmaxMax { λ (Q) } denotes the maximum characteristic value of Q, λminMin { λ (Q) } represents the minimum eigenvalue of Q.
Further, the third step specifically includes:
let yi＝[xi-xid,vi-vd]TAnd representing the tracking error, the error kinetic equation of the ith train is as follows:
definition of y (t) ═ y1(t)y2(t)…yn(t)]T，U(t)＝[u1(t)u2(t)…un(t)]TThen the error dynamics equation for multiple trains can be expressed as:
wherein the content of the first and second substances,
representing the Kronecker product, the goal for multi-train cooperative control can be expressed as:
wherein, | | · | | represents L2And (4) norm.
In a preferred embodiment of the present invention, in order to reduce the number of communications between vehicles and the number of times of switching controllers under the condition of ensuring the train control performance, an event-triggered control method is designed, as shown in fig. 4, specifically, by defining the following event-triggered conditions, determining whether a train needs to transmit the state information of the train to an oncoming vehicle and update the controller of the train, and within the interval of two event triggers, the trains do not need to communicate with each other, and the controller remains unchanged, and the obtained multi-train dispersion event-triggered cooperative control condition model includes:
wherein the content of the first and second substances,
indicating the kth trainiUpdate time of the secondary controller, yi(k tau) represents discrete sample state information for the train,
representing the state of the train when the last event triggered,
is the state information sent by the oncoming vehicle for the last time, and the parameters
Satisfy the requirement of
Mu is a range undetermined normal number, theta ═ P (omega) BBTP (omega), P (omega) satisfies the Riccati equation ATP(ω)+P(ω)A-P(ω)BBTP (ω) ═ - (ω) P (ω) solution. inf {. denotes the infimum of the collection.
Further, the multi-train low-gain anti-saturation cooperative controller is designed based on the analysis as follows:
wherein, β is a parameter to be designed, and ω satisfies the following relationship:
wherein
The speed of the train control system is improved by convergence under the condition that the train control function is saturated through the parameters, and the multi-train cooperative operation is ensured.
In summary, the method for triggering control of multiple trains based on discrete communication data according to the present invention includes the following steps: aiming at a plurality of trains running on the same line, carrying out longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train; analyzing the communication topology of multi-train cooperative control based on a graph theory to obtain a multi-train communication topology structure; defining a tracking target of a plurality of trains based on a single substance point model of the high-speed train and a multi-train communication topological structure, and converting the single substance point model of the high-speed train into a multi-train error kinetic equation; establishing a multi-train scattered event trigger cooperative control condition model based on a multi-train communication topological structure and the multi-train error kinetic equation; and establishing a multi-train low-gain anti-saturation cooperative controller based on a multi-train communication topological structure and a multi-train dispersion event trigger cooperative control condition model. The method provided by the invention has the following beneficial effects:
firstly, in the process of multi-train cooperative control, the periodic discrete characteristic of information in the actual acquisition, transmission and processing processes is considered, an event trigger control method is used, the vehicle control signal is updated only when the trigger event is met, and updated train state information is sent to the adjacent trains, so that the updating times of a controller and the communication times between the trains are reduced.
Secondly, due to the saturation phenomenon of the train controller, the output of the controller is bounded, and the low-gain anti-saturation cooperative controller is used in the design process of the controller, so that the effective cooperative operation of the train can be ensured, and the convergence speed of the system adjusting process is improved.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. A method for multi-train scatter event trigger control based on discrete communication data is characterized by comprising the following steps:
aiming at a plurality of trains running on the same line, carrying out longitudinal stress analysis on each train, and establishing a single substance point model of the high-speed train;
analyzing the communication topology of multi-train cooperative control based on a graph theory to obtain a multi-train communication topology structure;
defining a tracking target of a plurality of trains based on the high-speed train single substance point model and the multi-train communication topological structure, and converting the high-speed train single substance point model into a multi-train error dynamic equation;
establishing a multi-train scattered event trigger cooperative control condition model based on the multi-train communication topological structure and the multi-train error kinetic equation;
and establishing a multi-train low-gain anti-saturation cooperative controller based on the multi-train communication topological structure and the multi-train decentralized event trigger cooperative control condition model.
2. The method according to claim 1, wherein for a plurality of trains running on the same line, performing longitudinal stress analysis on each train, and establishing the single-point model of the high-speed train comprises:
aiming at n trains running on the same line, establishing a train longitudinal dynamics model:
wherein x isi(t)、vi(t) and mi(T) position, speed and mass of the ith train, Ti(t) is the control action, i.e. traction/braking force, of the ith train, f (v)i) The operating resistance per unit mass that the ith train receives is represented as f (v)i)＝c1+c2vi+c3vi 2Wherein c is1、c2And c3Are davis equation coefficients;
designing a traction/braking force T of the train based on the train longitudinal dynamics modeli(T) in the form of Ti(t)＝miui(t)+mif(vi) (2)，
Wherein u isi(t) is an anti-saturation cooperative control item to be designed for enabling the train to operate in accordance with the state of the adjacent train; m isiui(t) is a cooperative control item for controlling the train to cooperate in conformity with the state of the adjacent trainOperation, mif(vi) The resistance suffered by the train in operation is compensated;
substituting equation (2) into equation (1) to obtain
Let the target position and the target cruising speed of the ith train be respectively
And vdIn the formula IdThe minimum safe distance between trains;
defining a tracking interval n of adjacent trainsi＝xi-xi+1,i∈I[1,n-1]。
3. The method according to claim 2, wherein the analyzing the communication topology of the multi-train cooperative control based on the graph theory to obtain the multi-train communication topology comprises:
the method comprises the steps that bidirectional information transmission is carried out among all trains through a communication network, a communication topology of multi-train cooperative control is converted into a weighted undirected graph form, and a multi-train communication topology structure G is obtained as (V, W, A);
wherein V ═ { V ═ V1,v2,…,vnIs the set of nodes that the train makes up,
represents a set of edges, A ═ aij]∈Zn×nFor the adjacency matrix, if train i can communicate with train j, then aij>0, otherwise aij1 is equal to 0, and let aiiD is 0, and is the in-degree matrix of the weighted undirected graph G, denoted D ═ diag { deg. }in(vi),i∈I[1,n]Therein of
The laplacian matrix of the weighted undirected graph G is defined as L ═ D-a; definition of NiFor topology of trainSet of neighbors, denoted Ni＝{vj:(vj,vi),j∈I[1,n]}; if the train i can obtain the information of the radio block center and can obtain the target speed distance curve, hi1, otherwise, hi＝0；
Let H be diag { H1,h2,…,hnJ, define Q ═ L + H, λmaxMax { λ (Q) } denotes the maximum characteristic value of Q, λminMin { λ (Q) } represents the minimum eigenvalue of Q.
4. The method according to claim 3, wherein the defining a tracking target for multiple trains based on the high speed train single point model and the multi-train communication topology, and the converting the high speed train single point model into a multiple train error dynamics equation comprises:
let yi＝[xi-xid,vi-vd]TAnd representing the tracking error, the error kinetic equation of the ith train is as follows:
definition of y (t) ═ y1(t) y2(t)…yn(t)]T，U(t)＝[u1(t) u2(t)…un(t)]TObtaining the multi-train error dynamics equation
Wherein the content of the first and second substances,
the target expressing the Kronecker product and the multi-row vehicle cooperative control is expressed as
Wherein, | | · | | represents L2And (4) norm.
5. The method of claim 4, wherein the multi-train spread event triggering coordinated control condition model comprises:
wherein the content of the first and second substances,
indicating the kth trainiUpdate time of the secondary controller, yi(k tau) represents discrete sample state information for the train,
representing the state of the train when the last event triggered,
is the state information sent by the oncoming vehicle for the last time, and the parameters
Satisfy the requirement of
Mu is a range undetermined normal number, theta ═ P (omega) BBTP (omega), P (omega) satisfies the Riccati equation ATP(ω)+P(ω)A-P(ω)BBTP (ω) — (ω) a solution of P (ω), inf { · } represents the infimum of the set.
6. The method of claim 5, wherein the multi-train low-gain anti-saturation cooperative controller comprises:
wherein, β is a parameter to be designed, and ω satisfies the following relationship:
wherein
Mu satisfies
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