CN112836356B - Random noise-based local self-organizing large-scale group dynamic target tracking method - Google Patents
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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 uncertain dynamic targets and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing uncertain dynamic targets comprises: the HK model with the dynamic target perceived by only part of individuals and the HK model with the dynamic target independently existing; aiming at the HK model of which the dynamic target is only perceived by partial individuals, carrying out dynamic target tracking of incomplete information and verifying; aiming at the HK model with the independent dynamic target, the dynamic target tracking of incomplete information is carried out, and verification is carried out. The invention enriches the application of the 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 synchronous tracking problem caused by uncertainty, even unknowns, of dynamic diversity and the like of group targets in a large-scale complex system.
Description
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, research on population dynamics of complex systems is a current international hot spot problem. Cluster behaviors are commonly found in nature and human society, such as aggregation, migration, beeping, synchronization, formation, target tracking and the like, and complex and powerful cluster macroscopic behaviors exhibited in the task process which is not easy to realize by an individual are completed through local perception and a relatively simple interaction mode.
In the field of large-scale complex system population dynamics, the problem of population dynamic target tracking based on local self-organizing weaving becomes more and more important. For example, in the field of unmanned aerial vehicle applications, when an unmanned aerial vehicle performs a target tracking task, the difficulty of task execution is greatly increased due to uncertainty of a target state and unknown diversity of a target. Also, in some scenarios, a single drone is insufficient to accomplish the intended task, requiring multiple drones or even a cluster of drones to work cooperatively. However, in real life, because of uncertainty of the target, a dynamic tracking path cannot be planned for each unmanned aerial vehicle, and thus, it is necessary to study a dynamic target tracking method based on a large-scale cluster of local self-organization.
In another example, in a shop scheduling link of flexible manufacturing, in a global context, a huge number of customer demand orders and complex production environments are faced, and an effective scheduling optimization method must consider uncertain factors such as emergency conditions of the demand orders to ensure the robustness of the scheduling scheme (Wang Ling, deng, wang Shengyao. Distributed shop scheduling optimization algorithm research review [ J ]. Control and decision, 2016,31 (01): 1-11.). In addition, synergy with dynamic uncertainty and even unknown goals is also prevalent in large-scale complex systems in industrial production, economy, daily life, etc. (Liu Rechen, li Jianxia, liu Jing, etc.. Summary of dynamic multi-objective optimization studies [ J ]. Computer science, 2020,43 (07): 1246-1278.), especially in systems involving large populations of people.
In the field of population dynamics, the traditional control method is difficult to effectively solve, especially in self-organizing complex systems, in the face of the problem of tracking dynamics, unknown or even uncertain targets. In the research process of the prior synchronous control, because each individual cannot be endowed with a specific global motion plan to realize expected group behaviors (Chu Tian guang, yang Zhengdong, deng Kuiying and the like, a plurality of problems [ J ] in group dynamics and coordination control research, control theory and application, 2010,27 (1): 86-93), natural phenomena of wild goose migration, ant colony nesting, fish foraging and the like in the nature are simulated, and the group intelligence of the whole cooperative self-organization is further developed through mutual cooperation and local information interaction among some individuals. In the traditional control method, graph theory is an important analysis tool (Ren W,W Beard,Randal.Consensus seeking in multiagent systems under dynamically changing interaction topologies[J].IEEE Transactions on Automatic Control,2005,50(5):655-661.)(Lin Z,Francis B,Maggiore M.Necessary and sufficient graphical conditions for formation control of unicycles[J].IEEE Transactions onAutomatic Control,2005,50(1):121-127.)., and in addition, under the known fixed network topology, the control of the drag is gradually an effective method for researching the group synchronization control (Gu D B,Wang Z Y.Leader-follower flocking: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 delayed dynamical network to a homogenous trajectory[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2009,56(6):514-518.).
However, most existing methods rely on obtaining global information of the network topology in advance. Also, in the current field of population dynamics target tracking, the target is often dynamically uncertain, even unknown. Therefore, how to overcome the limitation that the traditional method is often dependent on the known global information, and design an efficient dynamic target tracking method is always a problem of high attention in the field of complex system group dynamics.
Disclosure of Invention
The invention aims to provide a local self-organizing large-scale group dynamic target tracking method based on random noise, which aims to solve the technical problem that incomplete information dynamic targets are difficult to track due to uncertainty and unknowns of environments and dynamic targets in the field of complex system group dynamics.
In order to solve the technical problems, the embodiment of the invention provides the following scheme:
a local self-organizing large-scale group dynamic target tracking method based on random noise comprises the following steps:
constructing an HK model containing uncertain dynamic targets and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing uncertain dynamic targets comprises: the HK model with the dynamic target perceived by only part of individuals and the HK model with the dynamic target independently existing;
aiming at the HK model of which the dynamic target is only perceived by partial individuals, carrying out dynamic target tracking of incomplete information and verifying;
aiming at the HK model with the independent dynamic target, the dynamic target tracking of incomplete information is carried out, and verification is carried out.
Preferably, said constructing an HK model containing uncertain dynamic objects comprises:
Constructing an HK model with dynamic targets perceived by only partial individuals, wherein the HK model comprises the following steps:
the HK model self-organizing rule that the dynamic target is only perceived by the system part individuals is designed:
Wherein the method comprises the steps of
And
A(t)＝A+Δ(t),|Δ(t)|＜Δ
Wherein: alpha epsilon [0,1] is the attraction strength of the dynamic target; And 1 < S < n > refers to an individual set containing a dynamic target; i {·} is an indicative function, and takes a value of 1 or 0 according to whether a condition is satisfied; /(I) A neighbor set of the agent i within a threshold range of the moment t; where |·| is the cardinality of the neighbor set or the absolute value of the real number; epsilon (0, 1) is a trust threshold value among individuals in a group, A (t) epsilon [0,1] is a dynamic target at the moment t, and the dynamic target continuously fluctuates within the delta (t) range of a fixed value A and meets delta > 0;
After adding random noise, the dynamic targets are perceived only by partial individuals as self-organizing rules of the HK model:
Wherein: is subject to the uniform and distribution on [ -delta, delta ] and satisfies delta > 0;
constructing an HK model with independent dynamic targets, which comprises the following steps:
for the situation that the dynamic target exists independently in unknown dynamic, an unknown dynamic agent is introduced and meets the requirements of
xΙ(t)≡A(t)＝A+Δ(t),t≥0
After adding random noise, the HK model self-organizing rule with independent dynamic targets:
Wherein the method comprises the steps of
Preferably, the spontaneous consistency definition of the model in the presence of the given noise comprises:
defining the system model to be consistent with the dynamic target finally:
then for/> If there is/>If true, the system will/>The precision achieves synchronization with a (t).
Preferably, the performing dynamic target tracking of incomplete information on the HK model where the dynamic target is perceived by only a part of individuals, and performing verification includes:
definition m= |s| represents the sum of the number of agents with dynamic target
And has a value of t.gtoreq.0
Wherein: n, α, δ, ε are intrinsic parameters consistent with the constructed HK model; Representing the maximum distance between an individual in the target agent set and the dynamic target at the time t; /(I) Representing the maximum distance between the individual in the non-target agent set and the dynamic target at time t; /(I)Defining an upper limit of random noise intensity; /(I)Representing the accuracy of the quasi-synchronization of the system with the dynamic target; delta is a conservatively estimated real number, and the allowed range is entirely dependent on the intrinsic parameters n, alpha, delta, epsilon of the system;
Based on the HK model that the dynamic target is only perceived by partial individuals, aiming at the dynamic target tracking of incomplete information when the dynamic target is only perceived by partial individuals:
If delta' 1,δ′2,δ1,δ2, delta, Exists, then for any initial value x (0) ∈ [0,1] n, ε (0, 1], δ ε (0, δ), and/>The model will be expressed as/>Accurately tracking a dynamic target;
to verify the above, introduce:
Assuming { z i, i=1, 2,.. Monotonically not decreasing or not increasing with respect to k;
Definition of the definition For 0 < alpha.ltoreq.1, if there is a finite time T, so that/>Then for 0 < delta +.delta, there is/> δ1≤δ′1,δ2≤δ′2；
The specific proving process is as follows:
At time T:
then at time T all agents are neighbors within the threshold range, i.e Thus, by the formula:
For 0 < alpha.ltoreq.1, if i.epsilon.S, then
Deriving
If it isThen
Deriving
Thus, when i.epsilon.S,
When (when)In the time-course of which the first and second contact surfaces,
The continued demonstration is as follows:
Definition of the definition If/>And/>The conclusion is directly established by the incoming content, otherwise, consider the following protocol: for all/>t＞0
When (when)When the random noise takes a positive value, the range is/>When/>When the random noise takes a negative value, the range is/>
From the introduction and the model constructed, according to the above equation, at least one of the following inequalities holds,
(iii)
(iv)
And at the same time haveEstablishment;
Since ζ i (t) obeys a uniform distribution [ -delta, +delta ], for all t≥1：
In the case of independent random noise,The probability of occurrence of the above equation at time t=1 is/>Thus (2)
Order theThe above procedure was performed L times to obtain/>Thus (2)
Defining events
E0＝Ω
X (0) is arbitrarily given, then there is a value for m.gtoreq.1
From the incoming content, get
Thus (2)
And (5) finishing verification.
Preferably, the performing dynamic target tracking of incomplete information for the HK model with independent dynamic target, and performing verification includes:
Define beta' = (n+2) (delta+delta),
Based on the HK model with independent dynamic targets, aiming at the condition that the dynamic targets exist independently, the dynamic target tracking of incomplete information is carried out:
For any initial value x (0) ∈ [0,1] n, ε (0, 1], for all The system realizes synchronization with the dynamic target A (t) with beta precision;
to verify the above, introduce:
Definition of the definition Assuming that the finite time T is not less than 0, if/>Then there isAnd satisfies beta < beta';
The specific proving process is as follows:
At the time instant T,
Then at time T all agents are neighbors within the threshold range forAccording to the following formula:
xΙ(t)≡A(t)＝A+Δ(t),t≥0
Obtaining
And
Continuing to prove according to the above: for any initial value x (0) ∈ [0,1] n, ε (0, 1], for allThe system achieves synchronization with the dynamic target a (t) with beta precision.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
(1) The invention improves on the basis of the traditional HK model, builds the HK model based on local self-organizing loom system and comprises uncertain dynamic targets, and provides two conditions of the dynamic targets. The invention allows the dynamic target to move in any unknown manner in a certain limited area in the model in consideration of the dynamic uncertainty of the target in the actual scene.
(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 self-organizing complex systems, tracking synchronous control of dynamic targets. Aiming at the problem of difficult tracking of a dynamic target caused by uncertainty and even unknowness of an environment and the dynamic target, the invention designs a large-scale group dynamic target tracking method based on random noise, overcomes the limitation that the traditional synchronous control method often 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. Aiming at two situations that a dynamic target is only perceived by partial individuals and the dynamic target exists independently, the invention provides a dynamic target tracking realization process of incomplete information, 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-organizing rule system. In addition, the invention further enriches the application of the noise control strategy and perfects the corresponding mathematical theory evidence.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a local self-organizing large-scale group dynamic target tracking method based on random noise provided by an embodiment of the invention;
fig. 2a, 3a are schematic diagrams of a model without noise, where all agents perceive a dynamic target, i.e. m= |s|=n, which indicates that all individuals remain synchronized with the dynamic target;
2b and 3b are schematic diagrams of making partial individuals perceive a dynamic target when the model does not contain noise, namely 1 is less than or equal to |S| < n, and taking m= |S|=n/2, wherein the diagrams show that only the individuals perceiving the dynamic target can keep synchronous with the dynamic target;
FIGS. 2c and 3c are diagrams showing that in the presence of random noise, even if some individuals of the system perceive a dynamic target, all individuals will eventually track the dynamic target and maintain synchronization for a finite period of time;
FIGS. 2d, 3d are diagrams of the evolution redrawn by the "half-log" function of Matlab;
FIGS. 4a and 5a are diagrams showing the system being able to track dynamic objects by some individuals when the system is free of noise, and the system will generate several groupings according to local rules;
FIGS. 4b and 5b are schematic diagrams of the system individual eventually tracking the dynamic target entirely and maintaining quasi-synchronization with the dynamic target in the presence of noise;
Fig. 4c, 5c are evolution diagrams redrawn by the "semilogarithmic" function of Matlab.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
In the current population dynamics target tracking field, the tracked target usually has uncertain factors such as dynamic and unknown factors, so that the target is difficult to track in a complex system, and the existing method mostly depends on obtaining global information of network topology in advance, and has a certain limitation in application to self-organizing complex systems.
To solve the above problems, an embodiment of the present invention provides a local self-organizing large-scale population 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 uncertain dynamic targets and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing uncertain dynamic targets comprises: the HK model with the dynamic target perceived by only part of individuals and the HK model with the dynamic target independently existing;
B. Aiming at the HK model of which the dynamic target is only perceived by partial individuals, carrying out dynamic target tracking of incomplete information and verifying;
C. Aiming at the HK model with the independent dynamic target, the dynamic target tracking of incomplete information is carried out, and verification is carried out.
The invention provides a dynamic target tracking theory of incomplete information for solving the synchronous tracking problem caused by the variability and uncertainty of a group dynamic target in a large-scale complex system, and analyzes and verifies the feasibility of the method. Specifically, under HK models that contain uncertain dynamic targets, the system cannot track all dynamic targets when the model is free of noise. However, after adding a certain intensity of random noise to the model, the invention mathematically analyzes strictly that for any initial state, the system can almost certainly track the dynamic target of incomplete information in a limited time and stay synchronized with the change of the dynamic target.
Further, in the step A, firstly, the traditional HK model is improved, the HK model containing uncertain dynamic targets is constructed, and the HK model with the dynamic targets perceived by only a part of individuals in the system and the HK model with the dynamic targets independently existing are respectively constructed. Second, a spontaneous consistency definition of the presence of noise is given.
The method comprises the following specific steps:
Step A1. Constructing an HK model with dynamic targets perceived by only some individuals of the system.
In the field of large-scale cluster dynamics, control inputs, environmental effects, and special individuals play an indispensable role in intervening and adjusting the overall motion of a population system, such as "leaders" in leader-follower, giving certain specific individuals special rules and information to move the overall system in a desired manner. Taking into account the uncertainty factors of the target, the target is allowed to move in an arbitrary unknown manner within a bounded area. Thus, HK model ad hoc rules are designed where dynamic targets are perceived only by the system part individuals:
Wherein the method comprises the steps of
And
A(t)＝A+Δ(t),|Δ(t)|＜Δ (3)
Wherein: alpha epsilon [0,1] is the attraction strength of the dynamic target; and 1 < S < n > refers to an individual set containing a dynamic target; i {·} denotes a sexual function, and takes on a value of 1 or 0 according to whether the condition is satisfied; /(I) A neighbor set of the agent i within a threshold range of the moment t; here |·| can be the cardinality of the neighbor set or the absolute value of a real number; epsilon (0, 1) is a trust threshold value among individuals in the group, A (t) epsilon [0,1] is a dynamic target at the moment t, and the dynamic target continuously fluctuates within the range of delta (t) of a fixed value A and meets delta > 0.
Considering the internet age today, the ubiquitous free stream of information affects everyone's view in a random way, either more or less, positive or negative. Therefore, unlike the HK model of formula (1), some random noise should be added. When the system part individuals are designed to perceive the dynamic target, the self-organizing rule of the noise HK model containing the uncertain dynamic target is as follows:
Wherein: Is subject to the uniform and distribution on [ -delta, delta ] and satisfies delta > 0.
A2, constructing an HK model with independent dynamic targets
For the situation that the dynamic target exists independently in the case of an unknown dynamic agent, the unknown dynamic agent is introduced and the requirement is met
xΙ(t)≡A(t)＝A+Δ(t),t≥0 (5)
When the design dynamic target exists independently, the self-organizing rule of the noise HK model containing the uncertain dynamic target:
Wherein the method comprises the steps of
Step A3 defining the spontaneous consistency of the model in the presence of noise
Due to the existence of the dynamic target and random noise, the system model is finally defined to be consistent with the dynamic target.
Definition 1: then for/> If there is/>If true, the system will/>The precision achieves synchronization with a (t).
Further, in the step B, aiming at the HK model that the dynamic target is only perceived by partial individuals, the invention provides a dynamic target tracking theory of incomplete information and performs strict mathematical analysis. In particular, when the model is noise-free, the system cannot track all dynamic targets, and in the presence of random noise, the invention strictly proves that the system will track dynamic targets almost certainly for a limited time, and stay synchronized with the changes in dynamic targets. The specific steps of the proving process are as follows:
Step b1 defining m= |s| to represent the sum of the number of sets with dynamic target agents
And has a value of t.gtoreq.0
Wherein: n, α, δ, ε are intrinsic parameters consistent with the constructed HK model; Representing the maximum distance between an individual in the target agent set and the dynamic target at the time t; /(I) Representing the maximum distance between the individual in the non-target agent set and the dynamic target at time t; /(I)Defining an upper limit of random noise intensity; /(I)Representing the accuracy of the quasi-synchronization of the system with the dynamic target; delta is a conservatively estimated real number, and the allowed range is entirely dependent on the intrinsic parameters n, alpha, delta, epsilon of the system.
Step B2, based on an HK model that the dynamic target is only perceived by partial individuals, aiming at the situation that the dynamic target is only perceived by partial individuals, a dynamic target tracking theory 1 of incomplete information is provided:
theory 1: if delta' 1,δ′2,δ1,δ2, delta, Exists, then for any initial value x (0) ∈ [0,1] n, ε (0, 1], δ ε (0, δ), and/>The model will almost certainly be in/>The accuracy tracks the dynamic target.
To demonstrate the theory above, the following quotation is required.
Lemma 1: assuming { z i, i=1, 2,..Monotonically not decreasing (not increasing) with respect to k.
And (4) lemma 2: definition of the definitionFor 0 < alpha.ltoreq.1, if there is a finite time T, so that/>Then for 0 < delta, almost certainly there isδ1≤δ1′,δ2≤δ2′。
And B3, proving the primer 2.
The demonstration of lemma 2 is as follows:
At time T, it can be seen that:
This means that at time T all agents are neighbors within the threshold, i.e Thus, for 0 < α.ltoreq.1, if i ε S, then
It can be derived that
If it isThen
/>
It can be derived that
Therefore, when i.epsilon.S,
When (when)In the time-course of which the first and second contact surfaces,
The syndrome is known.
Step B4. demonstrates the theory 1 as follows:
Definition of the definition If/>And/>The conclusion is directly established by the quotation 2, otherwise, the following protocol is considered: for all/>t＞0
When (when)When the random noise takes a positive value, the range is/>When/>When the random noise takes a negative value, the range is/>Intuitively, the invention aims to enable an individual in a system to continuously approach a dynamic target at the time t+1 when continuous random noise exists.
From theory 1 and the model, it is known that at least one of the following inequalities (i) or (ii) holds under formula (8),
And at the same time haveThis is true.
Further, since ζ i (t) follows a uniform distribution [ - δ, +δ ], allt≥1
/>
In the case of independent random noise,The probability of occurrence of formula (11) at time t=1 is/>Therefore, the formula (9) to formula (10) include
Order theThe above procedure was performed L times, and it was found that/>So that
Defining events
Since x (0) is arbitrarily given, there is a value for m.gtoreq.1 by formula (13)
From the quotation 2, it can be seen that
Therefore, the formula (15) to formula (16)
The syndrome is known.
Further, in the step C, aiming at the HK model with the independent dynamic target, the invention provides the dynamic target tracking theorem of incomplete information and performs strict mathematical analysis. In particular, when the model is noise free, some agents in the system cannot track dynamic targets. Thus, the present invention will demonstrate that the system can track dynamic targets completely, with the application of appropriate random noise. The specific steps of the proving process are as follows:
Step c1. Define beta' = (n+2) (delta+delta),
Step C2. proposes a dynamic target tracking theory 2 of incomplete information aiming at the condition that the dynamic target exists independently based on the HK model of the dynamic target exists independently.
Theory 2: for any initial value x (0) ∈ [0,1] n, ε (0, 1], for all The system will almost certainly achieve synchronization with the dynamic target a (t) with beta precision.
The key to proof of theory 2 is also to find the synchronization area of the system under noise disturbance. The present invention achieves this object by the following quotation.
And (3) lemma 3: definition of the definitionAssuming that the finite time T is not less than 0, if/>Then there is/>And satisfies beta < beta'.
Step C3. demonstrates the lemma 3 as follows:
At time T, it can be seen that This means that at time T all agents are neighbors within the threshold range. For/>From the formulae (5) to (7)
And
The syndrome is known.
Step c4. Proof of said theory 2.
With the primer 3, the invention firstly needs to design a noise protocol capable of driving the system to reach the synchronous region of the dynamic target, and then the primer 3 is applied to prove that the system can track the dynamic target in a limited time finally. This process is similar to that in step B4, and is omitted here.
In the simulation experiment, a large-scale complex system is used as an application scene. For step B, take n=30, x i (0),Randomly generating in the interval [0,1], setting trust threshold epsilon between system individuals to be 0.1, setting attraction strength alpha of a dynamic target to be 0.5, m=15, enabling random noise strength to meet delta=0.02=0.2 epsilon, and setting c=0.05 and A=0.8. Let the dynamic target delta (t+1) be a periodic square wave pulse with an amplitude of + -0.1, for delta, the conservative estimate of the invention is 0.05, i.e., |delta (t+1) |less than or equal to delta=0.05, as shown in fig. 2 a-2 d. Second, let the dynamic target Δ (t+1) be an aperiodic bounded function, except that c=0.1, |Δ (t+1) |++Δ=0.2, other initial conditions remain unchanged. As shown in fig. 3 a-3 d.
For step C, when the dynamic object exists independently, let a=0.5, first let the dynamic object Δ (t+1) be a periodic sine wave function, the noise intensity satisfies δ=0.01=0.1 ε, and other conditions remain the same as step B, as shown in fig. 4 a-4C. Next, let the dynamic target Δ (t+1) be the aperiodic triangular wave function, and the model evolution rules are shown in fig. 5 a-5 c.
Specifically, fig. 2 (a) and fig. 3 (a) show that the model is free of noise, so that all agents perceive the dynamic target, i.e., m= |s|=n, and all individuals are kept synchronous with the dynamic target. When the models in fig. 2 (b) and fig. 3 (b) are free of noise, part of individuals are enabled to perceive the dynamic target, namely 1 is less than or equal to |S| < n, m= |S|=n/2 is taken, and the images show that only the individuals perceiving the dynamic target can keep synchronous with the dynamic target. Fig. 2 (c) and 3 (c) show that in the presence of random noise, even if some individuals of the system perceive a dynamic target, all individuals will eventually track the dynamic target and remain synchronized for a limited period of time. Fig. 2 (d), 3 (d) are evolution diagrams redrawn by the "half-log" function of Matlab. Fig. 4 (a), 5 (a) show that when the system is noise free, some individuals of the system cannot track the dynamic target, but rather the system will generate several packets according to local rules. Fig. 4 (b) and fig. 5 (b) show that in the presence of noise, the individual system will eventually track the dynamic target entirely and maintain quasi-synchronization with the dynamic target. Fig. 4 (c), 5 (c) are evolution diagrams redrawn by the "half-log" function of Matlab.
The invention is based on previous researches, further enriches the application of control strategies 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 variability of group targets and even unknowns in a large-scale complex system, and is helpful for providing a dynamic real-time tracking method suitable for noise-based self-organizing systems with local rules.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (1)
1. The local self-organizing large-scale group dynamic target tracking method based on random noise, wherein the large-scale group dynamic target comprises an unmanned aerial vehicle cluster, and is characterized by comprising the following steps of:
constructing an HK model containing uncertain dynamic targets and giving a spontaneous consistency definition of the model in the presence of noise, wherein the HK model containing uncertain dynamic targets comprises: the HK model with the dynamic target perceived by only part of individuals and the HK model with the dynamic target independently existing;
aiming at the HK model of which the dynamic target is only perceived by partial individuals, carrying out dynamic target tracking of incomplete information and verifying;
aiming at the HK model with the independent dynamic target, the dynamic target tracking of incomplete information is carried out, and verification is carried out;
Wherein, the constructing the HK model with uncertain dynamic targets comprises the following steps:
Constructing an HK model with dynamic targets perceived by only partial individuals, wherein the HK model comprises the following steps:
the HK model self-organizing rule that the dynamic target is only perceived by the system part individuals is designed:
Wherein the method comprises the steps of
And
A(t)＝A+Δ(t),|Δ(t)|＜Δ
Wherein: alpha epsilon [0,1] is the attraction strength of the dynamic target; And 1 < S < n > refers to an individual set containing a dynamic target; i {·} is an indicative function, and takes a value of 1 or 0 according to whether a condition is satisfied; /(I) A neighbor set of the agent i within a threshold range of the moment t; where |·| is the cardinality of the neighbor set or the absolute value of the real number; epsilon (0, 1) is a trust threshold value among individuals in a group, A (t) epsilon [0,1] is a dynamic target at the moment t, and the dynamic target continuously fluctuates within the delta (t) range of a fixed value A and meets delta > 0;
After adding random noise, the dynamic targets are perceived only by partial individuals as self-organizing rules of the HK model:
Wherein: is subject to the uniform and distribution on [ -delta, delta ] and satisfies delta > 0;
constructing an HK model with independent dynamic targets, which comprises the following steps:
for the situation that the dynamic target exists independently in unknown dynamic, an unknown dynamic agent is introduced and meets the requirements of
xΙ(t)≡A(t)＝A+Δ(t),t≥0
After adding random noise, the HK model self-organizing rule with independent dynamic targets:
Wherein the method comprises the steps of
Wherein the spontaneous consistency definition of the model in the presence of the given noise comprises:
defining the system model to be consistent with the dynamic target finally:
then for/> If there is/>If true, the system will/>Synchronization with A (t) is achieved with precision;
wherein, the performing dynamic target tracking of incomplete information and verifying the HK model, which is perceived by only a part of individuals, comprises:
definition m= |s| represents the sum of the number of agents with dynamic target
And has a value of t.gtoreq.0
Wherein: n, α, δ, ε are intrinsic parameters consistent with the constructed HK model; Representing the maximum distance between an individual in the target agent set and the dynamic target at the time t; /(I) Representing the maximum distance between the individual in the non-target agent set and the dynamic target at time t; /(I)Defining an upper limit of random noise intensity; delta is a conservatively estimated real number, and the allowed range is entirely dependent on the intrinsic parameters n, alpha, delta, epsilon of the system;
Based on the HK model that the dynamic target is only perceived by partial individuals, aiming at the dynamic target tracking of incomplete information when the dynamic target is only perceived by partial individuals:
If the above, delta 1′,δ2′,δ1,δ2, delta, Exists, then for any initial value x (0) ∈ [0,1] n, ε (0, 1], δ ε (0, δ), and/>The model will be expressed as/>Accurately tracking a dynamic target;
to verify the above, introduce:
Assuming { z i, i=1, 2,.. Monotonically not decreasing or not increasing with respect to k;
Definition of the definition For 0 < alpha.ltoreq.1, if there is a finite time T, so that/>Then for 0 < delta +.delta, there is/>δ1≤δ1′,δ2≤δ2′；
The specific proving process is as follows:
At time T:
then at time T all agents are neighbors within the threshold range, i.e Thus, by the formula:
For 0 < alpha.ltoreq.1, if i.epsilon.S, then
Deriving
If it isThen
Deriving
Thus, when i.epsilon.S,
When (when)In the time-course of which the first and second contact surfaces,
The continued demonstration is as follows:
Definition of the definition If/>And/>The conclusion is directly established by the incoming content, otherwise, consider the following protocol: for all/>
When (when)When the random noise takes a positive value, the range is/>When/>When the random noise takes a negative value, the range is/>
From the introduction and the model constructed, according to the above equation, at least one of the following inequalities holds,
(i)
(ii)
And at the same time haveEstablishment;
Since ζ i (t) obeys a uniform distribution [ -delta, +delta ], for all
In the case of independent random noise,The probability of occurrence of the above equation at time t=1 is/>Thus (2)
Order theExecuting the above formula L times to obtain/>Thus (2)
Defining events
E0＝Ω
X (0) is arbitrarily given, then there is a value for m.gtoreq.1
From the incoming content, get
Thus (2)
After verification is finished;
Wherein, the performing dynamic target tracking of incomplete information and verifying the HK model which exists independently for the dynamic target comprises:
Define beta' = (n+2) (delta+delta),
Based on the HK model with independent dynamic targets, aiming at the condition that the dynamic targets exist independently, the dynamic target tracking of incomplete information is carried out:
For any initial value x (0) ∈ [0,1] n, ε (0, 1], for all The system realizes synchronization with the dynamic target A (t) with beta precision;
to verify the above, introduce:
Definition of the definition Assuming that the finite time T is not less than 0, if/>Then there isAnd satisfies beta < beta';
The specific proving process is as follows:
At the time instant T,
Then at time T all agents are neighbors within the threshold range forAccording to the following formula:
xΙ(t)≡A(t)＝A+Δ(t),t≥0
Obtaining
And
Continuing to prove according to the above: for any initial value x (0) ∈ [0,1] n, ε (0, 1], for all The system achieves synchronization with the dynamic target a (t) with beta precision.
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