CN113301562A - Second-order multi-autonomous system differential privacy convergence method and system for quantitative communication - Google Patents

Second-order multi-autonomous system differential privacy convergence method and system for quantitative communication Download PDF

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CN113301562A
CN113301562A CN202110553710.7A CN202110553710A CN113301562A CN 113301562 A CN113301562 A CN 113301562A CN 202110553710 A CN202110553710 A CN 202110553710A CN 113301562 A CN113301562 A CN 113301562A
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王炳昌
张文君
梁勇
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Abstract

The invention belongs to the field of multi-autonomous-body communication, and provides a quantized differential privacy convergence method and system of a second-order multi-autonomous-body system. The method comprises the steps that respective main bodies respectively generate Laplace noise with known parameters according to the updating state of a differential privacy convergence network, and the Laplace noise is added to a position state to serve as observable position information; each main body quantizes the observable position information to obtain an integer value and transmits the integer value to other main bodies which construct communication channels with the current main body; each main body receives the integer value from the communication channel and decodes the integer value to obtain the state estimation of other main bodies; and each main body designs control strategy information according to the obtained state estimation, updates the control strategy information to a differential privacy convergence network, judges whether the position states of all the main bodies meet a set threshold condition, if so, indicates that a convergence task is realized, otherwise, each main body continuously updates the state until the convergence task is realized.

Description

Second-order multi-autonomous system differential privacy convergence method and system for quantitative communication
Technical Field
The invention belongs to the field of multi-autonomous-body communication, and particularly relates to a quantized differential privacy convergence method and system of a second-order multi-autonomous-body system.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The multi-autonomous-body distributed convergence problem has wide application in engineering, military and other aspects, such as: each unmanned aerial vehicle in the unmanned aerial vehicle formation takes off from different places and cooperatively completes a certain task; each vehicle in the fleet of vehicles tracks a particular target. With more and more importance placed on the privacy protection problem, when a self-body system needs to protect privacy information (for example, unmanned aerial vehicle formation does not want to reveal information of takeoff places; vehicle formation does not want to reveal position tracks), the existing method cannot meet the requirement. Therefore, it is urgent and meaningful to design a multi-autonomous distributed convergence method that satisfies the privacy protection function.
In the current application of the multi-autonomous-body convergence problem, most methods assume that the accurate state information of an autonomous body can be transmitted to other autonomous bodies constructing communication channels with the autonomous body, and then share the respective state information on the basis of the accurate state information to complete the convergence task. However, the inventor found that in practical engineering applications, the state information of the self-body tends to have high accuracy, but since the capacity of the communication channel is limited, it is impractical to transmit accurate state information, and even if accuracy is lost, the state information of the self-body may require the capacity of the communication channel to be large enough because of a large difference range.
Disclosure of Invention
In order to solve the technical problems in the background art, the present invention provides a quantized difference privacy convergence method and system for a second-order multi-autonomous system, which is suitable for considering the situation that an autonomous system has privacy protection requirements and the capacity of a communication channel is limited, and enables the respective entities to transmit quantized integer values under the condition that the capacity of the communication channel is limited by a dynamic coding and decoding scheme while protecting the privacy of the autonomous location information.
In order to achieve the purpose, the invention adopts the following technical scheme:
a first aspect of the invention provides a quantized second-order multi-autonomous system differential privacy convergence method.
A quantized second-order multi-autonomous system differential privacy convergence method, comprising:
respectively generating Laplace noise with known parameters by respective main bodies according to the updating state of the differential privacy convergence network, and adding the Laplace noise on the position state as observable position information;
each main body quantizes the observable position information to obtain an integer value and transmits the integer value to other main bodies which construct communication channels with the current main body;
each main body receives the integer value from the communication channel and decodes the integer value to obtain the state estimation of other main bodies;
and each main body designs control strategy information according to the obtained state estimation, updates the control strategy information to a differential privacy convergence network, judges whether the position states of all the main bodies meet a set threshold condition, if so, indicates that a convergence task is realized, otherwise, each main body continuously updates the state until the convergence task is realized.
As an embodiment, the state of the respective body includes a position state and a velocity state.
As an embodiment, the differential privacy convergence network is:
xi(t+1)＝xi(t)+vi(t)+siηi(t)
vi(t+1)＝vi(t)+ui(t)
wherein xi(t)，vi(t)，ui(t) the position state, speed state and control strategy of the ith autonomous body at the time t, siIs a constant parameter, η, of the differential privacy algorithmi(t) is the noise generated by the ith autonomous body at time t for implementing the differential privacy algorithm.
As an embodiment, the probability distribution of the laplacian noise is subject to the expectation of 0, and the variance ciqi tWherein c isiAnd q isiT represents the time t, being a known parameter.
As an embodiment, the threshold condition is: the position states of any two self-bodies at the same time are not more than a set constant.
As an embodiment, before the respective agent quantizes the observable positional information, the method further includes:
and judging whether the input exceeds the upper limit of the quantizer memory of the respective main body, and if so, regenerating Laplace noise with known parameters.
As an embodiment, the quantizer has a level of 2K +1, where K is a predetermined constant, no information is sent when the quantizer output is 0, and the required memory size corresponding to the quantizer is 2K +1
Figure BDA0003076303330000038
A bit.
In one embodiment, the jth autonomous receives the quantized integer value ζ from the i transmission at time T +1i(t +1) is:
Figure BDA0003076303330000031
wherein
Figure BDA0003076303330000032
Figure BDA0003076303330000033
Respectively representing the position state and the speed state of the ith autonomous body at the t moment by the quantizer; g (t) ═ g0γt，0<γ<1 is an exponential function that decays with time; thetai(t +1) is a substitute value for the position state at time t + 1. Thetai(t+1)＝xi(t+1)+ηi(t +1), position state plus a Laplace variableThe sum of arrival serves as a surrogate value for the position status.
As an embodiment, the control policy information is:
Figure BDA0003076303330000034
wherein k is1，k2Is a proportionality coefficient ofijIs the communication weight between the entities i and j,
Figure BDA0003076303330000035
representing an estimate of the position of autonomous body j to autonomous body i,
Figure BDA0003076303330000036
representing an estimate of the position of the subject from i,
Figure BDA0003076303330000037
an estimate of the velocity from subject j to subject i,
Figure BDA0003076303330000041
representing an estimate of the speed of the subject i relative to his own.
A second aspect of the invention provides a quantized second-order multi-autonomous system.
A quantized second-order multi-autonomous system comprises a plurality of autonomous bodies which are communicated with each other, wherein the autonomous bodies adopt the second-order multi-autonomous system to communicate through quantized integer values and realize convergence tasks.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method is suitable for a second-order multi-autonomous-body convergence task with privacy protection requirements of the autonomous body and limited communication channels, and a differential privacy mechanism and a quantitative communication strategy are used, so that the autonomous-body system can protect initial position information and a current state track of the autonomous body while completing the convergence task by only using position information to carry out quantitative communication.
(2) The invention realizes the distributed convergence task by transmitting quantized integer values under the condition that the capacity of a communication channel of each main body is limited through a dynamic coding and decoding scheme while protecting the privacy of the position information of the main body.
Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.
FIG. 1 is a flow chart of a second-order multi-autonomous system differential privacy convergence method for quantitative communication according to an embodiment of the present invention;
FIG. 2 is a diagram illustrating that 5 autonomous bodies achieve a convergence task under the condition that the speed status is not measurable according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the estimation of velocity by 5 autonomous entities during the iteration of the algorithm according to an embodiment of the present invention;
FIG. 4 illustrates quantized integer values transmitted by a host during communication according to embodiment 5 of the present invention;
FIG. 5 is a graph of the 5 Laplace noises generated from the subject at each instant in time according to an embodiment of the present invention;
FIG. 6 shows the position of two sets of autonomous bodies at each time point, wherein the initial state of the embodiment of the invention satisfies delta proximity;
FIG. 7 shows two sets of quantized values of autonomous entities in communication with an initial state satisfying delta proximity according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The precondition for implementing the invention comprises the following:
assume one: the communication channels from the autonomous system are connected, i.e., each autonomous body in the system is able to communicate directly or indirectly with other autonomous bodies.
Assume two: the autonomous body can receive and transmit data at every fixed time interval.
The two assumed conditions are easy to satisfy, so that the invention is easy to apply in engineering and has good application value.
Example one
On the basis of satisfying the above two assumption conditions, as shown in fig. 1, the present embodiment provides a quantized second-order multi-autonomous system differential privacy convergence method, which specifically includes the following steps:
step S101: and respectively generating a Laplace noise with known parameters by the respective main bodies according to the updating state of the differential privacy convergence network, and adding the Laplace noise on the position state as observable position information.
In a specific implementation, the state parameters of the respective agents are initialized. The status parameters of the respective body include a position status and a velocity status. Respective body initialization state xi(0)，vi(0)，ui(0)＝0，ηi(0) Quantizer memory parameter K, threshold condition
Figure BDA0003076303330000061
Threshold condition
Figure BDA0003076303330000062
Given a smaller constant
Figure BDA0003076303330000063
When the position states of any ith and jth autonomous bodies satisfy
Figure BDA0003076303330000064
It indicates that the autonomous system has completed convergence.
The differential privacy convergence network comprises the following steps:
xi(t+1)＝xi(t)+vi(t)+siηi(t)
vi(t+1)＝vi(t)+ui(t)
wherein xi(t)，vi(t)，ui(t) the position state, speed state and control strategy of the ith autonomous body at the time t, siIs a constant parameter, η, of the differential privacy algorithmi(t) is the noise generated by the ith autonomous body at time t for implementing the differential privacy algorithm.
This embodiment uses the respective subject known parameters ciAnd q isiLaplace random noise, the probability distribution of which obeys the formula
Figure BDA0003076303330000065
Specifically, the noise generator produces an expected 0 with variance ciqi tLaplace noise η with time parameter ti(t +1) and adding the Laplace noise to a position state as an internal state theta of the self-bodyi(t+1)＝xi(t+1)+ηi(t+1)。
Step S102: and each main body quantizes the observable position information to obtain an integer value and transmits the integer value to other main bodies constructing a communication channel with the current main body.
In a specific implementation, before the respective agent quantizes the observable location information, the method further includes:
and judging whether the input exceeds the upper limit of the quantizer memory of the respective main body, and if so, regenerating Laplace noise with known parameters.
The present embodiment uses a finite level uniform quantizer obeying the following equation. The quantizer has a level of 2K +1, where K is a predetermined constant, no information is sent when the quantizer output is 0, and the required memory size corresponding to the quantizer is 2K +1
Figure BDA0003076303330000073
A bit.
Figure BDA0003076303330000074
Represents the smallest integer value of x or more.
Figure BDA0003076303330000071
If it is not
Figure BDA0003076303330000072
Then a laplacian noise with known parameters is regenerated.
Step S103: the respective agent receives the integer value from the communication channel and decodes it to obtain the state estimates of the other agents.
g(t)＝g0γt，0<γ<1 is an exponential function which decays with time, and the function of the 1 is to scale the input value, so as to avoid the quantizer exceeding the upper limit of the memory caused by overlarge input of the quantizer and to avoid the quantization error caused by too small input of the quantizer. The dynamic encoder (i.e., quantizer) and the decoder satisfy the following formulas, respectively
Figure BDA0003076303330000081
Figure BDA0003076303330000082
Wherein
Figure BDA0003076303330000083
Figure BDA0003076303330000084
Respectively representing the position state and the speed state of the quantizer relative to the ith autonomous body at the time t. the jth autonomous body receives zeta from i sending at t timei(t) and obtaining a position estimate and a velocity estimate of i
Figure BDA0003076303330000085
Figure BDA0003076303330000086
If the quantizer is not saturated then the quantization error of the final quantizer will tend to 0 over time, thus completing an accurate state estimation.
Respective agent updates encoder state
Figure BDA0003076303330000087
And
Figure BDA0003076303330000088
and obtaining an output value of the quantizer
Figure BDA0003076303330000089
And sends it to other autonomous bodies with whom it establishes a direct communication channel;
the respective agent obtains quantized values from other agents and decodes them into estimates of the states of the other agents
Figure BDA00030763033300000810
Step S104: and each main body designs control strategy information according to the obtained state estimation, updates the control strategy information to a differential privacy convergence network, judges whether the position states of all the main bodies meet a set threshold condition, if so, indicates that a convergence task is realized, otherwise, each main body continuously updates the state until the convergence task is realized.
In particular, the respective agent designs a control strategy based on known information
Figure BDA00030763033300000811
And judging whether the position state of the main body meets a threshold condition, if so, indicating that the convergence task is realized, otherwise, continuously updating the state by the main body until the convergence task is realized.
In a multi-autonomous system, for a given pair of initial state vectors x and x' satisfying δ proximity, it suffices if the two states are satisfied for an arbitrary set of observed sequences Φ and an arbitrary set of noise sequences Ω
Figure BDA0003076303330000091
It is stated that the system can implement differential privacy where phi denotes a particular observation sequence.
The multi-autonomous system is a stochastic system due to the addition of laplacian noise in the position state. According to research, in the embodiment, for two groups of multi-autonomous bodies with an initial state satisfying delta proximity, the two groups of multi-autonomous bodies have a certain probability of sending out identical information so as to confuse potential opponents, and therefore, a differential privacy protection function can be realized on the mechanism.
Where δ is close:
given a pair of N-dimensional vectors x and x', if there is one δ > 0, and one k e {1,2
Figure BDA0003076303330000092
Then the pair of n-dimensional vectors are δ -adjacent.
The present invention uses two examples to visualize the effectiveness of an algorithm. The first example is intended to demonstrate that under the algorithm, the multi-autonomous system communicates through quantized integer values and realizes convergence tasks; a second example is intended to demonstrate that under this algorithm a multi-autonomous system can implement differential privacy protection functions.
In the first exampleThe initial position state of the self-body is xi(0) I, initial velocity state vi(0) 0, initial control strategy is ui(0) 0, where i is 1, 2. g0＝10,γ＝0.998，si＝0.8,ci＝5,qi0.5. The quantizer scale K is 4 and the end-of-iteration threshold is 0.0001.
FIG. 2 shows that 5 autonomous bodies have performed convergence tasks in the case of an unmeasurable speed state; FIG. 3 shows 5 autonomous bodies obtaining estimates of velocity during the iteration of the algorithm; fig. 4 shows quantized integer values transmitted by 5 autonomous entities in the communication process, and it can be seen from fig. 4 that the size of the integer values transmitted in this example does not exceed 2, that is, the minimum memory capacity of the required quantizer is 2 bits; fig. 5 shows the laplacian noise generated from 5 subjects at each time, wherein the laplacian noise is exponentially attenuated.
In the second example, two sets of autonomous bodies are used whose initial states satisfy δ proximity. The state parameters of the first group of self-body are consistent with the first example, and the other parameters except x (5) is 0 of the second group of self-body are consistent with the first group, because the random system is difficult to describe, but privacy protection can be realized in probability. The algorithm satisfies the differential privacy definition, where FIGS. 6 and 7 are at an assumption of η5'(t)＝η5(t)+(1-s5)tDelta.
FIG. 6 shows the locus of position states for two initial state sets that satisfy δ proximity; fig. 7 shows that two initial state sets satisfying delta adjacency transmit exactly the same quantized values during communication, so that their states are the same as seen from the outside, and thus the outside can be confused to play a role in privacy protection.
Example two
The present embodiment provides a quantized second-order multi-autonomous system, which includes a plurality of autonomous bodies communicating with each other, where the autonomous bodies communicate with each other through quantized integer values using the second-order multi-autonomous system as described above and implement convergence tasks.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A quantized second-order multi-autonomous system differential privacy convergence method, comprising:
respectively generating Laplace noise with known parameters by respective main bodies according to the updating state of the differential privacy convergence network, and adding the Laplace noise on the position state as observable position information;
each main body quantizes the observable position information to obtain an integer value and transmits the integer value to other main bodies which construct communication channels with the current main body;
each main body receives the integer value from the communication channel and decodes the integer value to obtain the state estimation of other main bodies;
and each main body designs control strategy information according to the obtained state estimation, updates the control strategy information to a differential privacy convergence network, judges whether the position states of all the main bodies meet a set threshold condition, if so, indicates that a convergence task is realized, otherwise, each main body continuously updates the state until the convergence task is realized.
2. The quantized second-order multi-host system differential privacy convergence method of claim 1, wherein the states of the respective hosts comprise a location state and a velocity state.
3. The quantized second-order multi-autonomous system differential privacy convergence method of claim 1, wherein the differential privacy convergence network is:
xi(t+1)＝xi(t)+vi(t)+siηi(t)
vi(t+1)＝vi(t)+ui(t)
wherein xi(t)，vi(t)，ui(t) the position state, speed state and control strategy of the ith autonomous body at the time t, siIs a constant parameter, η, of the differential privacy algorithmi(t) is the noise generated by the ith autonomous body at time t for implementing the differential privacy algorithm.
4. The quantized second-order multi-autonomous system differential privacy convergence method of claim 1, wherein the probability distribution of the laplacian noise obeys expectation of 0, variance ciqi tWherein c isiAnd q isiT represents the time t, being a known parameter.
5. The quantized second-order multi-autonomous system differential privacy convergence method of claim 1, wherein the threshold condition is: the position states of any two self-bodies at the same time are not more than a set constant.
6. The method of quantified second-order multi-host system differential privacy convergence of claim 1, wherein prior to quantifying the observable location information by the respective agent, further comprising:
and judging whether the input exceeds the upper limit of the quantizer memory of the respective main body, and if so, regenerating Laplace noise with known parameters.
7. The method as claimed in claim 6, wherein the quantizer is ranked 2K +1, where K is a predetermined constant, no information is sent when the quantizer output is 0, and the required memory size corresponding to the quantizer is
Figure FDA0003076303320000021
A bit.
8. The quantized second-order multi-autonomous system differential privacy convergence method of claim 1, whereinAt time T +1, the jth autonomous receives the quantized integer value ζ from the i transmissioni(t +1) is:
Figure FDA0003076303320000022
wherein
Figure FDA0003076303320000023
Respectively representing the position state and the speed state of the ith autonomous body at the t moment by the quantizer; g (t) ═ g0γt，0<γ<1 is an exponential function that decays with time; thetai(t +1) is a substitute value for the position state at time t + 1.
9. The quantized second-order multi-autonomous system differential privacy convergence method of claim 1, wherein the control policy information is:
Figure FDA0003076303320000024
wherein k is1，k2Is a proportionality coefficient ofijIs the communication weight between the entities i and j,
Figure FDA0003076303320000025
representing an estimate of the position of autonomous body j to autonomous body i,
Figure FDA0003076303320000026
representing an estimate of the position of the subject from i,
Figure FDA0003076303320000027
representing an estimate of the velocity from subject j to subject i,
Figure FDA0003076303320000028
is represented by i pairs from the subjectAn estimate of the own velocity.
10. A quantized second order multi-autonomous system comprising a plurality of autonomous bodies communicating with each other, the autonomous bodies communicating by quantized integer values and implementing a convergence task using the second order multi-autonomous system according to any one of claims 1 to 9.
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