CN112348157A - Collaborative optimization method and device for formation configuration of multi-agent system - Google Patents

Collaborative optimization method and device for formation configuration of multi-agent system Download PDF

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CN112348157A
CN112348157A CN202011293262.3A CN202011293262A CN112348157A CN 112348157 A CN112348157 A CN 112348157A CN 202011293262 A CN202011293262 A CN 202011293262A CN 112348157 A CN112348157 A CN 112348157A
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CN112348157B (en
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王晓初
周庆瑞
孙昌浩
冯宇婷
邱华鑫
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China Academy of Space Technology CAST
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Abstract

The application discloses a collaborative optimization method and a device for formation configuration of a multi-agent system, wherein the method comprises the following steps: establishing a position variable x representing a position to be optimized for each agentiEstablishing an alignment variable θiEstablishing a gain variable gammai(ii) a Starting an iterative process for each agent, and in each iteration, performing at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable and updating gain variable; judging whether iteration is completed: determining the number of times each agent has iteratediWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxWhen the position variable x is changed, the iteration is completed, otherwise, the iteration process is repeated, and after the iteration is completed, the final position variable x of each intelligent agent is changediAs configuration-optimized location information; and arranging the intelligent bodies according to the position information optimized by the configuration.

Description

Collaborative optimization method and device for formation configuration of multi-agent system
Technical Field
The embodiment of the application relates to a signal processing technology, in particular to a collaborative optimization method and device for formation configuration of a multi-agent system.
Background
The intelligent agent generally refers to an autonomous body with intelligence, and generally has functions of computing capability, communication capability, response capability and the like, and common intelligent agents comprise artificial satellites, unmanned aerial vehicles, unmanned vehicles, intelligent electric appliances, intelligent hardware, electromechanical integrated sensors, cargo storage, generators and the like. The multi-agent system formed by a plurality of agents can realize more complex task functions by the cooperative work. For example, a wireless sensor network formed by the cooperative work of a plurality of sensors can realize area monitoring coverage, a synthetic aperture camera formed by the cooperative work of a plurality of small aperture cameras can realize equivalent large aperture observation, and a generator set formed by the cooperative work of a plurality of generators can realize high-power electric energy output.
The cooperative power of a multi-agent system is often dependent on the formation configuration, e.g., systems containing the same number of multi-agents, which differ in their formation configuration and their ability to perform tasks. Therefore, how to realize the optimization of the formation configuration of the multi-intelligent formation system so as to maximize the overall efficiency of the system is one of the key problems to be solved by the final trend of the multi-intelligent system to practical engineering application for a given multi-intelligent system. In some scenarios, the equivalent centroid of the multi-agent system needs to be kept constant due to site limitations, mission requirements, or natural constraints of the physical system, for example, in a multi-satellite formation mission, the equivalent centroid of the formation system needs to be kept constant at the designed orbit reference point regardless of the configuration change. Therefore, how to solve the problem of formation configuration optimization under the condition that the equivalent mass center of the multi-agent system is not changed is a key basis for the application of the system, and the method has important research and application significance.
Disclosure of Invention
In view of this, the present application provides a collaborative optimization method and apparatus for a formation configuration of a multi-agent system.
According to a first aspect of the present application, there is provided a method of collaborative optimization of a formation configuration of a multi-agent system, comprising:
establishing a location for each agent representing a location to be optimizedVariable xiEstablishing an alignment variable θiEstablishing a gain variable gammaiWherein x isiIs a column vector with the dimension of k and represents the coordinates of the ith agent in a k-dimensional space, i is the number of the agent, k is a positive integer, and thetaiIs a non-negative real number, γiIs a positive real number; at time t-0, each agent initializes xi＝Pi，θi＝0，γ i1, wherein PiThe current actual position of the ith agent is also a column vector with the dimension of k;
starting an iterative process for each agent, and in each iteration, performing at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable and updating gain variable;
judging whether iteration is completed: determining the number of times each agent has iteratediWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxWhen the iteration is finished, otherwise, the iteration process is repeated, wherein, the piiAnd pimaxAre all positive integers;
after the iteration is finished, each agent will obtain the final position variable xiAs configuration-optimized location information;
and arranging the intelligent bodies according to the position information optimized by the configuration.
As one implementation, the computing local performance gradients and constraint gradients includes:
calculating a local performance function u of agent ii(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000021
Envelope surface function omega of value space allowed by calculating position variablei(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000022
Wherein the local efficiencyFunction ui(xi) Is a vector xiIs a scalar-valued convex function of a variable, enveloping a surface function omegai(xi) Is a vector xiIs a scalar value type convex function of the variable, and the allowed value of the variable at any position meets the constraint relation omegai(xi) Less than or equal to 0; calculated therefrom
Figure BDA0002784593190000023
In order to be a local performance gradient,
Figure BDA0002784593190000024
to constrain the gradient.
As an implementation manner, the performing interaction coordination between neighbors includes:
having each agent i broadcast a position variable x to neighboring agentsiAlignment variable θiGain variable gammaiLocal performance gradient
Figure BDA0002784593190000031
Constrained gradient
Figure BDA0002784593190000032
And receiving related variable information sent by all neighbors, wherein the neighbor agents refer to agents which are adjacent to the network topology and can perform communication exchange and information interaction with the current agent.
As one implementation, the performing location variable update includes:
calculating the updated rate of change for each agent according to the following equation (1)
Figure BDA0002784593190000033
Then, the position variable x is updated according to the formula (2)i：
Figure BDA0002784593190000034
Figure BDA0002784593190000035
Wherein the content of the first and second substances,
Figure BDA0002784593190000036
set of neighbor agents representing all of the ith agent, miThe number is real number and represents the quality of the ith agent, and the value of Delta T is positive real number and represents the updating time step length.
As an implementation, the performing an alignment variable update includes:
make each agent i according to the updated position variable xiFor each neighbor agent
Figure BDA0002784593190000037
Calculating optimum according to the following formula (3)
Figure BDA0002784593190000038
And calculating an updated alignment variable theta according to equation (4)i：
Figure BDA0002784593190000039
Figure BDA00027845931900000310
Wherein, IkIs an identity matrix of order k,
Figure BDA00027845931900000311
represents the kronecker product operation of the matrix,
Figure BDA00027845931900000312
representing sets for positive integers
Figure BDA00027845931900000313
The number of inner elements, abs () representing absolute value operations, for each neighbor
Figure BDA00027845931900000314
Figure BDA00027845931900000315
And
Figure BDA00027845931900000316
are all real numbers.
As one implementation, the performing gain variable update includes:
make each agent i according to the updated position variable xiThe gain variable γ is updated according to the following equation (5)i：
γi＝exp(Ωi(xi)) (5)
Where exp () represents an exponential function operation with a natural constant e as the base.
According to a second aspect of the present application, there is provided a device for collaborative optimization of a formation configuration of a multi-agent system, the device comprising:
a building unit for building a position variable x representing the position to be optimized for each agentiEstablishing an alignment variable θiEstablishing a gain variable gammaiWherein x isiIs a column vector with the dimension of k and represents the coordinates of the ith agent in a k-dimensional space, i is the number of the agent, k is a positive integer, and thetaiIs a non-negative real number, γiIs a positive real number; at time t-0, each agent initializes xi＝Pi，θi＝0，γ i1, wherein PiThe current actual position of the ith agent is also a column vector with the dimension of k;
an iteration processing unit, configured to start an iteration process for each agent, and in each iteration, perform at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable and updating gain variable;
a judging unit, configured to judge whether the iteration is completed: determining the number of times each agent calculation has iteratedπiWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxWhen the iteration is finished, otherwise, the iteration process is repeated, wherein, the piiAnd pimaxAre all positive integers;
an arrangement unit for arranging the final position variable x of each agent after the iteration is finishediAs configuration-optimized location information; and arranging the intelligent bodies according to the position information optimized by the configuration.
As an implementation, the iterative processing unit is further configured to:
calculating a local performance function u of agent ii(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000046
Envelope surface function omega of value space allowed by calculating position variablei(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000041
Wherein the local performance function ui(xi) Is a vector xiIs a scalar-valued convex function of a variable, enveloping a surface function omegai(xi) Is a vector xiIs a scalar value type convex function of the variable, and the allowed value of the variable at any position meets the constraint relation omegai(xi) Less than or equal to 0; calculated therefrom
Figure BDA0002784593190000042
In order to be a local performance gradient,
Figure BDA0002784593190000043
is a constrained gradient;
having each agent i broadcast a position variable x to neighboring agentsiAlignment variable θiGain variable gammaiLocal performance gradient
Figure BDA0002784593190000044
Constrained gradient
Figure BDA0002784593190000045
And receiving related variable information sent by all neighbors, wherein the neighbor agents refer to agents which are adjacent to the network topology and can perform communication exchange and information interaction with the current agent.
As an implementation, the iterative processing unit is further configured to:
calculating the updated rate of change for each agent according to the following equation (1)
Figure BDA00027845931900000514
Then, the position variable x is updated according to the formula (2)i：
Figure BDA0002784593190000051
Figure BDA0002784593190000052
Wherein the content of the first and second substances,
Figure BDA0002784593190000053
set of neighbor agents representing all of the ith agent, miThe real number represents the quality of the ith agent, and the value of delta T is a positive real number and represents the updating time step;
make each agent i according to the updated position variable xiFor each neighbor agent
Figure BDA0002784593190000054
Calculating optimum according to the following formula (3)
Figure BDA0002784593190000055
And calculating an updated alignment variable theta according to equation (4)i：
Figure BDA0002784593190000056
Figure BDA0002784593190000057
Wherein, IkIs an identity matrix of order k,
Figure BDA0002784593190000058
represents the kronecker product operation of the matrix,
Figure BDA0002784593190000059
representing sets for positive integers
Figure BDA00027845931900000510
The number of inner elements, abs () representing absolute value operations, for each neighbor
Figure BDA00027845931900000511
Figure BDA00027845931900000512
And
Figure BDA00027845931900000513
are all real numbers.
As an implementation, the iterative processing unit is further configured to:
make each agent i according to the updated position variable xiThe gain variable γ is updated according to the following equation (5)i：
γi＝exp(Ωi(xi)) (5)
Where exp () represents an exponential function operation with a natural constant e as the base.
The collaborative optimization method and device for the formation configuration of the multi-agent system are suitable for the connected multi-agent system with any scale, have scale expandability, allow the collaborative optimization of the formation configuration of the multi-agent system under the premise that the equivalent mass center of the multi-agent system is not changed, and simultaneously meet the self constraint of the position to be optimized of each agent; the technical scheme of the embodiment of the application is suitable for a scene with an efficiency function of a convex function and a constraint of a convex constraint, does not need the intelligent agents to have global communication capacity or perform centralized calculation, is a completely distributed cooperative optimization processing technology, and can achieve an equivalent globally optimal formation configuration cooperative optimization result only based on distributed interactive cooperation among topological neighbor intelligent agents.
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FIG. 1 is a schematic flow chart of a collaborative optimization method for formation configuration of a multi-agent system according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a communication topology relationship between agents in a multi-agent system according to an embodiment of the present application;
FIG. 3 is a curve diagram illustrating an optimization process of a position to be optimized of each agent in the embodiment of the present application;
FIG. 4 is a graph illustrating the overall performance of the system in the embodiment of the present application;
fig. 5 is a schematic structural diagram of a cooperative optimization device in a formation configuration of a multi-agent system according to an embodiment of the present application.
Detailed Description
The technical solutions of the embodiments of the present application are further explained in detail below with reference to the accompanying drawings in combination with specific examples.
Fig. 1 is a schematic flowchart of a collaborative optimization method for a formation configuration of a multi-agent system according to an embodiment of the present application, and as shown in fig. 1, the collaborative optimization method for a formation configuration of an agent system according to an embodiment of the present application includes the following processing steps:
step 101, establishing variables for an agent and initializing; the method specifically comprises the following steps: establishing a position variable x representing a position to be optimized for each agentiEstablishing an alignment variable θiEstablishing a gain variable gammaiWherein x isiA column vector with the dimension of k represents the coordinates of the ith agent in a k-dimensional space, i is a positive integer representing the number of the agent, k is a positive integer representing the dimension, and thetaiIs a non-negative real number, γiIs a positive real number; at time t equal to 0, each timePersonal agent initialization xi＝Pi，θi＝0，γ i1, wherein PiThe current actual position of the ith agent is also a column vector with the dimension of k;
102, performing inter-neighbor coordination and iterative optimization on each agent, specifically comprising: enabling each agent to start an iterative process, specifically, in each iteration, performing at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable, updating gain variable, judging whether iteration is finished, and the like. The specific implementation of each processing step is described in detail below:
calculating a local performance gradient and a constraint gradient, specifically comprising: computing a local performance function u for each agent ii(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000071
Envelope surface function omega of value space allowed by calculating position variablei(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000072
Wherein the local performance function ui(xi) Is a vector xiIs a scalar-valued convex function of a variable, enveloping a surface function omegai(xi) Is a vector xiIs a scalar value type convex function of the variable, and the allowed value of the variable at any position meets the constraint relation omegai(xi) Less than or equal to 0; calculated therefrom
Figure BDA0002784593190000073
In order to be a local performance gradient,
Figure BDA0002784593190000074
to constrain the gradient.
Performing interaction coordination among neighbors, specifically comprising: let each agent i go to all its neighborsIntelligent agent broadcast transmission position variable xiAlignment variable θiGain variable gammaiLocal performance gradient
Figure BDA0002784593190000075
Constrained gradient
Figure BDA0002784593190000076
And simultaneously receiving related variable information sent by all neighbor agents, wherein the neighbor agents refer to agents which are adjacent to the network topology and can perform communication and information interaction with the current agent.
Updating the position variable specifically comprises: having each agent calculate an updated rate of change as in equation (1) below
Figure BDA0002784593190000077
Then, the position variable x is updated according to the formula (2)i：
Figure BDA0002784593190000078
Figure BDA0002784593190000079
Wherein the content of the first and second substances,
Figure BDA00027845931900000710
represents the set of all neighbors of the ith agent, miReal numbers represent the quality of the ith agent, and the value of delta T is that the real numbers represent the updating time step; it should be noted that all agents perform location variable update according to equations (1) and (2), and the summation of equations (1) and (2) over all agents results in that the equivalent centroid of the multi-agent location remains unchanged, which is also one of the significant features of the embodiments of the present application.
Updating the alignment variables, specifically comprising: make each agent i according to the updated position variable xiFor each neighbor agent
Figure BDA00027845931900000711
Calculating optimum according to the following formula (3)
Figure BDA00027845931900000712
And calculating an updated alignment variable theta according to equation (4)i：
Figure BDA0002784593190000081
Figure BDA0002784593190000082
Wherein, IkIs an identity matrix of order k,
Figure BDA0002784593190000083
represents the kronecker product operation of the matrix,
Figure BDA0002784593190000084
is a positive integer, representing a set
Figure BDA0002784593190000085
The number of internal elements, abs () representing absolute value operations, for each neighbor agent
Figure BDA0002784593190000086
Figure BDA0002784593190000087
And
Figure BDA0002784593190000088
are all real numbers.
Updating the gain variable specifically comprises: make each agent i according to the updated position variable xiThe gain variable γ is updated according to the following equation (5)i：
γi＝exp(Ωi(xi)) (5)
Where exp () represents an exponential function operation with a natural constant e as the base.
Judging whether the iteration process is finished or not, specifically comprising the following steps: calculating the number of times pi that has been iterated for the ith agentiWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxI.e. wheni≥πmaxIf the iteration process is judged to be completed, otherwise, the iteration process is judged to be not completed, the intelligent agent starts the iteration process repeatedly, and at least one of the following processes is executed again: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable, updating gain variable and the like. Wherein, piiAnd pimaxAre all positive integers.
Step 103, obtaining a configuration optimization result, specifically: after the iteration is finished, each agent will obtain the final position variable xiAs configuration-optimized location information; and arranging the intelligent bodies according to the position information optimized by the configuration.
As an example, for example, a specific two-dimensional formation configuration problem, a multi-intelligent system is composed of 4 intelligent agents, n is 4, each intelligent agent is numbered as 1, 2, 3, 4, and their topological connection relationship is shown in fig. 2, initially, the xy coordinates of the positions of the 4 intelligent agents are (7, 7), (-4, 8), (-10, -6), (12, -10), and their masses m are (7, 7), (-4, 8), (-10, -6), (12, -10), respectivelyiEqual and all 1kg, so the initial equivalent centroid position xy coordinates of the multi-agent system can be calculated as (1.25, -0.25). In this example, each agent i is constrained by the constraint Ω of the location to be optimizediThe centers of the corresponding rings are respectively marked as (p) for the inner part (including the boundary) of the ring in which the corresponding ring is positionedi,qi) For agents 1, 2, 3, 4, the specific circle centers are (5, 5), (-6, 6), (-7, -7), (8, -8), respectively. The local performance function of each agent i is ui＝5-ai(xi-pi)2-bi(yi-qi)2+ci(xi-pi)(yi-qi) Wherein a isi＝0.1i，bi＝0.05i，ci0.025i, the local performance function is the position coordinate (x)i,yi) A convex function of (a). It can be further calculated that the initial overall performance value of the intelligent system is Σ ui＝7.688。
Distributed cooperative configuration optimization is carried out by utilizing the cooperative optimization method for the formation configuration of the multi-agent system in the embodiment of the application, and the key parameter of the algorithm at the beginning is initialized to thetai＝0，γiAs 1, it should be noted that the alignment variable θiAnd a gain variable gammaiIn the foregoing iteration process of the embodiment of the present application, the update is also performed at any time. Setting the maximum iteration time to be 50 seconds, calculating by taking 0.1 second as a discrete unit, namely setting the maximum iteration times pi max500. Finally, the collaborative optimization process of the multi-agent system formation configuration of the embodiment of the application is shown in fig. 3, wherein the symbol of a "+" represents the initial position of the agent, and the symbol of a five-pointed star represents the position of the agent at which the optimization is finished; the dotted line represents the initial configuration of the agent, the dotted line represents the configuration at which the agent optimization is finished, and the dotted trace represents the optimization process of each agent. After the optimization is finished, the xy coordinates of the positions of the 4 agents are (5.802, 7.741), (-4.721, 6.784), (-5.501, -7.041), (9.420, -8.484), respectively. Based on the foregoing example, it can be calculated that the system equivalent centroid after the optimization is over, still is (1.25, -0.25). And can also calculate that the integral effect value of the intelligent system at the moment is sigma ui17.885. In the whole iteration process of the embodiment of the present application, an optimization curve of the overall performance of the system is shown in fig. 4, and the effectiveness of the embodiment of the present application is reflected as the iteration times are gradually increased.
Fig. 5 is a schematic structural diagram of a cooperative optimization apparatus for a formation configuration of multi-agent systems according to an embodiment of the present application, and as shown in fig. 5, the cooperative optimization apparatus for a formation configuration of multi-agent systems according to an embodiment of the present application includes:
a building unit 50 for building a position variable x representing the position to be optimized for each agentiEstablishing an alignment variable θiEstablishing a gain variable gammaiWherein x isiIs of dimension ofk column vectors representing coordinates of the ith agent in k-dimensional space, i being the agent number, k being a positive integer, θiIs a non-negative real number, γiIs a positive real number; at time t-0, each agent initializes xi＝Pi，θi＝0，γ i1, wherein PiThe current actual position of the ith agent is also a column vector with the dimension of k;
an iteration processing unit 51, configured to start an iteration process for each agent, and in each iteration, perform at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable and updating gain variable;
a judging unit 52, configured to judge whether the iteration is completed: determining the number of times each agent has iteratediWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxWhen the iteration is finished, otherwise, the iteration process is repeated, wherein, the piiAnd pimaxAre all positive integers;
an arrangement unit 53 for, after the iteration is completed, assigning each agent a final position variable xiAs configuration-optimized location information; and arranging the intelligent bodies according to the position information optimized by the configuration.
As an implementation manner, the iterative processing unit 51 is further configured to:
calculating a local performance function u of agent ii(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000101
Envelope surface function omega of value space allowed by calculating position variablei(xi) At the current position variable xiGradient value of
Figure BDA0002784593190000102
Wherein the local performance function ui(xi) Is a vector xiBeing scalar-valued convex functions, envelopes, of variablesFunction omega of curved surfacei(xi) Is a vector xiIs a scalar value type convex function of the variable, and the allowed value of the variable at any position meets the constraint relation omegai(xi) Less than or equal to 0; calculated therefrom
Figure BDA0002784593190000103
In order to be a local performance gradient,
Figure BDA0002784593190000104
is a constrained gradient;
having each agent i broadcast a position variable x to neighboring agentsiAlignment variable θiGain variable gammaiLocal performance gradient
Figure BDA0002784593190000105
Constrained gradient
Figure BDA0002784593190000106
And receiving related variable information sent by all neighbors, wherein the neighbor agents refer to agents which are adjacent to the network topology and can perform communication exchange and information interaction with the current agent.
As an implementation manner, the iterative processing unit 51 is further configured to:
calculating the updated rate of change for each agent according to the following equation (1)
Figure BDA0002784593190000107
Then, the position variable x is updated according to the formula (2)i：
Figure BDA0002784593190000108
Figure BDA0002784593190000109
Wherein the content of the first and second substances,
Figure BDA00027845931900001010
set of neighbor agents representing all of the ith agent, miThe real number represents the quality of the ith agent, and the value of delta T is a positive real number and represents the updating time step;
make each agent i according to the updated position variable xiFor each neighbor agent
Figure BDA0002784593190000111
Calculating optimum according to the following formula (3)
Figure BDA0002784593190000112
And calculating an updated alignment variable theta according to equation (4)i：
Figure BDA0002784593190000113
Figure BDA0002784593190000114
Wherein, IkIs an identity matrix of order k,
Figure BDA0002784593190000115
represents the kronecker product operation of the matrix,
Figure BDA0002784593190000116
representing sets for positive integers
Figure BDA0002784593190000117
The number of inner elements, abs () representing absolute value operations, for each neighbor
Figure BDA0002784593190000118
Figure BDA0002784593190000119
And
Figure BDA00027845931900001110
are all real numbers.
As an implementation manner, the iterative processing unit 51 is further configured to:
make each agent i according to the updated position variable xiThe gain variable γ is updated according to the following equation (5)i：
γi＝exp(Ωi(xi)) (5)
Where exp () represents an exponential function operation with a natural constant e as the base.
In an exemplary embodiment, the establishing Unit 50, the iterative Processing Unit 51, the judging Unit 52, the arranging Unit 53, etc. may be implemented by one or more Central Processing Units (CPUs), Graphics Processing Units (GPUs), Baseband Processors (BPs), Application Specific Integrated Circuits (ASICs), Digital Signal Processors (DSPs), a Programmable Logic Device (PLD), a Complex Programmable Logic Device (CPLD), a Field Programmable Gate Array (FPGA), a general processor, a Controller, a Microcontroller (MCU), a Microprocessor (Microprocessor), or other electronic components, and may be implemented in combination with one or more Radio Frequency (RF) antennas for performing information interaction in the foregoing embodiments.
In the embodiment of the present application, the specific manner in which each unit in the collaborative optimization apparatus in the multi-agent system formation configuration shown in fig. 5 performs operations has been described in detail in the embodiment related to the method, and will not be elaborated herein.
The present application further describes an electronic device comprising a processor, a transceiver, a memory and an executable program stored on the memory and capable of being executed by the processor, wherein the processor executes the executable program to perform the steps of the method for collaborative optimization of a formation configuration of a multi-agent system according to the previous embodiment.
The embodiments of the present application also describe a storage medium on which an executable program is stored, the executable program being executed by a processor to perform the steps of the method for collaborative optimization of a formation configuration of a multi-agent system of the aforementioned embodiments.
It should be appreciated that reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrases "in one embodiment" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. It should be understood that, in various embodiments of the present invention, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention. The above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The above-described device embodiments are only illustrative, for example, the division of the unit is only one logical function division, and there may be other division ways in actual implementation, such as: multiple units or components may be combined, or may be integrated into another system, or some features may be omitted, or not implemented. In addition, the coupling, direct coupling or communication connection between the components shown or discussed may be through some interfaces, and the indirect coupling or communication connection between the devices or units may be electrical, mechanical or other forms.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units; can be located in one place or distributed on a plurality of network units; some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, all the functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may be separately regarded as one unit, or two or more units may be integrated into one unit; the integrated unit can be realized in a form of hardware, or in a form of hardware plus a software functional unit.
The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or substitutions within the technical scope of the present invention, and all such changes or substitutions are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (10)

1. A method for collaborative optimization of formation configurations of multi-agent systems, the method comprising:
establishing a position variable x representing a position to be optimized for each agentiEstablishing an alignment variable θiEstablishing a gain variable gammaiWherein x isiIs a column vector with the dimension of k and represents the coordinates of the ith agent in a k-dimensional space, i is the number of the agent, k is a positive integer, and thetaiIs a non-negative real number, γiIs a positive real number; at time t-0, each agent initializes xi＝Pi，θi＝0，γi1, wherein PiIs the ithThe current actual position of the agent is also a column vector with the dimension k;
starting an iterative process for each agent, and in each iteration, performing at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable and updating gain variable;
judging whether iteration is completed: determining the number of times each agent has iteratediWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxWhen the iteration is finished, otherwise, the iteration process is repeated, wherein, the piiAnd pimaxAre all positive integers;
after the iteration is finished, each agent will obtain the final position variable xiAs configuration-optimized location information;
and arranging the intelligent bodies according to the position information optimized by the configuration.
2. The method of claim 1, wherein the calculating local performance gradients and constraint gradients comprises:
calculating a local performance function u of agent ii(xi) At the current position variable xiGradient value of
Figure FDA0002784593180000011
Envelope surface function omega of value space allowed by calculating position variablei(xi) At the current position variable xiGradient value of
Figure FDA0002784593180000012
Wherein the local performance function ui(xi) Is a vector xiIs a scalar-valued convex function of a variable, enveloping a surface function omegai(xi) Is a vector xiIs a scalar value type convex function of the variable, and the allowed value of the variable at any position meets the constraint relation omegai(xi) Less than or equal to 0; calculated therefrom
Figure FDA0002784593180000013
In order to be a local performance gradient,
Figure FDA0002784593180000014
to constrain the gradient.
3. The method of claim 2, wherein the inter-neighbor interaction coordination comprises:
having each agent i broadcast a position variable x to neighboring agentsiAlignment variable θiGain variable gammaiLocal performance gradient
Figure FDA0002784593180000021
Constrained gradient
Figure FDA0002784593180000022
And receiving related variable information sent by all neighbors, wherein the neighbor agents refer to agents which are adjacent to the network topology and can perform communication exchange and information interaction with the current agent.
4. The method of claim 3, wherein the performing location variable updates comprises:
calculating the updated rate of change for each agent according to the following equation (1)
Figure FDA0002784593180000023
Then, the position variable x is updated according to the formula (2)i：
Figure FDA0002784593180000024
Figure FDA0002784593180000025
Wherein the content of the first and second substances,
Figure FDA0002784593180000026
set of neighbor agents representing all of the ith agent, miThe number is real number and represents the quality of the ith agent, and the value of Delta T is positive real number and represents the updating time step length.
5. The method of claim 4, wherein the performing an alignment variable update comprises:
make each agent i according to the updated position variable xiFor each neighbor agent
Figure FDA0002784593180000027
Calculating optimum according to the following formula (3)
Figure FDA0002784593180000028
And calculating an updated alignment variable theta according to equation (4)i：
Figure FDA0002784593180000029
Figure FDA00027845931800000210
Wherein, IkIs an identity matrix of order k,
Figure FDA00027845931800000211
represents the kronecker product operation of the matrix,
Figure FDA00027845931800000212
representing sets for positive integers
Figure FDA00027845931800000213
Internal elementThe number of elements, abs () representing absolute value operations, for each neighbor
Figure FDA00027845931800000214
Figure FDA00027845931800000215
And
Figure FDA00027845931800000216
are all real numbers.
6. The method of claim 5, wherein the performing gain variable updates comprises:
make each agent i according to the updated position variable xiThe gain variable γ is updated according to the following equation (5)i：
γi＝exp(Ωi(xi)) (5)
Where exp () represents an exponential function operation with a natural constant e as the base.
7. A device for collaborative optimization of a formation configuration of a multi-agent system, the device comprising:
a building unit for building a position variable x representing the position to be optimized for each agentiEstablishing an alignment variable θiEstablishing a gain variable gammaiWherein x isiIs a column vector with the dimension of k and represents the coordinates of the ith agent in a k-dimensional space, i is the number of the agent, k is a positive integer, and thetaiIs a non-negative real number, γiIs a positive real number; at time t-0, each agent initializes xi＝Pi，θi＝0，γi1, wherein PiThe current actual position of the ith agent is also a column vector with the dimension of k;
an iteration processing unit, configured to start an iteration process for each agent, and in each iteration, perform at least one of the following processes: calculating local efficiency gradient and constraint gradient, performing interaction coordination between neighbors, updating position variable, updating alignment variable and updating gain variable;
a judging unit, configured to judge whether the iteration is completed: determining the number of times each agent has iteratediWhen number of times piiGreater than or equal to a given maximum number of iterations pimaxWhen the iteration is finished, otherwise, the iteration process is repeated, wherein, the piiAnd pimaxAre all positive integers;
an arrangement unit for arranging the final position variable x of each agent after the iteration is finishediAs configuration-optimized location information; and arranging the intelligent bodies according to the position information optimized by the configuration.
8. The apparatus of claim 7, wherein the iterative processing unit is further configured to:
calculating a local performance function u of agent ii(xi) At the current position variable xiGradient value of
Figure FDA0002784593180000031
Envelope surface function omega of value space allowed by calculating position variablei(xi) At the current position variable xiGradient value of
Figure FDA0002784593180000032
Wherein the local performance function ui(xi) Is a vector xiIs a scalar-valued convex function of a variable, enveloping a surface function omegai(xi) Is a vector xiIs a scalar value type convex function of the variable, and the allowed value of the variable at any position meets the constraint relation omegai(xi) Less than or equal to 0; calculated therefrom
Figure FDA0002784593180000033
In order to be a local performance gradient,
Figure FDA0002784593180000034
is a constrained gradient;
having each agent i broadcast a position variable x to neighboring agentsiAlignment variable θiGain variable gammaiLocal performance gradient
Figure FDA0002784593180000041
Constrained gradient
Figure FDA0002784593180000042
And receiving related variable information sent by all neighbors, wherein the neighbor agents refer to agents which are adjacent to the network topology and can perform communication exchange and information interaction with the current agent.
9. The apparatus of claim 8, wherein the iterative processing unit is further configured to:
calculating the updated rate of change for each agent according to the following equation (1)
Figure FDA0002784593180000043
Then, the position variable x is updated according to the formula (2)i：
Figure FDA0002784593180000044
Figure FDA0002784593180000045
Wherein the content of the first and second substances,
Figure FDA0002784593180000046
set of neighbor agents representing all of the ith agent, miThe real number represents the quality of the ith agent, and the value of delta T is a positive real number and represents the updating time step;
make each agent i according to the updated position variable xiFor each neighbor agent
Figure FDA0002784593180000047
Calculating optimum according to the following formula (3)
Figure FDA0002784593180000048
And calculating an updated alignment variable theta according to equation (4)i：
Figure FDA0002784593180000049
Figure FDA00027845931800000410
Wherein, IkIs an identity matrix of order k,
Figure FDA00027845931800000411
represents the kronecker product operation of the matrix,
Figure FDA00027845931800000412
representing sets for positive integers
Figure FDA00027845931800000413
The number of inner elements, abs () representing absolute value operations, for each neighbor
Figure FDA00027845931800000414
Figure FDA00027845931800000415
And
Figure FDA00027845931800000416
are all real numbers.
10. The apparatus of claim 9, wherein the iterative processing unit is further configured to:
make each agent i according to the updated position variable xiThe gain variable γ is updated according to the following equation (5)i：
γi＝exp(Ωi(xi)) (5)
Where exp () represents an exponential function operation with a natural constant e as the base.
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