CN115016526A - Cluster self-organizing control method for double-layer defense - Google Patents

Cluster self-organizing control method for double-layer defense Download PDF

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CN115016526A
CN115016526A CN202210476976.0A CN202210476976A CN115016526A CN 115016526 A CN115016526 A CN 115016526A CN 202210476976 A CN202210476976 A CN 202210476976A CN 115016526 A CN115016526 A CN 115016526A
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cluster
individual
defense
intrusion
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CN115016526B (en
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彭星光
邹秉运
宋保维
潘光
李乐
张福斌
高剑
张立川
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Northwestern Polytechnical University
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Abstract

The invention relates to a cluster self-organizing control method for double-layer defense, wherein a defense cluster and an intrusion cluster respectively have different individual attributes and interaction strategies, wherein for the defense cluster, a defense potential field force is formed by constructing a defense potential field to realize a double-layer defense effect, and a position synergistic item, a speed synergistic item, a self-driving item, an anti-intrusion item and a random noise item are also present, and the position synergistic item, the speed synergistic item, the self-driving item, the anti-intrusion item and the random noise item are set to cope with the intrusion of an intruder by setting different weight coefficients; for an intrusion cluster, a certain difference exists between a cooperative rule and a defense cluster, and main cooperative items include: the position collaborative item, the self-driven item, the individual intrusion item, the back-driven item-by-item and the random noise item are set through the collaborative item weight coefficient to complete the intrusion task. And making a rule for the cooperation rule and the interaction strategy of the two-party cluster, further determining a defense cluster parameter according to the defense effect, and finally realizing the successful cluster defense.

Description

Cluster self-organizing control method for double-layer defense
Technical Field
The invention relates to the technical field of cluster intelligence, in particular to a self-organization control method for cluster defense and confrontation by utilizing a double-layer defense potential field.
Background
The phenomenon of cluster motion is widely found in nature, and suggests that the fish from whirling to migrating of the bird colony and the ant colony from cooperating to forming of the flora. The individual ability of the group is limited and does not have complex intelligent thinking, and the group formed by the individuals finally can show a complex, ordered and diverse intelligent clustering phenomenon, which is also called cluster self-organizing emerging behavior. The core of cluster movement is the basic rule followed by individuals in a cluster, and the abundant phenomenon finally emerges at the cluster level through the individuals following the rule. By referring to the natural clustering rules, people construct various artificial cluster systems, which are embodied in military use and civil use. If the system is applied to the unmanned aerial vehicle cluster, complex environment exploration, forest fire prevention and control, personnel search and rescue under disasters can be completed by the unmanned aerial vehicle cluster, and even cross-domain cooperation can be realized by the cluster technology. Meanwhile, various cluster models such as a social force model, a Viscek model, a Couzin model and the like are also provided on a theoretical level by realizing actual artificial clustering.
While the most basic model for defending against intrusion is called: target-intruder-defender confrontation model (TAD game). This basic countermeasure model contains three participants, a target, an intruder and a defender. The intruder aims to catch the target while avoiding attack by the defender. Defenders attempt to protect the target while also capturing the intruder as much as possible. The target has no defense capability for the intruder, and can only avoid the attack of the intruder in an escape mode. Solutions for TAD models are mainly divided into two categories: and dividing the leading area according to the initial position, selecting an optimal strategy and constructing a dynamic update state of a differential equation. The TAD problem is directed to the problem of intrusion prevention for a single individual, and when the TAD problem is directed to intrusion prevention among a plurality of individuals (groups), a target matching is generally performed between an defender and an intruder by using a distribution algorithm, and a conventional TAD solution is used after one-to-one matching is completed. That is, the current idea for the inter-group defense intrusion problem is to decompose the inter-group defense into two steps: individual matching and individual defense. The method simply considers the group as the accumulation sum of a plurality of individuals, changes the group defense into a plurality of individual defenses which are carried out simultaneously, and does not fully highlight the group advantages.
Therefore, how to arouse population dominance is a core problem for the current population defense. The use of a cluster self-organization approach to defend against intrusion is an option, and how to design cluster individual rules to enable the emergence of defense behavior is a problem worthy of intensive study.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a cluster defense self-organizing control method, which updates the motion state of an individual by the design of an individual interaction mechanism in a cluster and an individual interaction mechanism among clusters and combining a social force model, and finally realizes the self-organizing control of the cluster defense.
Technical scheme
A cluster self-organizing control method of double-layer defense is characterized in that: setting a cooperative rule of an individual in the defense cluster and an individual in the intrusion cluster;
1) the expression of the cooperative rule of the individuals in the defense cluster is as follows:
Figure BDA0003626140370000021
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003626140370000022
in order to be a self-driving item,
Figure BDA0003626140370000023
in the case of a location-collaborative item,
Figure BDA0003626140370000024
in order to be a speed-coordinated term,
Figure BDA0003626140370000025
in order to protect the terms of the potential field,
Figure BDA0003626140370000026
as anti-invasive term, η xi i Is random noise;
the self-driving item
Figure BDA0003626140370000027
Figure BDA0003626140370000028
Where α represents the maximum value of defensive clustering speed, | | v i (t) | | represents the magnitude of defensive clustering speed;
the position cooperation item
Figure BDA0003626140370000029
Figure BDA00036261403700000210
Figure BDA00036261403700000211
Represents a gravitational-repulsive force equilibrium position adjustment parameter, representing repulsive force when the individual pitch is smaller than the value, and attractive force when it is larger than the value;
Figure BDA0003626140370000031
represents the subgroup spacing, the repulsive force between subgroups reaches a maximum when the individual spacing equals this value;
Figure BDA0003626140370000032
representing neighbor individuals to individuals D i In the direction ofA unit vector of quantities;
N i as set of perceptual neighbors:
N i ＝{k|d ik ＜R sen ,k∈{1,...,N D },k≠i}
wherein d is ik Representing the distance, R, between individuals within a defensive cluster sen The perception radius of the defense cluster is more than 0;
the velocity co-ordination term
Figure BDA0003626140370000033
Figure BDA0003626140370000034
Figure BDA0003626140370000035
Representing the speed of the neighbor individual with the largest angle change in the neighbors;
said potential field protection term
Figure BDA0003626140370000036
Figure BDA0003626140370000037
Wherein d is ip Indicating the distance of the defending individual to the protected object,
Figure BDA0003626140370000038
representing an individual D i A unit vector to a location vector of the protected object;
Figure BDA0003626140370000039
respectively corresponding to potential field boundary distances around the protected object;
the anti-intrusion item
Figure BDA00036261403700000310
Figure BDA00036261403700000311
T i Set of perceived intruders:
T i ＝{k|d ik ＜R sen ,k∈{1,...,N I }}
wherein d is ik Representing protection of an individual against an intruder T within the perception domain i At a distance of (2), here
Figure BDA00036261403700000312
Representing an individual D i To the intruder T in the perception domain i A unit vector of the position vector of (a);
the random noise eta xi i Representing random noise with intensity of eta > 0, let
Figure BDA00036261403700000313
Is in the range of [ -0.5,0.5 [)] 2 Random vectors satisfying uniform distribution;
2) the expression of the cooperative rule of the individual in the intrusion cluster is as follows:
Figure BDA00036261403700000314
wherein the self-driving force
Figure BDA0003626140370000041
And random noise η ξ j The expression is consistent with that of a defender, only the parameters of the self-driving force of the invading individual, namely the speed maximum value beta is different from the self-driving force parameter alpha of the defending individual, and the beta is more than alpha; the remaining items including location coordination items
Figure BDA0003626140370000042
Individual intrusion item
Figure BDA0003626140370000043
Anti-evictionItem(s)
Figure BDA0003626140370000044
The specific expression is as follows:
the described self-driving force
Figure BDA0003626140370000045
Figure BDA0003626140370000046
Wherein beta represents the maximum value of the invasion cluster speed, and beta is more than alpha and | v j (t) | | represents the size of the intrusion cluster speed;
the position cooperation item
Figure BDA0003626140370000047
Figure BDA0003626140370000048
Wherein the content of the first and second substances,
Figure BDA0003626140370000049
representing neighbor individuals to individuals I j A unit vector of the position vector of (a);
N j the set of perceived neighbors is:
N j ＝{k|d jk ＜r sen ,k∈{1,...,N I },k≠j}
wherein d is jk Represents the distance, r, between individuals within an intrusion cluster sen The sensing radius of the intrusion cluster is more than 0;
the individual invasion item
Figure BDA00036261403700000410
Figure BDA00036261403700000411
Figure BDA00036261403700000412
Represents an individual I j A unit vector to a location vector of the protected object;
the back drive item by item
Figure BDA00036261403700000413
Figure BDA00036261403700000414
T j The set of imperceptible defenders is:
T j ＝{k|d jk ＜r sen ,k∈{1,...,N D }}
N D representing a defensive cluster;
the random noise eta xi j Random noise with intensity eta > 0, order
Figure BDA00036261403700000415
Is in the range of [ -0.5,0.5 [)] 2 Uniformly distributed random vectors.
A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, which when executed by the one or more processors, cause the one or more processors to implement the above-described method.
A computer-readable storage medium having stored thereon computer-executable instructions for performing the above-described method when executed.
A computer program comprising computer executable instructions which when executed perform the method described above.
Advantageous effects
The cluster self-organizing control method for double-layer defense provided by the invention solves the problem of defense intrusion countermeasures by utilizing the cluster self-organizing control method. Through the design of individual interaction mechanisms in the groups and the individual interaction mechanisms among the groups, the motion state of the individual is updated by combining the social force model, and finally the self-organization control of the cluster defense is realized. The defense cluster and the intrusion cluster respectively have different individual attributes and interaction strategies, wherein for the defense cluster, a defense potential field force is formed by constructing a defense potential field so as to realize a double-layer defense effect, and in addition, a position coordination item, a speed coordination item, a self-driving item, an anti-intrusion item and a random noise item are also present, and the position coordination item, the speed coordination item, the self-driving item, the anti-intrusion item and the random noise item are used for coping with the intrusion of an intruder by setting different weight coefficients; for an intrusion cluster, a certain difference exists between a cooperative rule and a defense cluster, and main cooperative items include: the method comprises the steps of setting a position cooperative item, a self-driven item, an individual invasion item, a back-drive item by item and a random noise item, and completing an invasion task by setting a cooperative item weight coefficient. And making a rule for the cooperative rules and the interaction strategies of the two-party clusters, further determining the defense cluster parameters according to the defense effect, and finally realizing the successful cluster defense.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, wherein like reference numerals are used to designate like parts throughout.
FIG. 1 is a schematic diagram of a potential field design of a double-layer defense ring.
FIG. 2 is a diagram of a simulation interface in the method of the present invention.
FIG. 3 is a simulation of the formation of a double layer defense circle by a subgroup of defense in the method of the present invention.
FIG. 4 is a simulation diagram of the radius of capture of an intruder entering defender in the method of the present invention.
FIG. 5 is a simulation diagram of the inner and outer defense subgroups surrounding an intruder in the method of the present invention.
FIG. 6 is a simulation diagram of successful defense of the defense cluster in the method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a cluster defense model capable of realizing defense intrusion confrontation between two clusters, which ensures that a cluster can emerge cooperative defense behaviors in the motion process and finally realizes an effective self-organizing defense effect. The cluster defense system has the following characteristics:
1. the individuals in the group are isomorphic and consistent in rule. That is, the individual attributes in the same group are consistent, and the individual behavior rules are also the same. Wherein the individual attributes comprise kinematics (maximum speed, maximum acceleration, etc.), perception capabilities, capturing capabilities, etc.
2. The individuals in the groups are heterogeneous and have different rules. That is, there is a difference in individual attributes between groups of different camps, such as a difference between a defender and an intruder in the maximum speed and the maximum acceleration, and also a difference in the perception level, and the specific parameters are shown in table one.
3. The individuals within all groups are identical. Namely, the identity of the individual cannot be identified through the external or signal, all the individuals are consistent in expression in the cluster, and no specificity exists.
4. Individual decision making is performed autonomously, and centralized distribution is not available. All individuals in the group are autonomously sensed, the individual states are autonomously updated according to the cluster rule, autonomous decision is made, and upper and lower levels among the individuals or following dependence do not exist.
5. The fight between clusters is embodied in a captured form. The defender intercepts the invader to catch the invader until the invader enters the capturing radius of the defender, the defender and the invader share the same meaning to represent the confrontation of the defender to the invader, and the invader escapes from the defender to catch the protected object until the protected object enters the capturing radius of the invader, which represents the successful confrontation of the invader.
The defense cluster and the invasion cluster are constructed according to the five-point characteristics, wherein the defense cluster is named as D and comprises N D (ii) individuals; the intrusion cluster is named I, whichIn which contains N I (ii) individuals; the protected object is named P. Wherein the individual D i (i＝1,...,N D )，I j (j＝1,...,N I ) A position vector of
Figure BDA0003626140370000071
The velocity vector is
Figure BDA0003626140370000072
Regardless of the individual shape characteristics, the individual mass is assumed to be m 1. The individual satisfies Newton's law of mechanics, where individual synergies are divided into intra-cluster synergies and inter-cluster synergies. The defense individual position speed updating formula is as follows:
Figure BDA0003626140370000073
wherein u is i (t) denotes defensive individuals D i Since the mass is 1, the resultant force and the acceleration are equivalent, where u is i (t) denotes a defensive individual D i Of the acceleration of (2). The intrusion individual position speed updating formula is the same as the defense cluster updating formula, and the cooperative items of the individuals in the two clusters are different, as follows:
first is the cooperative rule that defends individuals within a cluster, as follows:
Figure BDA0003626140370000074
defending against clustered individual collaborative items including self-driven items
Figure BDA0003626140370000075
Location collaborative items
Figure BDA0003626140370000076
Velocity synergy term
Figure BDA0003626140370000077
Potential field protection term
Figure BDA0003626140370000078
Anti-intrusion entry
Figure BDA0003626140370000079
And random noise eta xi i . The specific rule settings are as follows:
(1) self-driving item
Figure BDA00036261403700000710
Where α represents the maximum value of the velocity, | | v i (t) | | represents the velocity magnitude.
(2) Sports synergy item
Individual interaction is based on the motion state of a neighbor partner, and it is assumed that an individual can sense the motion state information (position and speed) of a neighbor in a certain neighborhood in real time. Wherein the perceived radius of the defensive cluster is R sen > 0, the set of perceptual neighbors is:
N i ＝{k|d ik ＜R sen ,k∈{1,...,N D },k≠i} (4)
wherein d is ik Representing the distance between individuals within a defensive cluster.
The motion coordination item includes a position coordination item
Figure BDA0003626140370000081
And velocity synergy term
Figure BDA0003626140370000082
Figure BDA0003626140370000083
The position coordination term formula is shown above, and the model is short-distance repulsion-long-distance attraction-medium-distance repulsion.
Figure BDA0003626140370000084
Indicates the attractive force-repulsive forceAn equilibrium position adjustment parameter that exhibits repulsion when the individual spacing is less than the value and attraction when greater than the value;
Figure BDA0003626140370000085
indicating the subgroup spacing, the repulsion between the subgroups reaches a maximum when the individual spacing equals this value.
Figure BDA0003626140370000086
Representing neighbor individuals to individuals D i The unit vector of the position vector of (2).
The speed cooperative item adopts a non-average rule, and selects a neighbor individual with the largest angle change from the neighbors
Figure BDA0003626140370000087
And to refer to its velocity bearing.
Figure BDA0003626140370000088
(3) Potential field protection term
And (3) constructing a double-layer defense potential field by combining artificial potential field theory, as shown in figure 1. The defense power is expressed as follows:
Figure BDA0003626140370000089
where the defending individual is globally aware of the protected object, d ip Indicating the distance of the defending individual to the protected object,
Figure BDA00036261403700000810
representing an individual D i A unit vector to a location vector of the protected object. When the defending individual is in different potential fields and is subjected to potential field forces in different directions, the positive and negative of the potential field protection force correspond to two actions of approaching to a protected object and departing from the protected object. Wherein
Figure BDA00036261403700000811
Respectively correspond to the circumferenceThe potential field boundary distance around the protected object, as shown in figure 1. The defense clusters thus finally form a double-layered defense circle around the protected object.
(4) Anti-intrusion entry
This is an inter-group interaction term, i.e. defending an individual from interacting with an invading individual. The defense individual can locally sense the invading individual, and the sensing radius of the defending individual to the invading individual is also R sen If > 0, the set of perceived intruders is:
T i ＝{k|d ik ＜R sen ,k∈{1,...,N I }} (8)
the anti-intrusion force is the resultant force direction of each intruder in the approaching perception range, and the distance from the intruder to the defender influences the corresponding weight, and the specific form is as follows:
Figure BDA0003626140370000091
wherein d is ik Representing protection of an individual against an intruder T within the perception domain i At a distance of (2), here
Figure BDA0003626140370000092
Representing an individual D i Perception of an intra-domain intruder T i The unit vector of the position vector of (2).
(5) Random noise
ηξ i Random noise with intensity eta > 0, order
Figure BDA0003626140370000093
Is in the range of [ -0.5,0.5 [)] 2 The upper satisfies a uniformly distributed random vector.
Then, the cooperative rule of the individual in the intrusion cluster is expressed as follows:
Figure BDA0003626140370000094
wherein the self-driving force
Figure BDA0003626140370000095
And random noise η ξ j The expression is consistent with that of defenders, only the parameters of the self-driving force of the invading individual, namely the speed maximum value beta is different from the self-driving force parameter alpha of the defending individual, and the general value is beta>α. The remaining items including location coordination items
Figure BDA0003626140370000096
Individual invasion item
Figure BDA0003626140370000097
Back drive item by item
Figure BDA0003626140370000098
The specific expression is as follows:
(1) location coordination items
There is also a local perception of intruders, where the perception radius of the intrusion cluster is r sen > 0, the set of perceptual neighbors is:
N j ＝{k|d jk ＜r sen ,k∈{1,...,N I },k≠j} (11)
the positions of the invading individuals and the neighbors in the perception domain thereof cooperatively follow the principle of 'exclusive only', namely, the individuals are only in collision avoidance, and aggregation does not exist, and the specific expression is as follows:
Figure BDA0003626140370000099
(2) individual intrusion item
The invading individual has an invading trend and an individual invading force to the protected object, which are specifically expressed as follows:
Figure BDA0003626140370000101
(3) back drive item by item
The item is an inter-group interaction item of the invading individual, namely, the invading individual interacts with the defending individual. The invading individual can locally sense the defending individual and defendThe perception radius of the individual is also r sen If the ratio is more than 0, the set of the sensible defenders is as follows:
T j ＝{k|d jk ＜r sen ,k∈{1,...,N D }} (14)
the back-driving gradual force is the resultant force direction of each defender far away from the sensing range, and the distance from the defender to the invader influences the corresponding weight, and the specific form is as follows:
Figure BDA0003626140370000102
simulation result
The above algorithm is simulated, the simulation object is composed of three parts of a defense cluster, an intrusion cluster and a protection object, and the simulation interface is shown in fig. 2. According to the cooperative rules, the speed and position information of the individuals in the cluster are updated in real time, and the simulation result finally shows that the defense cluster can spontaneously emerge various defense behaviors in the cluster defense confrontation, for example, the defense subgroups form a double-layer defense ring, the inner and outer defense subgroups surround an attack invader, the outer ring directly attacks and captures the invader, and finally the cluster self-organization defense is successfully realized, the specific effect is shown in fig. 3-6, and the double-layer defense ring is formed again to cope with the next invasion after the defense cluster defense succeeds.
Table-cluster parameter
Figure BDA0003626140370000103
Figure BDA0003626140370000111
While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and various equivalent modifications or substitutions can be easily made by those skilled in the art within the technical scope of the present disclosure.

Claims (4)

1. A cluster self-organizing control method of double-layer defense is characterized in that: setting a cooperative rule of an individual in the defense cluster and an individual in the intrusion cluster;
1) the expression of the cooperative rule of the individuals in the defense cluster is as follows:
Figure FDA0003626140360000011
wherein the content of the first and second substances,
Figure FDA0003626140360000012
in order to be a self-driving item,
Figure FDA0003626140360000013
in the case of a location-collaborative item,
Figure FDA0003626140360000014
in order to be a speed-coordinated term,
Figure FDA0003626140360000015
in order to protect the terms of the potential field,
Figure FDA0003626140360000016
eta xi, an anti-intrusive term i Is random noise;
the self-driving item
Figure FDA0003626140360000017
Figure FDA0003626140360000018
Where α represents the maximum value of defensive clustering speed, | | v i (t) | | represents the magnitude of the defensive clustering speed;
the position cooperation item
Figure FDA0003626140360000019
Figure FDA00036261403600000110
Figure FDA00036261403600000111
Expressing a gravitational-repulsive force equilibrium position adjustment parameter, expressing a repulsive force when the individual pitch is smaller than the value, and expressing a gravitational force when it is larger than the value;
Figure FDA00036261403600000112
represents the subgroup spacing, the repulsive force between subgroups reaches a maximum when the individual spacing equals this value;
Figure FDA00036261403600000113
representing neighbor individuals to individuals D i A unit vector of the position vector of (a);
N i as a set of perceptual neighbors:
N i ＝{k|d ik ＜R sen ,k∈{1,...,N D },k≠i}
wherein d is ik Representing the distance, R, between individuals within a defensive cluster sen The perception radius of the defense cluster is more than 0;
the velocity co-ordination term
Figure FDA00036261403600000114
Figure FDA00036261403600000115
Figure FDA00036261403600000116
Representing the speed of the neighbor individual with the largest angle change in the neighbors;
said potential field protection term
Figure FDA00036261403600000117
Figure FDA0003626140360000021
Wherein d is ip Indicating the distance of the defending individual to the protected object,
Figure FDA0003626140360000022
representing an individual D i A unit vector to a location vector of the protected object;
Figure FDA0003626140360000023
respectively corresponding to potential field boundary distances around the protected object;
the anti-intrusion item
Figure FDA0003626140360000024
Figure FDA0003626140360000025
T i Set of perceived intruders:
T i ＝{k|d ik ＜R sen ,k∈{1,...,N I }}
wherein d is ik Representing protection of an individual against an intruder T within the perception domain i At a distance of (2), here
Figure FDA0003626140360000026
Representing an individual D i Perception of an intra-domain intruder T i A unit vector of the position vector of (a);
the random noise eta xi i Random noise with intensity eta > 0, order
Figure FDA0003626140360000027
Is in the range of [ -0.5,0.5 [)] 2 Random vectors which are uniformly distributed are satisfied;
2) the expression of the cooperative rule of the individual in the intrusion cluster is as follows:
Figure FDA0003626140360000028
wherein the self-driving force
Figure FDA0003626140360000029
And random noise eta xi j The expression is consistent with that of a defender, only the parameters of the self-driving force of the invading individual, namely the speed maximum value beta is different from the self-driving force parameter alpha of the defending individual, and the beta is more than alpha; the remaining items including location coordination items
Figure FDA00036261403600000210
Individual intrusion item
Figure FDA00036261403600000211
Back drive item by item
Figure FDA00036261403600000212
The specific expression is as follows:
the described self-driving force
Figure FDA00036261403600000213
Figure FDA00036261403600000214
Wherein beta represents the maximum value of the invasion cluster speed, and beta is more than alpha and | v | j (t) | | represents the size of the intrusion cluster speed;
the above-mentionedLocation coordination item of
Figure FDA00036261403600000215
Figure FDA00036261403600000216
Wherein the content of the first and second substances,
Figure FDA0003626140360000031
representing neighbor individuals to individuals I j A unit vector of the position vector of (a);
N j the set of perceived neighbors is:
N j ＝{k|d jk ＜r sen ,k∈{1,...,N I },k≠j}
wherein d is jk Represents the distance, r, between individuals within an intruding cluster sen The sensing radius of the invading cluster is more than 0;
the individual invasion item
Figure FDA0003626140360000032
Figure FDA0003626140360000033
Figure FDA0003626140360000034
Represents an individual I j A unit vector to a location vector of the protected object;
the back drive item by item
Figure FDA0003626140360000035
Figure FDA0003626140360000036
T j The set of imperceptible defenders is:
T j ＝{k|d jk ＜r sen ,k∈{1,...,N D }}
N D representing a defensive cluster;
the random noise eta xi j Random noise with intensity eta > 0, order
Figure FDA0003626140360000037
Is in the range of [ -0.5,0.5 [)] 2 The upper satisfies a uniformly distributed random vector.
2. A computer system, comprising: one or more processors, a computer readable storage medium, for storing one or more programs, wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method of claim 1.
3. A computer-readable storage medium having stored thereon computer-executable instructions for, when executed, implementing the method of claim 1.
4. A computer program comprising computer executable instructions which when executed perform the method of claim 1.
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