CN112298281A - Train operation control method in time-lag communication network environment - Google Patents

Train operation control method in time-lag communication network environment Download PDF

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CN112298281A
CN112298281A CN202011147017.1A CN202011147017A CN112298281A CN 112298281 A CN112298281 A CN 112298281A CN 202011147017 A CN202011147017 A CN 202011147017A CN 112298281 A CN112298281 A CN 112298281A
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train
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CN112298281B (en
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董海荣
白卫齐
张子轩
张琦
荀径
王洪伟
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Beijing Jiaotong University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L15/00—Indicators provided on the vehicle or train for signalling purposes
    • B61L15/0018—Communication with or on the vehicle or train
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L23/00—Control, warning or like safety means along the route or between vehicles or trains
    • B61L23/08—Control, warning or like safety means along the route or between vehicles or trains for controlling traffic in one direction only
    • B61L23/14—Control, warning or like safety means along the route or between vehicles or trains for controlling traffic in one direction only automatically operated
    • B61L23/18—Control, warning or like safety means along the route or between vehicles or trains for controlling traffic in one direction only automatically operated specially adapted for changing lengths of track sections in dependence upon speed and traffic density
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L27/00—Central railway traffic control systems; Trackside control; Communication systems specially adapted therefor
    • B61L27/20—Trackside control of safe travel of vehicle or train, e.g. braking curve calculation
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L27/00—Central railway traffic control systems; Trackside control; Communication systems specially adapted therefor
    • B61L27/70—Details of trackside communication
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B61—RAILWAYS
    • B61L—GUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L27/00—Central railway traffic control systems; Trackside control; Communication systems specially adapted therefor
    • B61L27/20—Trackside control of safe travel of vehicle or train, e.g. braking curve calculation
    • B61L2027/204—Trackside control of safe travel of vehicle or train, e.g. braking curve calculation using Communication-based Train Control [CBTC]

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Abstract

The invention provides a train operation control method in a time-lag communication network environment, which comprises the following steps: collecting real-time state information in the running process of the train, train running interference and related parameters of system time lag; establishing a multi-train system time-lag control model according to the real-time state information and the related parameters; establishing an information transmission topological model of running information interaction between different trains; establishing a multi-train control model under communication time lag by adopting nonlinear transformation on the train dynamics model; and controlling the current train according to the train control model by using a distributed cooperative low gain control algorithm. The method provided by the invention has the following beneficial effects: the problem of multi-train cooperative operation control under the time lag of a communication network is solved through a distributed time-varying coordination low-noise system gain feedback controller; by utilizing the time-varying gain characteristic of the controller, the speed coordination of the train is realized, the train runs at intervals of safe distance, and the rapidity of train state convergence is ensured.

Description

Train operation control method in time-lag communication network environment
Technical Field
The invention relates to the technical field of train operation control, in particular to a train operation control method in a time-lag communication network environment.
Background
The high-speed train operation control process is a strong nonlinear problem which is restricted by a plurality of factors such as vehicle characteristics, line conditions and the like, and the train operation performance is directly influenced by the performance of a train control algorithm. In recent years, with the development of technologies such as communication and control, cooperative train control has become a research focus. In the process of considering the cooperative operation of multiple trains, on the premise of ensuring high confidence rate in the information interaction process between the vehicle-mounted control subsystem and the ground control subsystem, the phenomenon of information transmission time lag is difficult to avoid, the transmission time lag in the information interaction process has numerous factors and complex mechanism, and time lag information is difficult to accurately model. Therefore, how to compensate the complex information interaction time lag phenomenon, and realizing accurate and stable control of multiple trains still deserves further thinking and research.
In the process of multi-train cooperative operation, if a cooperative control algorithm with robustness on communication network time lag is designed by neglecting the influence of the communication network time lag, the control performance of a train is reduced, even the whole system is unstable, and the rapidity and the stability of the train cooperative operation process are damaged. Therefore, the method has important theoretical practical significance for developing research aiming at the problem of cooperative control of the high-speed train under the transmission time lag constraint of communication network information interaction.
Disclosure of Invention
The embodiment of the invention provides a train operation control method in a time-lag communication network environment, which is used for solving the technical problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme.
A train operation control method in a time-lag communication network environment comprises the following steps:
acquiring real-time state information in the running process of the train and running parameters when the running of the train is disturbed and a train system lags;
establishing a multi-train system time-lag control model based on the real-time state information and the operation parameters;
defining an information interaction mechanism in the process of multi-train cooperative operation, and establishing an information transmission topological model of operation information interaction between different trains;
carrying out nonlinear transformation processing on the multi-train system time-lag control model, and establishing a multi-train control model of a communication time-lag environment;
solving a multi-train control model of a communication time lag environment through a distributed cooperative time-varying gain control algorithm to obtain control parameters of the train;
and controlling the train based on the control parameters and by combining the information transfer topological model.
Preferably, the real-time status information includes a real-time location and a real-time speed of the train, and the operational parameters include external resistance, traction/brake unit inertia time lag.
Preferably, establishing a multi-train system time lag control model based on the real-time status information and the operating parameters comprises:
defining a high-speed train multi-train system consisting of N trains, and establishing a dynamic model of the ith train
Figure BDA0002740045060000021
Figure BDA0002740045060000022
Figure BDA0002740045060000023
In the formula, pi(t),vi(t) and miRespectively representing the position, running speed and train mass of the train i, fi(t) shows the tractive effort and braking effort obtained for train i, FiIndicating a control command received by the traction unit or the brake unit, miR(vi) Indicating the basic resistance to the train i in the direction of travel,
Figure BDA0002740045060000024
c0,cvand caIs the davis coefficient; and iota represents the inertia time lag coefficient of the traction unit/the brake unit.
Preferably, the nonlinear transformation processing is performed on the multi-train system time lag control model, and the building of the multi-train control model of the communication time lag environment comprises the following steps:
establishing multi-row vehicle error model
Figure BDA0002740045060000025
For obtaining position x in real-time running state of traini,1And the desired tracking position p0Error therebetween, and train speed xi,2Reference cruising speed v of high-speed rail multi-train system0Error between; in the formula, pr,i＝p0- (i-1) l, l represents a train minimum safe tracking interval;
for tractive force F in train dynamics modeli(t) braking force fi(t) and the basic resistance m received in the running direction of the train iiR(vi) Performing transformation to obtain
Figure BDA0002740045060000026
Based on the formula (3), the following formula is obtained
Figure BDA0002740045060000031
Figure BDA0002740045060000032
Figure BDA0002740045060000033
Defining a train operating state variable xi＝[xi,1,xi,2,zi]T(5) And
Figure BDA0002740045060000034
obtaining simplified train dynamics equations
Figure BDA0002740045060000035
Wherein the content of the first and second substances,
Figure BDA0002740045060000036
establishing a multi-train control model of a communication time lag environment under a constant communication time lag tau environment by combining a simplified train dynamics equation
Figure BDA0002740045060000037
Preferably, the obtaining of the control parameters of the train by solving the multi-train control model of the communication time lag environment through a distributed cooperative time-varying gain control algorithm comprises:
establishing a distributed cooperative control law
Figure BDA0002740045060000038
Wherein if i is 1, the first train in the fleet is considered, and b is taken at the moment11, otherwise, b i0; if the information interaction exists between the ith train and the jth train in the information transfer topological model, ai,j1, otherwise, ai,j0; rho is a known normal number to be designed; p (gamma (t)) is an algebraic Riccati equation positive solution; gamma (t) is a time-varying low-gain parameter, and meets the requirements
Figure BDA0002740045060000039
h is a sufficiently small normal number that satisfies:
Figure BDA00027400450600000310
in the formula (10), the first and second groups are,
Figure BDA00027400450600000311
h is a time-varying lag maximum
Figure BDA00027400450600000312
In time, for any train, there are
Figure BDA00027400450600000313
And
Figure BDA00027400450600000314
for any j epsilon I [1, N-1]，
Figure BDA00027400450600000315
Figure BDA00027400450600000316
Figure BDA00027400450600000317
Parameter(s)
Figure BDA00027400450600000318
Satisfies the following conditions:
Figure BDA0002740045060000041
as can be seen from the technical solutions provided by the embodiments of the present invention, the present invention provides a train operation control method in a time-lag communication network environment, including: collecting real-time state information in the running process of the train, train running interference and related parameters of system time lag; establishing a multi-train system time-lag control model according to the real-time state information and the related parameters; establishing an information transmission topological model of running information interaction between different trains; establishing a multi-train control model under communication time lag by adopting nonlinear transformation on the train dynamics model; and controlling the current train according to the train control model by using a distributed cooperative low gain control algorithm. The method provided by the invention has the following beneficial effects: the problem of multi-train cooperative operation control under the time lag of a communication network is solved through a distributed time-varying coordination low-noise system gain feedback controller; by utilizing the time-varying gain characteristic of the controller, the speed coordination of the train is realized, the train runs at intervals of safe distance, and the rapidity of train state convergence is ensured.
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.
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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 train operation control method in a time-lag communication network environment according to the present invention;
fig. 2 is a schematic diagram of the coordinated operation of multiple trains in the train operation control method in a time-lag communication network environment according to the present invention;
fig. 3 is a schematic diagram of a multi-train cooperative operation speed curve in the train operation control method in a time-lag communication network environment according to the present invention;
fig. 4 is a schematic diagram of a curve of relative distances between multiple trains in cooperation operation in a train operation control method in a time-lag communication network environment according to the present invention;
fig. 5 is a schematic control input diagram in the train operation control method in the time-lag communication network environment 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.
Referring to fig. 1, the train operation control method in a time-lag communication network environment provided by the present invention includes:
acquiring real-time state information in the running process of the train and running parameters when the running of the train is disturbed and a train system lags;
establishing a multi-train system time-lag control model based on the real-time state information and the operation parameters;
defining an information interaction mechanism in the process of multi-train cooperative operation, and establishing an information transmission topological model of operation information interaction between different trains;
carrying out nonlinear transformation processing on the multi-train system time-lag control model, and establishing a multi-train control model of a communication time-lag environment;
solving a multi-train control model of a communication time lag environment through a distributed cooperative time-varying gain control algorithm to obtain control parameters of the train;
and controlling the train based on the control parameters and in combination with the information transfer topological model.
Further, the real-time status information in the running process of the train includes: the current position and speed of the train. The running parameters of the train when running is disturbed and the train system time lag comprise external resistance, inertia time lag of a traction/brake unit and the like.
Further, in some preferred embodiments, the second step specifically includes:
according to real-time state information in the running process of the train, running parameters when the running of the train is interfered and the train system lags, a high-speed train multi-train system consisting of N trains is considered, and a dynamics model is established by taking the ith train in the system as an example
Figure BDA0002740045060000061
Figure BDA0002740045060000062
Figure BDA0002740045060000063
In the formula, pi(t),vi(t) and miRespectively indicating the position, the running speed and the quality of the train iAmount fi(t) shows the tractive effort and braking effort obtained for train i, FiIndicating a control command received by the traction unit or the brake unit, miR(vi) Indicating the basic resistance to the train i in the direction of travel,
Figure BDA0002740045060000064
c0,cvand caIs the davis coefficient; and iota represents the inertia time lag coefficient of the traction unit/the brake unit.
Further, in some preferred embodiments, the third step specifically includes: defining an information interaction mechanism in the process of multi-train cooperative operation, wherein an information interaction structure between trains is shown in figure 2; and establishing an information transmission topological model for running information interaction between different trains, wherein the time lag in the information interaction process is unknown but has an upper limit.
Further, in some preferred embodiments, the performing a nonlinear transformation process on the multi-train system time lag control model to establish the multi-train control model of the communication time lag environment includes:
establishing multi-row vehicle error model
Figure BDA0002740045060000066
For obtaining position x in real-time running state of traini,1And the desired tracking position p0Error therebetween, and train speed xi,2Reference cruising speed v of high-speed rail multi-train system0Error between; in the formula, pr,i＝p0- (i-1) l, l represents a train minimum safe tracking interval.
Simplifying the train dynamics model by adopting a nonlinear transformation method, including the traction force and the braking force f in the train dynamics equationi(t) and the basic resistance m to the running direction of the train iiR(vi) Performing transformation, taking the transformation
Figure BDA0002740045060000071
Then, defining a train dynamics equation after simplifying the state variables as follows:
Figure BDA0002740045060000072
further defining train running state variable xi＝[xi,1,xi,2,zi]T(5) And:
Figure BDA0002740045060000073
the train dynamics equation can be simplified as:
Figure BDA0002740045060000074
wherein the content of the first and second substances,
Figure BDA0002740045060000075
Figure BDA0002740045060000076
establishing a multi-train control model of a communication time lag environment under the constant communication time lag tau environment by combining the simplified train dynamics equation
Figure BDA0002740045060000077
Furthermore, the design establishes a distributed cooperative control law,
Figure BDA0002740045060000078
wherein if i is 1, the first train in the fleet is considered, and b is taken at the moment11, otherwise, b i0; if the information interaction exists between the ith train and the jth train in the information transmission topological model established in the third step, ai,j1, otherwise, ai,j0; rho is a known normal number to be designed; p (gamma (t)) is an algebraic Riccati equation positive solution; gamma (t) is a time-varying low-gain parameter, and meets the requirements
Figure BDA0002740045060000079
h is a sufficiently small normal number that satisfies:
Figure BDA00027400450600000710
wherein the content of the first and second substances,
Figure BDA0002740045060000081
h is a time-varying lag maximum
Figure BDA0002740045060000082
In time, for any train, there are
Figure BDA0002740045060000083
And
Figure BDA0002740045060000084
for any j epsilon I [1, N-1]，
Figure BDA0002740045060000085
In particular, it is possible to use, for example,
Figure BDA0002740045060000086
Figure BDA0002740045060000087
parameter(s)
Figure BDA0002740045060000088
Satisfies the following conditions:
Figure BDA0002740045060000089
namely: the cooperative control law can ensure that in a high-speed rail multi-train dynamic system consisting of N trains, under the condition that an information interaction network between the trains has unknown time lag tau (the upper bound of the time lag tau is known), the high-speed rail multi-train can be realized by the technical scheme provided by the multi-train cooperative operation control method under the time lag constraint of the communication network, the invention establishes a train dynamics model and an error model considering the time lag of communication and the system by acquiring the real-time operation state of the trains, the traction brake inertia time lag and the information interaction network between the trains, and establishes a multi-train control model through nonlinear transformation, thereby ensuring that a plurality of trains track an expected position-speed curve under the communication time lag and cooperatively operate at the minimum tracking distance.
The invention also provides an embodiment, which is used for verifying the effectiveness of the train operation control method in the time-lag communication network environment, and MATLAB is adopted for simulation experiment verification, and the specific process is as follows:
the parameters used in the simulation are shown in the following table:
Figure BDA00027400450600000810
Figure BDA0002740045060000091
the initial state of each train is shown in the following table:
Figure BDA0002740045060000092
the information transfer topology model constructed in the simulation can be described as: in a fleet formed by four trains, any two other trains can carry out bidirectional information transmission except that the first train and the fourth train can not carry out direct information interaction.
Based on the above parameters, the control method proposed by the present invention is subjected to simulation verification, and the results shown in fig. 3 to 5 are obtained. Fig. 3 and 4 are a speed curve and a train relative interval curve of a train operation control method using the time-lag communication network environment of the present invention, respectively, and fig. 5 shows a control input curve of a multi-train cooperative operation control method under the time-lag constraint of the communication network disclosed by the present invention. As can be seen from fig. 3 and 4, in the presence of a communication network, when the train is in a standstill, the train can quickly reach a desired speed while maintaining a safe interval, and the cooperative operation is realized, that is, the present invention has good stability and rapidity.
In summary, the present invention provides a train operation control method in a time-lag communication network environment, including: collecting real-time state information in the running process of the train, train running interference and related parameters of system time lag; establishing a multi-train system time-lag control model according to the real-time state information and the related parameters; establishing an information transmission topological model of running information interaction between different trains; establishing a multi-train control model under communication time lag by adopting nonlinear transformation on the train dynamics model; and controlling the current train according to the train control model by using a distributed cooperative low gain control algorithm. The method provided by the invention has the following beneficial effects: the problem of multi-train cooperative operation control under the time lag of a communication network is solved through a distributed time-varying coordination low-noise system gain feedback controller; by utilizing the time-varying gain characteristic of the controller, the speed coordination of the train is realized, the train runs at intervals of safe distance, and the rapidity of train state convergence is ensured.
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 (5)

1. A train operation control method in a time-lag communication network environment, comprising:
acquiring real-time state information in the running process of the train and running parameters when the running of the train is disturbed and a train system lags;
establishing a multi-train system time-lag control model based on the real-time state information and the operation parameters;
defining an information interaction mechanism in the process of multi-train cooperative operation, and establishing an information transmission topological model of operation information interaction between different trains;
carrying out nonlinear transformation processing on the multi-train system time-lag control model, and establishing a multi-train control model of a communication time-lag environment;
solving a multi-train control model of the communication time lag environment through a distributed cooperative time-varying gain control algorithm to obtain control parameters of the train;
and controlling the train based on the control parameters and in combination with the information transfer topological model.
2. The method of claim 1, wherein the real-time status information includes a real-time location and a real-time speed of the train, and the operational parameters include external drag, traction/brake unit inertia time lag.
3. The method of claim 2, wherein establishing a multi-train system time lag control model based on the real-time status information and the operating parameters comprises:
defining a high-speed train multi-train system consisting of N trains, and establishing a dynamic model of the ith train
Figure FDA0002740045050000011
Figure FDA0002740045050000012
Figure FDA0002740045050000013
In the formula, pi(t),vi(t) and miRespectively representing the position, running speed and train mass of the train i, fi(t) shows the tractive effort and braking effort obtained for train i, FiIndicating a control command received by the traction unit or the brake unit, miR(vi) Indicating the basic resistance to the train i in the direction of travel,
Figure FDA0002740045050000014
c0,cvand caIs davisA coefficient; and iota represents the inertia time lag coefficient of the traction unit/the brake unit.
4. The method according to claim 3, wherein the performing a nonlinear transformation on the multi-train system time lag control model, and the establishing a multi-train control model of a communication time lag environment comprises:
establishing multi-row vehicle error model
Figure FDA0002740045050000021
For obtaining position x in real-time running state of traini,1And the desired tracking position p0Error therebetween, and train speed xi,2Reference cruising speed v of high-speed rail multi-train system0Error between; in the formula, pr,i＝p0- (i-1) l, l represents a train minimum safe tracking interval;
for tractive force F in the train dynamics modeli(t) braking force fi(t) and the basic resistance m received in the running direction of the train iiR(vi) Performing transformation to obtain
Figure FDA0002740045050000022
Based on the formula (3), the following formula is obtained
Figure FDA0002740045050000023
Figure FDA0002740045050000024
Figure FDA0002740045050000025
Defining a train operating state variable xi＝[xi,1,xi,2,zi]T(5) And
Fi＝miιui+(1+ι(cv+2cavi))fi-miι(cv+2cavi)R(vi) (6) obtaining a simplified train dynamics equation
Figure FDA0002740045050000026
Wherein the content of the first and second substances,
Figure FDA0002740045050000027
establishing a multi-train control model of a communication time lag environment under the constant communication time lag tau environment by combining the simplified train dynamics equation
Figure FDA0002740045050000028
5. The method of claim 4, wherein the solving the multi-train control model of the communication time lag environment through a distributed cooperative time-varying gain control algorithm to obtain the control parameters of the train comprises:
establishing a distributed cooperative control law
Figure FDA0002740045050000029
Wherein if i is 1, the first train in the fleet is considered, and b is taken at the moment11, otherwise, bi0; if the information interaction exists between the ith train and the jth train in the information transmission topological model, ai,j1, otherwise, ai,j0; rho is a known normal number to be designed;
p (gamma (t)) is an algebraic Riccati equation positive solution; gamma (t) is a time-varying low-gain parameter, and meets the requirements
Figure FDA00027400450500000210
h is a sufficiently small normal number that satisfies:
Figure FDA0002740045050000031
in the formula (10), the first and second groups are,
Figure FDA0002740045050000032
h is a time-varying lag maximum
Figure FDA0002740045050000033
In time, for any train, there are
Figure FDA0002740045050000034
And
Figure FDA0002740045050000035
for any j epsilon I [1, N-1]，
Figure FDA0002740045050000036
Figure FDA0002740045050000037
Parameter(s)
Figure FDA0002740045050000038
Satisfies the following conditions:
Figure FDA0002740045050000039
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