CN112836356A - Local self-organizing large-scale group dynamic target tracking method based on random noise - Google Patents

Local self-organizing large-scale group dynamic target tracking method based on random noise Download PDF

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CN112836356A
CN112836356A CN202110050734.0A CN202110050734A CN112836356A CN 112836356 A CN112836356 A CN 112836356A CN 202110050734 A CN202110050734 A CN 202110050734A CN 112836356 A CN112836356 A CN 112836356A
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王丽君
李阳
苏伟
徐平海
陈先中
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University of Science and Technology Beijing USTB
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Abstract

The invention discloses a local self-organizing large-scale group dynamic target tracking method based on random noise, which comprises the following steps: constructing an HK model containing an uncertain dynamic target, and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing the uncertain dynamic target comprises the following steps: an HK model in which the dynamic target is perceived by only a part of individuals and an HK model in which the dynamic target independently exists; aiming at the HK model of which the dynamic target is only sensed by partial individuals, tracking the dynamic target of incomplete information and verifying the dynamic target; and tracking the dynamic target of incomplete information aiming at the HK model in which the dynamic target independently exists, and verifying. The invention enriches the application of a control strategy based on noise, perfects the corresponding mathematical theory analysis, and provides a novel dynamic real-time tracking method based on noise for solving the problem of synchronous tracking caused by uncertainty, even unknown, such as dynamic diversity of group targets in a large-scale complex system.

Description

Local self-organizing large-scale group dynamic target tracking method based on random noise
Technical Field
The invention relates to the technical field of industrial process control, in particular to a local self-organizing large-scale group dynamic target tracking method based on random noise.
Background
In recent years, the study of the group dynamics of complex systems is a current international hot issue. The cluster behaviors are ubiquitous in the nature and human society, such as aggregation, migration, bee crowding, synchronization, formation, target tracking and the like, and the complex and powerful cluster macroscopic behaviors which are developed in the task process that an individual is not easy to realize are completed through local perception and a relatively simple interaction mode.
In the field of large-scale complex system group dynamics, the group dynamic target tracking problem based on a local self-organization mechanism becomes more and more important. For example, in the field of unmanned aerial vehicle applications, when an unmanned aerial vehicle executes a target tracking task, the difficulty of task execution is greatly increased due to uncertainty of a target state and unknown diversity of targets. Moreover, in some scenarios, a single drone is not enough to complete a predetermined task, and multiple drones or even a cluster of drones are needed to work cooperatively. However, in real life, due to uncertainty of the target, a dynamic tracking path cannot be planned for each unmanned aerial vehicle, and therefore, it is necessary to research a dynamic target tracking method based on a local self-organized large-scale cluster.
For another example, in a workshop scheduling link of flexible manufacturing, in a global context, a large number of customer demand orders and a complex production environment are faced, and an effective scheduling optimization method must consider uncertain factors such as an emergency situation of the demand orders to ensure the robustness of a scheduling scheme (review on distributed workshop scheduling optimization algorithm [ J ] control and decision, 2016,31(01):1-11 ]). In addition, synergy with uncertain dynamics and even unknown objectives is also ubiquitous in large-scale complex systems of industrial production, economy, daily life, etc. (Liu Ruo Cheng, Li Jian Xia, Liu Jing, etc.. dynamic multiobjective optimization research reviews [ J ] computer reports 2020,43(07): 1246-.
In the field of population dynamics, when the problem of tracking dynamic, unknown or even uncertain targets is faced, the traditional control method is difficult to effectively solve, and is particularly applied to a self-organizing complex system. In the conventional synchronous control research process, because a specific global motion plan cannot be given to each individual to realize the expected group behaviors (Chutian Guangdong, Yangzhendong, Dunkui and the like, a plurality of problems [ J ] in group dynamics and coordination control research, 2010,27(1):86-93.), the natural phenomena of wild goose migration, ant colony nesting, fish foraging and the like in the nature are simulated, and the cluster intelligence of overall cooperation self-organization is developed through mutual cooperation and local information interaction among individuals. In the conventional Control method, graph theory is an important analysis tool (Ren W, W Beard, random. sensory cutting in multiagent systems under dynamic changing interaction protocols [ J ]. IEEE Transactions on Automatic Control,2005,50(5):655 and 661.) (Lin Z, Francis B, Maggiore M.Necessary and knowledge graphics Control for formatting Control [ J ]. IEEE Transactions on Automatic Control,2005,50(1):121 and 127.). Furthermore, with known fixed network topologies, containment Control is also becoming an effective method for studying group synchronization Control (Gu D B, Wang Z Y. leader-follower flooding: algorithms and experiments [ J ]. IEEE Transactions on Control Systems Technology,2009,17(5):1211 1219.) (ZHao C J, Lu A J, ZHang J Q. Pinning a complex ordered dynamic network to a homology projects [ J ]. IEEE Transactions on Circuits and Systems II: Briefs,2009,56(6): 514): 518.).
However, existing approaches mostly rely on obtaining global information of the network topology in advance. Also, in the current field of population dynamics target tracking, targets are often dynamically uncertain, even unknown. Therefore, how to overcome the limitation that the traditional method usually depends on the known global information and design an efficient dynamic target tracking method has been a difficult problem with high attention in the field of group dynamics of complex systems.
Disclosure of Invention
The invention aims to provide a local self-organizing large-scale group dynamic target tracking method based on random noise, and aims to solve the technical problem that incomplete information dynamic targets are difficult to track due to uncertainty and unknownness of environments and dynamic targets in the group dynamics field of complex systems.
To solve the above technical problem, an embodiment of the present invention provides the following solutions:
a local self-organizing large-scale group dynamic target tracking method based on random noise comprises the following steps:
constructing an HK model containing an uncertain dynamic target, and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing the uncertain dynamic target comprises the following steps: an HK model in which the dynamic target is perceived by only a part of individuals and an HK model in which the dynamic target independently exists;
aiming at the HK model of which the dynamic target is only sensed by partial individuals, tracking the dynamic target of incomplete information and verifying the dynamic target;
and tracking the dynamic target of incomplete information aiming at the HK model in which the dynamic target independently exists, and verifying.
Preferably, the constructing the HK model containing the uncertain dynamic objects comprises:
constructing an HK model with dynamic targets only perceived by part of individuals, comprising:
designing HK model self-organization rules with dynamic targets individually perceived by only system parts:
Figure BDA0002898964680000031
wherein
Figure BDA0002898964680000032
And is
A(t)＝A+Δ(t),|Δ(t)|＜Δ
In the formula: alpha is belonged to 0,1]Is the attraction strength of the dynamic target;
Figure BDA0002898964680000033
and | S | more than or equal to 1 is less than or equal to n and refers to an individual set containing a dynamic target; i is{·}Taking a value 1 or 0 according to whether the condition is satisfied or not as an indicative function;
Figure BDA0002898964680000034
a neighbor set of the agent i within a threshold range at the time t; where | is the absolute value of the cardinality or real number of the neighbor set; ε ∈ (0, 1)]Is a trust threshold among individuals in a group; a (t) epsilon [0,1]Is a dynamic target at time t, which fluctuates continuously within a range of Δ (t) of a fixed value A and satisfies Δ > 0;
self-organizing rules for HK model with dynamic targets perceived by only a fraction of individuals after random noise addition:
Figure BDA0002898964680000035
in the formula:
Figure BDA0002898964680000036
subject to [ - δ, δ]The above is even and distributed, and delta is more than 0;
constructing a dynamic target independent HK model, comprising:
aiming at the condition that the dynamic target independently exists in an unknown dynamic state, an unknown dynamic agent is introduced and the requirement is met
xΙ(t)≡A(t)＝A+Δ(t),t≥0
After random noise is added, the HK model self-organization rule of the dynamic target independent existence:
Figure BDA0002898964680000037
wherein
Figure BDA0002898964680000038
Preferably, the definition of spontaneous correspondence of the model given the presence of noise comprises:
and finally defining the system model to be consistent with the dynamic target:
Figure BDA0002898964680000041
then for
Figure BDA0002898964680000042
If there is
Figure BDA0002898964680000043
If true, the system is operated as
Figure BDA0002898964680000044
The precision is synchronized with A (t).
Preferably, the performing dynamic target tracking of incomplete information for the HK model in which the dynamic target is perceived by only a part of individuals and verifying includes:
define m ═ S | represents the number with dynamic target agent set and
Figure BDA0002898964680000045
Figure BDA0002898964680000046
Figure BDA0002898964680000047
and for t ≧ 0 has
Figure BDA0002898964680000048
Wherein: n, α, δ, ε are intrinsic parameters consistent with the HK model constructed;
Figure BDA0002898964680000049
representing the maximum distance between the individual in the target agent set and the dynamic target at the moment t;
Figure BDA00028989646800000410
representing the maximum distance between the individual in the non-target agent set and the dynamic target at the time t;
Figure BDA00028989646800000411
defining an upper limit of random noise intensity;
Figure BDA00028989646800000412
representing the accuracy of the system quasi-synchronization with the dynamic target; Δ is a conservative real number, and the allowed range depends entirely on the intrinsic parameters n, α, δ, ε of the system;
based on the HK model that the dynamic target is only sensed by partial individuals, aiming at the situation that the dynamic target is only sensed by partial individuals, the dynamic target tracking of incomplete information is carried out:
delta 'or more'1,δ′2,δ1,δ2,δ,
Figure BDA00028989646800000413
If so, then for any initial value x (0) ∈ [0,1 ]]n，ε∈(0,1]，δ∈(0,δ]And is and
Figure BDA00028989646800000414
the model will be as follows
Figure BDA00028989646800000415
Accurately tracking the dynamic target;
to verify the above, the following is introduced:
suppose { z i1,2, is an invariant sequence of real numbers, then for any integer s ≧ 0, the sequence
Figure BDA00028989646800000416
Monotonically non-decreasing or non-increasing with respect to k;
definition of
Figure BDA00028989646800000417
For 0 < alpha.ltoreq.1, if there is a finite time T, so that
Figure BDA00028989646800000418
Then for 0 < delta ≦δExistence of
Figure BDA00028989646800000419
Figure BDA00028989646800000420
δ1≤δ′1，δ2≤δ′2；
The specific demonstration process is as follows:
at time T:
Figure BDA00028989646800000421
then all agents are neighbors within the threshold range at time T, i.e.
Figure BDA00028989646800000422
Therefore, by the formula:
Figure BDA0002898964680000051
for 0 < alpha ≦ 1, if i ∈ S, then
Figure BDA0002898964680000052
To obtain
Figure BDA0002898964680000053
If it is
Figure BDA0002898964680000054
Then
Figure BDA0002898964680000055
To obtain
Figure BDA0002898964680000056
Therefore, when i ∈ S,
Figure BDA0002898964680000061
when in use
Figure BDA0002898964680000062
When the temperature of the water is higher than the set temperature,
Figure BDA0002898964680000063
continuing to demonstrate the following:
definition of
Figure BDA0002898964680000064
If it is
Figure BDA0002898964680000065
And
Figure BDA0002898964680000066
the conclusion is directly held by the incoming content, otherwise the following protocol is considered: for all
Figure BDA0002898964680000067
t＞0
Figure BDA0002898964680000068
When in use
Figure BDA0002898964680000069
The random noise takes positive value in the range
Figure BDA00028989646800000610
When in use
Figure BDA00028989646800000611
The random noise takes a negative value in the range
Figure BDA00028989646800000612
From the imported content and the constructed model, at least one of the following inequalities holds according to the above equation,
(iii)
Figure BDA00028989646800000613
(iv)
Figure BDA00028989646800000614
and at the same time carve
Figure BDA00028989646800000615
If true;
due to xii(t) obeys a uniform distribution [ - δ, + δ]Therefore, for all
Figure BDA00028989646800000616
t≥1：
Figure BDA00028989646800000617
With respect to the independent random noise, it is,
Figure BDA00028989646800000618
the probability of the occurrence of the above equation at the time when t is 1 is
Figure BDA00028989646800000619
Thus, it is possible to provide
Figure BDA00028989646800000620
Order to
Figure BDA00028989646800000621
Executing the above program L times to obtain
Figure BDA00028989646800000622
Thus, it is possible to provide
Figure BDA0002898964680000071
Defining events
E0＝Ω
Figure BDA0002898964680000072
x (0) is arbitrarily given, then for m ≧ 1 there is
Figure BDA0002898964680000073
According to the introduction, obtain
Figure BDA0002898964680000074
Thus, it is possible to provide
Figure BDA0002898964680000075
And finishing the verification.
Preferably, the performing dynamic target tracking of incomplete information for the HK model in which the dynamic target exists independently, and the verifying includes:
define β' ═ n + 2(Δ + δ),
Figure BDA0002898964680000076
based on the HK model in which the dynamic target independently exists, aiming at the dynamic target independently existing, the dynamic target tracking of incomplete information is carried out:
for any initial value x (0) is belonged to [0,1 ∈]n，ε∈(0,1]For all
Figure BDA0002898964680000077
The system realizes synchronization with a dynamic target A (t) with beta precision;
to verify the above, the following is introduced:
definition of
Figure BDA0002898964680000081
Assuming there is a finite time T ≧ 0, if
Figure BDA0002898964680000082
Then there are
Figure BDA0002898964680000083
And beta is less than or equal to beta';
the specific demonstration process is as follows:
at the time of the T-time, the time,
Figure BDA0002898964680000084
then all agents at time T are neighbors within the threshold range for
Figure BDA0002898964680000085
According to the following equation:
xΙ(t)≡A(t)＝A+Δ(t),t≥0
Figure BDA0002898964680000086
Figure BDA0002898964680000087
to obtain
Figure BDA0002898964680000088
And is
Figure BDA0002898964680000089
From the above, it is continued to prove that: for any initial value x (0) is belonged to [0,1 ∈]n，ε∈(0,1]For all
Figure BDA00028989646800000810
The system achieves synchronization with the dynamic target a (t) with β precision.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
(1) the method is improved on the basis of the traditional HK model, constructs the HK model which is based on a local self-organizing mechanism and contains uncertain dynamic targets, and provides two conditions of the dynamic targets. In consideration of the dynamic uncertainty of the target in the actual scene, the invention allows the dynamic target to move in an arbitrary unknown manner within a certain bounded area in the model.
(2) The invention designs a large-scale group dynamic target tracking method based on random noise. In the field of population dynamics, synchronous control of clusters is a challenging problem, especially in tracking synchronous control of dynamic targets in a self-organizing complex system. Aiming at the problem that the dynamic target is difficult to track due to uncertainty or even unknown of the environment and the dynamic target, the invention designs the large-scale group dynamic target tracking method based on random noise, overcomes the limitation that the traditional synchronous control method usually depends on preset global information, and provides a new thought for solving the problem of tracking the dynamic target in a complex self-organizing system.
(3) The invention provides an incomplete information dynamic target tracking method based on an HK model, and verification is carried out. The invention provides a dynamic target tracking realization process of incomplete information respectively aiming at two conditions that a dynamic target is only partially sensed by individuals and the dynamic target independently exists, provides feasibility analysis of the large-scale group dynamic target tracking method based on random noise, and solves the target tracking problem based on a local self-organization rule system. In addition, the invention further enriches the application of the noise control strategy and perfects the corresponding mathematical theory proof.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be 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 flowchart of a local self-organizing large-scale group dynamic target tracking method based on random noise according to an embodiment of the present invention;
fig. 2a and fig. 3a are schematic diagrams of models without noise, which let all agents perceive a dynamic target, i.e. m ═ S ═ n, and show that all individuals keep synchronization with the dynamic target;
fig. 2b and fig. 3b are schematic diagrams of letting some individuals perceive a dynamic target when the model does not contain noise, that is, 1 ≦ S ≦ n, and take m ≦ S ≦ n/2, which shows that an individual with only a perceptual dynamic target may keep synchronization with the dynamic target;
2c, 3c are schematic diagrams showing that even if some individuals in the system perceive the dynamic target, all individuals will eventually track the dynamic target and keep synchronization within a limited time when random noise exists;
FIGS. 2d, 3d are evolution diagrams redrawn by the "semilogarithmic" function of Matlab;
FIGS. 4a and 5a are schematic diagrams illustrating that when the system does not contain noise, a part of the system individuals cannot track the dynamic target, and the system generates several groups according to local rules;
4b and 5b are schematic diagrams of the system individuals finally and completely tracking the dynamic target and keeping quasi-synchronization with the dynamic target when noise exists;
fig. 4c, 5c are evolution diagrams redrawn by the "semilogarithmic" function of Matlab.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
In the current group dynamics target tracking field, a tracking target usually has uncertain factors such as dynamic and unknown factors, which causes difficulty in tracking the target in a complex system, while the existing method mostly depends on obtaining global information of network topology in advance, and has certain limitation when being applied to a self-organizing complex system.
In order to solve the above problem, an embodiment of the present invention provides a local self-organizing large-scale group dynamic target tracking method based on random noise, as shown in fig. 1, the method includes the following steps:
A. constructing an HK model containing an uncertain dynamic target, and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing the uncertain dynamic target comprises the following steps: an HK model in which the dynamic target is perceived by only a part of individuals and an HK model in which the dynamic target independently exists;
B. aiming at the HK model of which the dynamic target is only sensed by partial individuals, tracking the dynamic target of incomplete information and verifying the dynamic target;
C. and tracking the dynamic target of incomplete information aiming at the HK model in which the dynamic target independently exists, and verifying.
The invention provides a dynamic target tracking theory of incomplete information for solving the synchronous tracking problem caused by the variability and uncertainty of group dynamic targets in a large-scale complex system, and analyzes and verifies the feasibility of the method. Specifically, under the HK model containing uncertain dynamic targets, the system cannot track all the dynamic targets when the model does not contain noise. However, after adding random noise of a certain intensity into the model, the invention strictly analyzes mathematically that for any initial state, the system can track dynamic targets of incomplete information almost certainly within a limited time and keep synchronization with the change of the dynamic targets.
Further, the step A firstly improves the traditional HK model, constructs the HK model containing the uncertain dynamic targets, and respectively constructs the HK model with the dynamic targets individually perceived by only the system part and the HK model with the independent dynamic targets. Second, a definition of spontaneous coherence in the presence of noise is given.
The method comprises the following specific steps:
a1, constructing an HK model with a dynamic target which is only individually perceived by a system part.
In the field of large-scale clustering dynamics, control inputs, environmental effects, and special individuals play an indispensable role in intervening and regulating the overall movement of a population system, such as "leaders" in leaders-followers, giving certain specific individuals special rules and information to move the entire system in an intended manner. The uncertainty factor of the target is taken into account, allowing the target to move in an arbitrary unknown manner within a certain bounded area. Therefore, the HK model self-organization rule of which the dynamic target is only individually perceived by the system part is designed:
Figure BDA0002898964680000111
wherein
Figure BDA0002898964680000112
And is
A(t)＝A+Δ(t),|Δ(t)|＜Δ (3)
In the formula: alpha is belonged to 0,1]Is the attraction strength of the dynamic target;
Figure BDA0002898964680000113
and | S | more than or equal to 1 is less than or equal to n and refers to an individual set containing a dynamic target; i is{·}An indicative function, which takes a value of 1 or 0 according to whether the condition is satisfied;
Figure BDA0002898964680000114
a neighbor set of the agent i within a threshold range at the time t; here | can be the cardinality of the neighbor set or the absolute value of a real number; ε ∈ (0, 1)]Is a trust threshold among individuals in a group; a (t) epsilon [0,1]Is a dynamic target at time t, which fluctuates continuously over a range Δ (t) of a fixed value A and satisfies Δ > 0.
Considering today's internet age, ubiquitous free information flow affects everyone's view in a random manner, more or less, either positively or negatively. Therefore, unlike the HK model described by equation (1), some random noise should be added. When a part of system individuals are designed to sense the dynamic targets, the self-organization rule of the noise HK model containing the uncertain dynamic targets is as follows:
Figure BDA0002898964680000115
in the formula:
Figure BDA0002898964680000116
subject to [ - δ, δ]Is uniformly distributed, and satisfies delta > 0.
Step A2, constructing an HK model with a dynamic target independently existing
Aiming at the condition that the dynamic target independently exists in the condition of an unknown dynamic proxy, an unknown dynamic proxy is introduced and the requirement is met
xΙ(t)≡A(t)＝A+Δ(t),t≥0 (5)
Designing a self-organizing rule of a noise HK model containing uncertain dynamic targets when the dynamic targets exist independently:
Figure BDA0002898964680000121
wherein
Figure BDA0002898964680000122
Step A3, defining spontaneous consistency of the model when noise exists
And finally defining the system model to be consistent with the dynamic target due to the existence of the dynamic target and random noise.
Definition 1:
Figure BDA0002898964680000123
then for
Figure BDA0002898964680000124
If there is
Figure BDA0002898964680000125
If true, the system is operated as
Figure BDA0002898964680000126
The precision is synchronized with A (t).
Further, in the step B, aiming at the HK model in which the dynamic target is only partially sensed by the individual, the invention provides a dynamic target tracking theory of incomplete information and performs strict mathematical analysis. In particular, when the model is free of noise, the system cannot track the dynamic target in its entirety, and in the presence of random noise, the present invention strictly demonstrates that the system will track the dynamic target almost certainly and keep in synchronization with the changes of the dynamic target for a limited time. The proving process comprises the following specific steps:
step b1. define m ═ S | to denote the number with dynamic target agent set and
Figure BDA0002898964680000127
Figure BDA0002898964680000128
Figure BDA0002898964680000129
and for t ≧ 0 has
Figure BDA00028989646800001210
Wherein: n, α, δ, ε are intrinsic parameters consistent with the HK model constructed;
Figure BDA00028989646800001211
representing the maximum distance between the individual in the target agent set and the dynamic target at the moment t;
Figure BDA00028989646800001212
representing the maximum distance between the individual in the non-target agent set and the dynamic target at the time t;
Figure BDA00028989646800001213
defining an upper limit of random noise intensity;
Figure BDA00028989646800001214
representing the accuracy of the system quasi-synchronization with the dynamic target; delta is a conservative estimated real number and the allowed range depends entirely on the intrinsic parameters n, alpha, delta, epsilon of the system.
And B2, based on the HK model that the dynamic target is only sensed by partial individuals, aiming at the situation that the dynamic target is only sensed by partial individuals, providing a dynamic target tracking theory 1 of incomplete information:
theory 1: delta 'or more'1,δ′2,δ1,δ2,δ,
Figure BDA0002898964680000131
If so, then for any initial value x (0) e [0 ∈,1]n，ε∈(0,1]，δ∈(0,δ]And is and
Figure BDA0002898964680000132
the model will almost certainly be such that
Figure BDA0002898964680000133
And precisely tracking the dynamic target.
To prove the above theory, the following reasoning is required.
Introduction 1: suppose { z i1,2, is an invariant sequence of real numbers, then for any integer s ≧ 0, the sequence
Figure BDA0002898964680000134
Monotonically non-decreasing (non-increasing) with respect to k.
2, leading: definition of
Figure BDA0002898964680000135
For 0 < alpha.ltoreq.1, if there is a finite time T, so that
Figure BDA0002898964680000136
Then for 0 < delta ≦δExists almost certainly
Figure BDA0002898964680000137
δ1≤δ1′，δ2≤δ2′。
And B3, proving the theorem 2.
The proof of lemma 2 is as follows:
at time T, it can be seen that:
Figure BDA0002898964680000138
this means that all agents are neighbors within a threshold range at time T, i.e., time T
Figure BDA0002898964680000139
Figure BDA00028989646800001310
Thus, with respect to 0 < α ≦ 1, if i ∈ S, according to formula (4)
Figure BDA00028989646800001311
Can be derived from
Figure BDA00028989646800001312
If it is
Figure BDA00028989646800001313
Then
Figure BDA0002898964680000141
Can be derived from
Figure BDA0002898964680000142
Therefore, when i ∈ S,
Figure BDA0002898964680000143
when in use
Figure BDA0002898964680000144
When the temperature of the water is higher than the set temperature,
Figure BDA0002898964680000145
after the syndrome is confirmed.
Step B4. demonstrates that theory 1 as described, the process is as follows:
definition of
Figure BDA0002898964680000146
If it is
Figure BDA0002898964680000147
And
Figure BDA0002898964680000148
the conclusion is then directly held by lemma 2, otherwise the following protocol is considered: for all
Figure BDA0002898964680000149
t＞0
Figure BDA00028989646800001410
When in use
Figure BDA00028989646800001411
The random noise takes positive value in the range
Figure BDA00028989646800001412
When in use
Figure BDA00028989646800001413
The random noise takes a negative value in the range
Figure BDA00028989646800001414
Intuitively, in the presence of persistent random noise, the present invention aims to keep the individuals in the system approaching the dynamic target at time t + 1.
From theory 1 and the model, it can be seen that in equation (8), at least one of the following inequalities (i) or (ii) holds,
Figure BDA00028989646800001415
Figure BDA0002898964680000151
and at the same time carve
Figure BDA0002898964680000152
This is true.
Further, due to xii(t) obeys a uniform distribution [ - δ, + δ]Therefore, for all
Figure BDA0002898964680000153
t≥1
Figure BDA0002898964680000154
With respect to the independent random noise, it is,
Figure BDA0002898964680000155
the probability that equation (11) occurs at the time when t is 1 is given by
Figure BDA0002898964680000156
Thus, the following expressions (9) to (10) include
Figure BDA0002898964680000157
Order to
Figure BDA0002898964680000158
After executing the above-mentioned program L times, it can be known that
Figure BDA0002898964680000159
Therefore, it is not only easy to use
Figure BDA00028989646800001510
Defining events
Figure BDA00028989646800001511
Since x (0) is arbitrarily given, then for m ≧ 1, there is
Figure BDA00028989646800001512
From introduction 2, it is clear
Figure BDA00028989646800001513
Therefore, the following equations (15) to (16)
Figure BDA0002898964680000161
After the syndrome is confirmed.
Further, in the step C, aiming at the HK model in which the dynamic target independently exists, the invention provides a dynamic target tracking theorem of incomplete information and performs strict mathematical analysis. In particular, some agents in the system cannot track dynamic targets when the model is free of noise. Thus, the present invention will demonstrate that with the application of suitable random noise, the system can fully track dynamic objects. The proving process comprises the following specific steps:
step c1. define β' ═ n + 2(Δ + δ),
Figure BDA0002898964680000162
step C2. is based on HK model in which dynamic targets independently exist, and proposes a dynamic target tracking theory 2 of incomplete information when dynamic targets independently exist.
Theory 2: for any initial value x (0) is belonged to [0,1 ∈]n，ε∈(0,1]For all
Figure BDA0002898964680000163
Figure BDA0002898964680000164
The system will almost certainlySynchronization with the dynamic target a (t) is achieved with β precision.
The proof of theory 2 also lies in finding the synchronous region of the system under noise disturbance. The present invention achieves this object by the following lemma.
And 3, introduction: definition of
Figure BDA0002898964680000165
Assuming there is a finite time T ≧ 0, if
Figure BDA0002898964680000166
Then there are
Figure BDA0002898964680000167
And satisfies beta ≦ beta'.
Step C3. proves the following for lemma 3:
at time T, it is known
Figure BDA0002898964680000168
This means that all agents are neighbors within the threshold range at time T. For the
Figure BDA0002898964680000169
From the formulas (5) to (7)
Figure BDA0002898964680000171
And is
Figure BDA0002898964680000172
After the syndrome is confirmed.
And C4, proving the theory 2.
With the lemma 3, the invention firstly needs to design a noise protocol capable of driving the system to reach the dynamic target synchronization region, and then the lemma 3 is applied to prove that the system can finally track the dynamic target in a limited time. This process is similar to the process in step B4 and is omitted here.
In the simulation experiment, a large-scale complex system is taken as an application scene. For step B, take n-30, xi(0)，
Figure BDA0002898964680000173
In the interval [0,1]The internal random generation is performed, the confidence threshold epsilon between the system individuals is set to 0.1, the attraction strength alpha of the dynamic target is set to 0.5, m is 15, the random noise strength satisfies that delta is 0.02 and 0.2 epsilon, c is 0.05, and a is 0.8. First, assuming that the dynamic target Δ (t +1) is a periodic square wave pulse with an amplitude of ± 0.1, the conservative estimate of the present invention is 0.05 for Δ, i.e., | Δ (t +1) | ≦ Δ ≦ 0.05, as shown in fig. 2 a-2 d. Second, let the dynamic target Δ (t +1) be a non-periodic bounded function, except that c is 0.1, | Δ (t +1) | ≦ Δ ≦ 0.2, and other initial conditions remain unchanged. As shown in fig. 3 a-3 d.
In step C, when the dynamic target exists independently, let a be 0.5, first, let the dynamic target Δ (t +1) be a periodic sine wave function, and the noise intensity satisfy that δ be 0.01 to 0.1 ∈, and the other conditions are consistent with step B, as shown in fig. 4a to 4C. Secondly, a dynamic target delta (t +1) is set as a non-periodic triangular wave function, and the model evolution rule is shown in fig. 5 a-5 c.
Specifically, fig. 2(a) and fig. 3(a) show that the model has no noise, and all agents perceive the dynamic target, i.e., m ═ S ═ n, and the graph shows that all individuals keep synchronization with the dynamic target. Fig. 2(b) and fig. 3(b) show that when the model does not contain noise, part of individuals are allowed to perceive the dynamic target, i.e. 1 ≦ S ≦ n, and m ≦ S ≦ n/2, which indicates that only the individual perceiving the dynamic target can keep synchronization with the dynamic target. Fig. 2(c) and 3(c) show that when random noise exists, even if a part of the system individually perceives the dynamic target, all the individuals eventually track the dynamic target and keep synchronization in a limited time. Fig. 2(d), 3(d) are evolution diagrams redrawn by Matlab's "semilogarithmic" function. Fig. 4(a) and 5(a) show that when the system does not contain noise, part of the system individuals cannot track the dynamic target, and instead, the system generates several groups according to local rules. Fig. 4(b) and 5(b) show that when noise exists, the system individuals will eventually all track the dynamic target and keep quasi-synchronization with the dynamic target. Fig. 4(c), 5(c) are evolution diagrams redrawn by Matlab's "semilogarithmic" function.
Based on previous research, the invention further enriches the application of a control strategy based on noise and perfects the corresponding mathematical theory analysis. In addition, the invention provides a new strategy for solving the synchronous tracking problem caused by uncertainty such as dynamic diversity of group targets and even unknown in a large-scale complex system, and is favorable for providing a dynamic real-time tracking method suitable for a self-organizing system with local rules based on noise.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (5)

1. A local self-organizing large-scale group dynamic target tracking method based on random noise is characterized by comprising the following steps:
constructing an HK model containing an uncertain dynamic target, and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing the uncertain dynamic target comprises the following steps: an HK model in which the dynamic target is perceived by only a part of individuals and an HK model in which the dynamic target independently exists;
aiming at the HK model of which the dynamic target is only sensed by partial individuals, tracking the dynamic target of incomplete information and verifying the dynamic target;
and tracking the dynamic target of incomplete information aiming at the HK model in which the dynamic target independently exists, and verifying.
2. The method for tracking local self-organizing large-scale group dynamic targets based on random noise according to claim 1, wherein the constructing the HK model containing uncertain dynamic targets comprises the following steps:
constructing an HK model with dynamic targets only perceived by part of individuals, comprising:
designing HK model self-organization rules with dynamic targets individually perceived by only system parts:
Figure FDA0002898964670000011
wherein
Figure FDA0002898964670000012
And is
A(t)＝A+Δ(t),|Δ(t)|＜Δ
In the formula: alpha is belonged to 0,1]Is the attraction strength of the dynamic target;
Figure FDA0002898964670000016
and | S | more than or equal to 1 is less than or equal to n and refers to an individual set containing a dynamic target; i is{·}Taking a value 1 or 0 according to whether the condition is satisfied or not as an indicative function;
Figure FDA0002898964670000013
a neighbor set of the agent i within a threshold range at the time t; where | is the absolute value of the cardinality or real number of the neighbor set; ε ∈ (0, 1)]Is a trust threshold among individuals in a group; a (t) epsilon [0,1]Is a dynamic target at time t, which fluctuates continuously within a range of Δ (t) of a fixed value A and satisfies Δ > 0;
self-organizing rules for HK model with dynamic targets perceived by only a fraction of individuals after random noise addition:
Figure FDA0002898964670000014
in the formula:
Figure FDA0002898964670000015
subject to [ - δ, δ]The above is even and distributed, and delta is more than 0;
constructing a dynamic target independent HK model, comprising:
aiming at the condition that the dynamic target independently exists in an unknown dynamic state, an unknown dynamic agent is introduced and the requirement is met
xΙ(t)≡A(t)＝A+Δ(t),t≥0
After random noise is added, the HK model self-organization rule of the dynamic target independent existence:
Figure FDA0002898964670000021
wherein
Figure FDA0002898964670000022
3. The local self-organizing large-scale group dynamic target tracking method based on random noise according to claim 2, wherein the definition of spontaneous consistency of the model in the presence of the given noise comprises:
and finally defining the system model to be consistent with the dynamic target:
Figure FDA0002898964670000023
then for
Figure FDA0002898964670000024
If there is
Figure FDA0002898964670000025
If true, the system is operated as
Figure FDA0002898964670000026
The precision is synchronized with A (t).
4. The local self-organizing large-scale group dynamic target tracking method based on random noise according to claim 3, wherein the performing incomplete information dynamic target tracking and verification on the HK model of which the dynamic target is only perceived by partial individuals comprises:
define m ═ S | represents the number with dynamic target agent set and
Figure FDA0002898964670000027
Figure FDA0002898964670000028
Figure FDA0002898964670000029
and for t ≧ 0 has
Figure FDA00028989646700000210
Wherein: n, α, δ, ε are intrinsic parameters consistent with the HK model constructed;
Figure FDA00028989646700000211
representing the maximum distance between the individual in the target agent set and the dynamic target at the moment t;
Figure FDA00028989646700000212
representing the maximum distance between the individual in the non-target agent set and the dynamic target at the time t;
Figure FDA00028989646700000213
defining an upper limit of random noise intensity;
Figure FDA00028989646700000214
representing the accuracy of the system quasi-synchronization with the dynamic target; delta is a conservative estimateThe allowed range depends entirely on the intrinsic parameters n, α, δ, ε of the system;
based on the HK model that the dynamic target is only sensed by partial individuals, aiming at the situation that the dynamic target is only sensed by partial individuals, the dynamic target tracking of incomplete information is carried out:
if above delta1′,δ2′,δ1,δ2,δ,
Figure FDA0002898964670000031
If so, then for any initial value x (0) ∈ [0,1 ]]n，ε∈(0,1]，δ∈(0,δ]And is and
Figure FDA0002898964670000032
the model will be as follows
Figure FDA0002898964670000033
Accurately tracking the dynamic target;
to verify the above, the following is introduced:
suppose { zi1,2, is an invariant sequence of real numbers, then for any integer s ≧ 0, the sequence
Figure FDA0002898964670000034
Monotonically non-decreasing or non-increasing with respect to k;
definition of
Figure FDA0002898964670000035
For 0 < alpha.ltoreq.1, if there is a finite time T, so that
Figure FDA0002898964670000036
Then for 0 < δ ≦ δ, there is
Figure FDA0002898964670000037
Figure FDA0002898964670000038
δ1≤δ1′，δ2≤δ2′；
The specific demonstration process is as follows:
at time T:
Figure FDA0002898964670000039
then all agents are neighbors within the threshold range at time T, i.e.
Figure FDA00028989646700000310
Therefore, by the formula:
Figure FDA00028989646700000311
for 0 < alpha ≦ 1, if i ∈ S, then
Figure FDA00028989646700000312
To obtain
Figure FDA0002898964670000041
If it is
Figure FDA0002898964670000042
Then
Figure FDA0002898964670000043
To obtain
Figure FDA0002898964670000044
Therefore, when i ∈ S,
Figure FDA0002898964670000045
when in use
Figure FDA0002898964670000046
When the temperature of the water is higher than the set temperature,
Figure FDA0002898964670000047
continuing to demonstrate the following:
definition of
Figure FDA0002898964670000048
If it is
Figure FDA0002898964670000049
And
Figure FDA00028989646700000410
the conclusion is directly held by the incoming content, otherwise the following protocol is considered: for all
Figure FDA00028989646700000411
t＞0
Figure FDA00028989646700000412
When in use
Figure FDA00028989646700000413
The random noise takes positive value in the range
Figure FDA00028989646700000414
When in use
Figure FDA00028989646700000415
The random noise takes a negative value in the range
Figure FDA00028989646700000416
From the imported content and the constructed model, at least one of the following inequalities holds according to the above equation,
(i)
Figure FDA0002898964670000051
(ii)
Figure FDA0002898964670000052
and at the same time carve
Figure FDA0002898964670000053
If true;
due to xii(t) obeys a uniform distribution [ - δ, + δ]Therefore, for all
Figure FDA0002898964670000054
t≥1：
Figure FDA0002898964670000055
For independent random noise, { ξi(t), i ∈ V, t ≧ 1}, and the probability of occurrence of the above equation at the time when t ≧ 1 is
Figure FDA0002898964670000056
Thus, it is possible to provide
Figure FDA0002898964670000057
Order to
Figure FDA0002898964670000058
Executing the above program L times to obtain
Figure FDA0002898964670000059
Thus, it is possible to provide
Figure FDA00028989646700000510
Defining events
E0＝Ω
Figure FDA00028989646700000511
x (0) is arbitrarily given, then for m ≧ 1 there is
Figure FDA00028989646700000512
According to the introduction, obtain
Figure FDA00028989646700000513
Thus, it is possible to provide
Figure FDA0002898964670000061
And finishing the verification.
5. The method for tracking the local self-organizing large-scale group dynamic target based on the random noise according to claim 3, wherein the performing the dynamic target tracking of the incomplete information aiming at the HK model in which the dynamic target exists independently and performing the verification comprises:
define β' ═ n + 2(Δ + δ),
Figure FDA0002898964670000062
based on the HK model in which the dynamic target independently exists, aiming at the dynamic target independently existing, the dynamic target tracking of incomplete information is carried out:
for any initial value x (0) is belonged to [0,1 ∈]n，ε∈(0,1]For all
Figure FDA0002898964670000063
The system realizes synchronization with a dynamic target A (t) with beta precision;
to verify the above, the following is introduced:
definition of
Figure FDA0002898964670000064
Assuming there is a finite time T ≧ 0, if
Figure FDA0002898964670000065
Then there are
Figure FDA0002898964670000066
And beta is less than or equal to beta';
the specific demonstration process is as follows:
at the time of the T-time, the time,
Figure FDA0002898964670000067
then all agents at time T are neighbors within the threshold range for
Figure FDA0002898964670000068
According to the following equation:
xΙ(t)≡A(t)＝A+Δ(t),t≥0
Figure FDA0002898964670000069
Figure FDA00028989646700000610
to obtain
Figure FDA0002898964670000071
And is
Figure FDA0002898964670000072
From the above, it is continued to prove that: for any initial value x (0) is belonged to [0,1 ∈]n，ε∈(0,1]For all
Figure FDA0002898964670000073
The system achieves synchronization with the dynamic target a (t) with β precision.
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