CN112637120B - Multi-agent system consistency control method, terminal and storage medium - Google Patents

Multi-agent system consistency control method, terminal and storage medium Download PDF

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CN112637120B
CN112637120B CN202011277400.9A CN202011277400A CN112637120B CN 112637120 B CN112637120 B CN 112637120B CN 202011277400 A CN202011277400 A CN 202011277400A CN 112637120 B CN112637120 B CN 112637120B
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consistency control
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尉越
李昱祺
丁玉隆
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Peng Cheng Laboratory
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Abstract

The invention discloses a multi-agent system consistency control method, a terminal and a storage medium, wherein an interactive topology of the multi-agent system is constructed according to communication relations among agents in the multi-agent system, a consistency control model of the multi-agent system is further constructed according to an interactive topological graph, constraints of the model are set to comprise consistency condition constraints and non-smooth inequality constraints, an optimal decoupling terminal of the consistency control model is designed, and a control protocol of the multi-agent system is determined according to the optimal decoupling terminal, so that the multi-agent system can simultaneously meet the consistency condition constraints and the non-smooth inequality constraints.

Description

Multi-agent system consistency control method, terminal and storage medium
Technical Field
The invention relates to the technical field of multi-agent system control, in particular to a multi-agent system consistency control method, a terminal and a storage medium.
Background
The multi-agent system can be regarded as a self-organizing intelligent unmanned platform group, numerous group tasks can be completed through interaction of information and actions, the intelligent degree of the whole group is greatly improved through cooperative behaviors among agents in the multi-agent system, complex tasks which cannot be completed by single bodies can be met, and the multi-agent system is widely applied to the fields of sensor group deployment, multi-unmanned aerial vehicle formation control, multi-mechanical arm cooperative carrying and the like.
In distributed control of a multi-agent system, the states of the multi-agent system are generally required to be consistent when the optimal solution of an optimization problem is achieved, and in addition, constraint conditions are required to be processed, for example, the motion range constraint of the multi-agent system is described as a constraint function of an indication function as the optimization problem.
Thus, there is a need for improvements and enhancements in the art.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a multi-agent system consistency control method, a terminal and a storage medium, and aims to solve the problem that in the prior art, a consistency control protocol with consistency constraint and non-smooth inequality constraint conditions does not exist in a multi-agent system consistency control scheme.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
in a first aspect of the present invention, there is provided a multi-agent system consistency control method, the method comprising:
acquiring communication relations among all agents in a multi-agent system, and constructing an interactive topology of the multi-agent system according to the communication relations;
constructing a consistency control model of the multi-agent system according to the interaction topology, wherein constraints of the consistency control model comprise consistency condition constraints and non-smooth inequality constraints;
designing a decoupling operator of an optimal solution of the consistency control model;
determining a control protocol of the multi-agent system according to a decoupling operator of the optimal solution, such that the individual agents in the multi-agent system control their own motion according to the control protocol.
The multi-agent system consistency control method, wherein the constructing an interactive topology of the multi-agent system according to the communication relation, comprises:
the laplacian matrix of the interaction topology is: l isnD-a, wherein the matrix
Figure GDA0003530551890000021
Associated with agent i
Figure GDA0003530551890000022
Is a diagonal matrix of diagonal elements, i belongs to {1, 2., n }, n is the number of agents in the multi-agent system, and an agent j and an agent i are connected through an information interaction edge eijE belongs to E connection and information interaction edge EijE represents that the agent i and the agent j can exchange information in two directions, if the information exchange is carried out, EijE, then aij＝aji> 0, otherwise aij＝0，
Figure GDA0003530551890000023
Is a weighted adjacency matrix.
The multi-agent system consistency control method, wherein the building of the consistency control model of the multi-agent system according to the interaction topology includes:
obtaining cost functions and non-smooth inequality constraint information of each agent in the multi-agent system, and constructing a consistency control model of the multi-agent system according to the interactive topology and the kinematics model as follows:
Figure GDA0003530551890000024
Figure GDA0003530551890000025
wherein the content of the first and second substances,
Figure GDA0003530551890000026
i belongs to {1, 2.,. n }, n is the number of agents in the multi-agent system,
Figure GDA0003530551890000027
for the two local cost functions of agent i,
Figure GDA0003530551890000028
is a smooth convex function of the image to be displayed,
Figure GDA0003530551890000031
non-smooth convex function, state
Figure GDA0003530551890000032
Is a position state vector of agent i, is a q-dimensional vector, and
Figure GDA0003530551890000033
0nqis a zero vector of the nq-dimension,
Figure GDA00035305518900000323
is a matrix LnAnd IqKronecker product of LnLaplace matrix, I, which is the topology of the information interactionqIs a q-dimensional unit matrix and is,
Figure GDA0003530551890000034
is a non-smooth inequality constraint for agent i,
Figure GDA0003530551890000035
is a non-smooth convex function that can be approximated,
Figure GDA0003530551890000036
and
Figure GDA0003530551890000037
are respectively
Figure GDA0003530551890000038
-Liphoxitz in continuous with
Figure GDA0003530551890000039
-Liphoz continuous.
The multi-agent system consistency control method, wherein the designing a decoupling operator of an optimal solution of the consistency control model comprises:
the decoupling operator for designing the optimal solution of the consistency control model is as follows:
Figure GDA00035305518900000310
Figure GDA00035305518900000311
wherein, the lambda and the mu are Lagrange multipliers,
Figure GDA00035305518900000312
as an auxiliary variable, the number of variables,
Figure GDA00035305518900000313
for introducing parameters, alpha and beta are preset parameters, for any
Figure GDA00035305518900000314
i ∈ {1, …, n }, each having:
Figure GDA00035305518900000315
z*satisfies the following conditions:
Figure GDA00035305518900000316
and is
Figure GDA00035305518900000317
The multi-agent system consistency control method comprises the following control protocols of the multi-agent system:
Figure GDA00035305518900000318
Figure GDA00035305518900000319
Figure GDA00035305518900000320
Figure GDA00035305518900000321
wherein beta is more than 0 and less than 1/Lambdamax(L),0＜γ＜1-βΛmax(L),
Figure GDA00035305518900000322
Figure GDA0003530551890000041
0＜α＜mink＝1,2,3[οk]C is a constant, t is a time variable, Λmax(L) is the maximum eigenvalue of L,
Figure GDA0003530551890000042
the multi-agent system consistency control method, wherein the designing an optimal solution of the consistency control model, comprises:
the decoupling operator for designing the optimal solution of the consistency control model is as follows:
Figure GDA0003530551890000043
Figure GDA0003530551890000044
wherein, the lambda and the mu are Lagrange multipliers,
Figure GDA0003530551890000045
as an auxiliary variable, the number of variables,
Figure GDA0003530551890000046
for introducing parameters, alpha and beta are preset parameters, for any
Figure GDA0003530551890000047
i ∈ {1, …, n }, each having:
Figure GDA0003530551890000048
z*satisfies the following conditions:
Figure GDA0003530551890000049
and is
Figure GDA00035305518900000410
The multi-agent system consistency control method comprises the following control protocols of the multi-agent system:
Figure GDA00035305518900000411
Figure GDA00035305518900000412
Figure GDA00035305518900000413
Figure GDA00035305518900000414
wherein beta is more than 0 and less than 1/Lambdamax(L),0＜γ＜1-βΛmax(L),
Figure GDA00035305518900000415
Figure GDA00035305518900000416
0＜α＜mink＝1,2,3[οk]C is a constant, t is a time variable, Λmax(L) is the maximum eigenvalue of L,
Figure GDA0003530551890000051
the multi-agent system consistency control method is characterized in that the kinematic model of the agents in the multi-agent system is as follows:
Figure GDA0003530551890000052
wherein u isi(t) is the speed control quantity of agent i at time t,
Figure GDA0003530551890000053
is the location state of agent i, which is a q-dimensional vector.
In a second aspect of the present invention, there is provided a terminal comprising a processor, a storage medium communicatively connected to the processor, the storage medium adapted to store a plurality of instructions, and the processor adapted to invoke the instructions in the storage medium to perform the steps of implementing the multi-agent system consistency control method according to any one of the above.
In a third aspect of the present invention, there is provided a storage medium storing one or more programs, the one or more programs being executable by one or more processors to implement the steps of the multi-agent system consistency control method of any of the above.
Compared with the prior art, the multi-agent system consistency control method, the terminal and the storage medium are provided by the invention, the multi-agent system consistency control method constructs the interactive topology of the multi-agent system according to the communication relation among the agents in the multi-agent system, further constructs the consistency control model of the multi-agent system according to the interactive topology, sets the constraints of the model to comprise consistency condition constraints and non-smooth inequality constraints, designs the optimal decoupling terminal of the consistency control model, and determines the control protocol of the multi-agent system according to the optimal decoupling terminal, so that the multi-agent system can simultaneously meet the consistency condition constraints and the non-smooth inequality constraints.
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FIG. 1 is a flow chart of an embodiment of a multi-agent system consistency control method provided by the present invention;
FIG. 2 is a schematic diagram of an interaction topology of a multi-agent system in an embodiment of a multi-agent system consistency control method provided by the present invention;
FIG. 3 is a first schematic diagram illustrating the validity verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 4 is a schematic diagram illustrating a second validity verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 5 is a third schematic diagram illustrating the validity verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 6 is a fourth schematic diagram illustrating the validity verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 7 is a schematic diagram showing the validity verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 8 is a diagram illustrating a sixth verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 9 is a seventh schematic diagram illustrating the validity verification result of the consistency control method of the multi-agent system according to the present invention;
FIG. 10 is a diagram illustrating the validity verification result of the consistency control method of the multi-agent system according to the present invention;
fig. 11 is a schematic diagram illustrating an embodiment of a terminal according to the present invention.
Detailed Description
In order to make the objects, technical solutions and effects of the present invention clearer and clearer, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example one
The multi-agent system consistency control method provided by the invention can be applied to a terminal, and the terminal can determine the control protocol of the multi-agent system through the multi-agent system consistency control method provided by the invention, so that each agent in the multi-agent system controls the self-movement according to the control protocol, and the multi-agent system consistency is realized.
In this specification, the euclidean norm is denoted by |, and
Figure GDA0003530551890000061
representing a set of real numbers.
Figure GDA0003530551890000062
Representing a set of all non-negative real n-dimensional vectors. Matrix array
Figure GDA0003530551890000063
Representing diagonal matrices, wherein the ith matrix diagonal element is corresponding to i e {1, …, n }
Figure GDA0003530551890000071
(Vector)
Figure GDA0003530551890000072
Representing an n-dimensional vector with all zero elements. (.)TRepresenting a transpose operation of the matrix.
As shown in fig. 1, in one embodiment of the multi-agent system consistency control method, the method comprises the steps of:
s100, obtaining the communication relation among all agents in the multi-agent system, and constructing the interactive topology of the multi-agent system according to the communication relation.
As shown in fig. 2, in the multi-agent system, a plurality of agents are included, and the information interaction relationship between the agents can be represented by a weighted undirected topology G (V, E, a), where V ═ 1, …, n is a set of information nodes identified by the agents in the topology, E is a set of information interactions formed between nodes in the topology,
Figure GDA0003530551890000073
is a weighted adjacency matrix, and n is the number of agent nodes. An information interaction edge eijE means that agent i and agent j can interact information in both directions. If the information interaction is edge eijE, then aij＝aji> 0, otherwise aijA is 0 andiii ∈ I, I is the set of agent numbers. Agent j ∈ NiIndicating that agent j is a neighbor of agent i, i.e. agent j and agent i interact via information edge eijIs E connected to NiA set of agent i neighbors. Both the in-degree and out-degree of agent i
Figure GDA0003530551890000074
The topology may be represented by a Laplace matrix of the topology, and the Laplace matrix of the interaction topology of the multi-agent system may be represented by a Laplace matrix of the interaction topology of the multi-agent systemIs LnWherein, L is ═ D-anRepresenting the subject matrix as an n-dimensional matrix, the matrix
Figure GDA0003530551890000075
Associated with agent i
Figure GDA0003530551890000076
Is a diagonal matrix of diagonal elements.
After determining the interaction topology of the multi-agent system, the multi-agent system consistency control method provided by the embodiment further includes the steps of:
s200, constructing a consistency control model of the multi-agent system according to the interactive topology.
Constraints in the consistency control model include consistency condition constraints and non-smooth inequality constraints, and particularly, the agents in the multi-agent system need to consider the problems of shortest execution time, minimum energy consumption, shortest path and the like in task execution, so that the completion of the tasks of the multi-agent system involves optimizing one or more cost functions, that is, the control of the agents in the multi-agent system needs to make the cost function values as small as possible. Based on this, a consistency control model of the multi-agent system can be constructed as follows:
Figure GDA0003530551890000081
Figure GDA0003530551890000082
wherein the content of the first and second substances,
Figure GDA0003530551890000083
i belongs to {1, 2.,. n }, n is the number of agents in the multi-agent system,
Figure GDA0003530551890000084
for the two local cost functions of agent i,
Figure GDA0003530551890000085
is a smooth convex function of the image to be displayed,
Figure GDA0003530551890000086
non-smooth convex function, state
Figure GDA0003530551890000087
Is a position state vector of agent i, is a q-dimensional vector, and
Figure GDA0003530551890000088
0nqis a zero vector of the nq-dimension,
Figure GDA0003530551890000089
is a matrix LnAnd IqKronecker product of LnLaplace matrix, I, which is the topology of the information interactionqIs a q-dimensional unit matrix and is,
Figure GDA00035305518900000810
is a non-smooth inequality constraint for agent i,
Figure GDA00035305518900000811
is a non-smooth convex function that can be approximated,
Figure GDA00035305518900000812
and
Figure GDA00035305518900000813
are respectively
Figure GDA00035305518900000814
-Liphoxitz in continuous with
Figure GDA00035305518900000815
-Liphoz continuous.
The consistency constraint is defined by Lx being 0nqRepresenting, non-smooth inequality constraints by
Figure GDA00035305518900000816
That is, in this embodiment, the cost function of the multi-agent system needs to be optimized based on the consistency condition and the non-smooth inequality constraint condition.
In this embodiment, the agent in the multi-agent system is a first-order integrator model, i.e. the kinematic model is:
Figure GDA00035305518900000817
wherein u isi(t) is the speed control quantity of agent i at time t,
Figure GDA00035305518900000818
is the location state of agent i, which is a q-dimensional vector. That is, in the consistency control model, the position state is a variable,
Figure GDA00035305518900000819
is the goal of consistency control.
S300, designing a decoupling operator of the optimal solution of the consistency control model.
After the consistency control model is established, designing a decoupling operator of an optimal solution of the consistency control model, and further designing a control protocol of the multi-agent system according to the decoupling operator of the optimal solution, so that the consistency control model can realize the optimal solution.
Specifically, the decoupling operator for designing the optimal solution of the consistency control model is as follows:
Figure GDA00035305518900000820
Figure GDA0003530551890000091
wherein, the lambda and the mu are Lagrange multipliers,
Figure GDA0003530551890000092
as an auxiliary variable, the number of variables,
Figure GDA0003530551890000093
for introducing parameters, alpha and beta are preset parameters, for any
Figure GDA0003530551890000094
i ∈ {1, …, n }, each having:
Figure GDA0003530551890000095
z*satisfies the following conditions:
Figure GDA0003530551890000096
and is
Figure GDA0003530551890000097
Specifically, in this embodiment, the design premise of the decoupling operator of the optimal solution includes:
1: for agent i e {1, …, n },
Figure GDA0003530551890000098
is a quadratic continuous differentiable function and is strongly convex, i.e. there is a constant c > 0 such that there is a contribution to agent i
Figure GDA0003530551890000099
Wherein
Figure GDA00035305518900000910
Figure GDA00035305518900000911
Without loss of generality, c > 1 can be assumed.
2: for all i e {1, …, n }, each
Figure GDA00035305518900000912
And
Figure GDA00035305518900000913
are (non-smooth) semi-continuous, tight, suitably convex functions at the bottom, and are approximatable.
3: the weighted topology G is connectionless.
4: in the inequality constraint
Figure GDA00035305518900000914
And
Figure GDA00035305518900000915
are respectively
Figure GDA00035305518900000916
-Liphoxitz in continuous with
Figure GDA00035305518900000917
-Liphoxitz continuous, wherein for j ═ 1,2 there are
Figure GDA00035305518900000918
5: there is always at least one feasible solution to the consistency control model.
For two non-smooth functions carried in the consistency control model
Figure GDA00035305518900000919
And
Figure GDA00035305518900000920
and (3) designing a decoupling double-near-end operator by a near-end technology and a segmentation method, and designing a smooth control protocol for the next step. First, the definition and correlation properties of the near-end operator are introduced. For a next semicontinuous convex function f (x), where
Figure GDA00035305518900000921
Which is at
Figure GDA00035305518900000922
Near-end operator of
Figure GDA00035305518900000923
Wherein
Figure GDA00035305518900000924
Represents the sub-gradient of f (x). f (x) being convex means
Figure GDA00035305518900000925
Monotonous, i.e. for all
Figure GDA00035305518900000926
And
Figure GDA00035305518900000927
are all provided with
Figure GDA00035305518900000928
x＝proxf[y]Is equivalent to
Figure GDA00035305518900000929
The specific form of the augmented Lagrange equation corresponding to the consistency control model is as follows:
K(x,λ,μ)＝F(x)+λT[g1(x)+g2(x)]+μTLx+xTLx
wherein
Figure GDA00035305518900000930
j is 1,2 and
Figure GDA00035305518900000931
under the above 5 premises, there is a feasible point
Figure GDA0003530551890000101
Is a feasible solution to the consistency control model if and only if there is one
Figure GDA0003530551890000102
For the location state to which the respective agent states eventually converge consistently,
Figure GDA0003530551890000103
and
Figure GDA0003530551890000104
so that
Figure GDA0003530551890000105
g1(x*)+g2(x*)≤0n,(λ*)T[g1(x*)+g2(x*)]＝0,Lx*＝0nqWherein
Figure GDA0003530551890000106
Figure GDA0003530551890000107
And is
Figure GDA0003530551890000108
Figure GDA0003530551890000109
Due to F1(x)+λTg2(x) The method is not possible to realize proximity, is inspired by a segmentation method, provides a decoupling operator based on a near-end technology, and needs to introduce a group of auxiliary variables
Figure GDA00035305518900001010
And parameters
Figure GDA00035305518900001011
To estimate
Figure GDA00035305518900001012
So that there is a set of z*Satisfy the requirement of
Figure GDA00035305518900001013
And is
Figure GDA00035305518900001014
Designing an optimal solution x of the consistency control problem (1) according to the properties of a near-end operator*The decoupled double near-end operator of (1) is:
Figure GDA00035305518900001018
Figure GDA00035305518900001015
wherein for any
Figure GDA00035305518900001016
i is equal to {1, …, n }, all have
Figure GDA00035305518900001017
Referring to fig. 1 again, after designing the decoupling operator of the optimal solution, the method for controlling consistency of a multi-agent system provided in this embodiment further includes the steps of:
s400, determining a control protocol of the multi-agent system according to the decoupling operator of the optimal solution, so that each agent in the multi-agent system controls the agent to move according to the control protocol.
Specifically, determining the control protocol of the multi-agent system according to the decoupling operator of the optimal solution is as follows:
Figure GDA0003530551890000111
Figure GDA0003530551890000112
Figure GDA0003530551890000113
Figure GDA0003530551890000114
wherein beta is more than 0 and less than 1/Lambdamax(L),0＜γ＜1-βΛmax(L),
Figure GDA0003530551890000115
Figure GDA0003530551890000116
0＜α＜mink＝1,2,3[οk]C is a constant, t is a time variable, Λmax(L) is the maximum eigenvalue of L,
Figure GDA0003530551890000117
each agent in the multi-agent system controls its own motion according to the control protocol so that the state of the multi-agent system reaches the optimal solution, and as described above, the kinematic model of the agent in the multi-agent system is:
Figure GDA0003530551890000118
wherein u isi(t) is the speed control quantity of agent i at time t,
Figure GDA0003530551890000119
the position state of the agent i is a q-dimensional vector, so that the speed control quantity of the agent at different moments can be obtained according to the position state x (t), and the agent controls the speed according to the speed control quantity to realize the consistency control of the system.
According to the control protocol, for a first-order integrator model multi-agent system under the control of the control protocol, a system state x, a Lagrange multiplier lambda corresponding to inequality constraint and respective optimal point value x*And λ*There is the following relationship between:
Figure GDA00035305518900001110
let (x)*,z*,λ*,μ*) Is a balance point of the control protocol. Firstly, a Lyapunov alternative function V (x, z, lambda, mu) is given1(x,z,λ)+V2(x,μ)+V3(x, λ) wherein each term is represented by
Figure GDA00035305518900001111
Figure GDA00035305518900001112
Figure GDA00035305518900001113
Wherein
Figure GDA0003530551890000121
For a multi-agent system containing n first-order integrator model agents, the following conclusions exist:
driven by the control protocol, x (t) converges over time and
Figure GDA0003530551890000122
is an optimal solution of the consistency control model, i.e., the state x (t) of the multi-agent system will eventually agree on the location of the optimal solution of the consistency control model and satisfy all local non-smooth inequality constraints. That is, according to the control protocol, it is possible to achieve consistency control of the multi-agent system, to achieve minimization of the total cost function of the system, and to satisfy consistency constraints and non-smooth inequality constraints.
This conclusion is demonstrated below: due to the fact that
Figure GDA0003530551890000123
The convexity of i e {1, …, n }, so that a conclusion can be drawn
Figure GDA0003530551890000124
Where G is a diagonal matrix whose diagonal elements are
Figure GDA0003530551890000125
And
Figure GDA0003530551890000126
note that 0 < beta < 1/Λmax(L) and xTLx≤Λmax(L)‖x‖2Thus, therefore, it is
Figure GDA0003530551890000127
From this, V is known2(x) Is more than or equal to 0. While noting λ*＞0nThus, therefore, it is
Figure GDA0003530551890000128
And is
Figure GDA0003530551890000129
Wherein h is1＝1-βΛmax(L)＞0。
From the above, it is clear that V (x, z, λ, μ) is non-negative and radially unbounded, V (x, z, λ, μ) ≧ 0, and V (x, z, λ, μ) ≧ 0 and only if (x, z, λ, μ) ═ x*,z*,λ*,μ*)。
Need to explain later
Figure GDA00035305518900001210
Derivable from the control protocol
Figure GDA0003530551890000131
Figure GDA0003530551890000132
Figure GDA0003530551890000133
Figure GDA0003530551890000134
Figure GDA0003530551890000135
Figure GDA0003530551890000136
And is provided with
Figure GDA0003530551890000137
Figure GDA0003530551890000138
Figure GDA0003530551890000139
From this, the Lyapunov alternative function V (x, y, V) can be known1,v2) Trajectory of derivative satisfies
Figure GDA00035305518900001310
Wherein
Figure GDA00035305518900001311
Presence of a normal number delta satisfying
Figure GDA00035305518900001312
And b is1＞0,b2Is greater than 0. And because of
Figure GDA00035305518900001313
Thus, it can be seen that
Figure GDA0003530551890000141
Further, since V (x, z, λ, μ) is positive, radially unbounded, and has a lower bound, (x) is known*,z*,λ*,μ*) Is Lyapunov stable and bounded by trajectories (x (t), z (t), λ (t), μ (t)). According to the principle of the Lassel invariant set, and the control protocol balance point is the optimal solution of the optimization problem in the consistency control model, it can be known that x (t) converges over time and
Figure GDA0003530551890000142
is an optimal solution of the consistency control model, i.e., the state x (t) of the multi-agent system will eventually agree on the location of the optimal solution of the consistency control model and satisfy all local non-smooth inequality constraints.
Due to a non-smooth cost function F in the consistency control model1(x) Representing a certain practical physical meaning, such as an indication function of a local area constraint that is satisfied when the location of an agent is required, while the above-mentioned control protocol fails to characterize the processing priorities of two non-smooth functions in the consistency control model, so that, in one possible implementation, a non-smooth cost function F is considered1(x) Is a high priority, i.e. a non-smooth cost function F1(x) Is/are as followsThe priority is higher than that of a non-smooth inequality constraint function, and a decoupling operator for designing the optimal solution of the consistency control model is as follows:
Figure GDA0003530551890000143
Figure GDA0003530551890000144
wherein, the lambda and the mu are Lagrange multipliers,
Figure GDA0003530551890000145
as an auxiliary variable, the number of variables,
Figure GDA0003530551890000146
for introducing parameters, alpha and beta are preset parameters, for any
Figure GDA0003530551890000147
i ∈ {1, …, n }, each having:
Figure GDA0003530551890000148
z*satisfies the following conditions:
Figure GDA0003530551890000149
and is
Figure GDA00035305518900001410
The corresponding control protocol is:
Figure GDA0003530551890000151
Figure GDA0003530551890000152
Figure GDA0003530551890000153
Figure GDA0003530551890000154
wherein beta is more than 0 and less than 1/Lambdamax(L),0＜γ＜1-βΛmax(L),
Figure GDA0003530551890000155
Figure GDA0003530551890000156
0＜α＜mink＝1,2,3[οk]C is a constant, t is a time variable, Λmax(L) is the maximum eigenvalue of L,
Figure GDA0003530551890000157
likewise, the system state x (t) converges over time and, by means of the control protocol, takes into account the priority and
Figure GDA0003530551890000158
is an optimal solution of the consistency control model, i.e., the state x (t) of the multi-agent system will eventually agree on the location of the optimal solution of the consistency control model and satisfy all local non-smooth inequality constraints. The certification process may be generalized simply from the foregoing conclusion certification and will not be discussed in detail herein.
The effectiveness of the multi-agent system consistency control method provided by this embodiment is verified through the corresponding simulation of the multi-agent system consistency control task with the non-smooth cost function and the non-smooth inequality constraint under the control protocol given in the multi-agent system consistency control method provided by this embodiment. Suppose the system consists of four agents modeled as first-order integrators, moving over a flat ground surface. The specific form of the multi-agent system consistency control model aiming at the simulation and having the non-smooth inequality constraint optimization problem is
minf(x)＝f0(x)+f1(x)
＝‖x-q‖2+Ω(x)
Figure GDA0003530551890000159
Wherein
Figure GDA0003530551890000161
In the unsmooth inequality constraint
Figure GDA0003530551890000162
And
Figure GDA0003530551890000163
local cost function f of agent ii(xi) Consisting of the following functions:
Figure GDA0003530551890000164
Figure GDA0003530551890000165
wherein
Figure GDA0003530551890000166
And
Figure GDA0003530551890000167
respectively represent a smooth cost function and a local limit set xi∈ΩiIs used to indicate the function. Cost function
Figure GDA0003530551890000168
The derivative of (a) of (b),
Figure GDA0003530551890000169
and
Figure GDA00035305518900001610
respectively of the near-end operator
Figure GDA00035305518900001611
Figure GDA00035305518900001612
Figure GDA00035305518900001613
Wherein
Figure GDA00035305518900001614
Piecewise function phii(x, y) is
Figure GDA00035305518900001615
The Laplace matrix of the undirected information interaction topology G of the multi-agent system is
Figure GDA00035305518900001616
Initial position of agent is x1(0)＝[-5m,4.3m]T，x2(0)＝[5.6m,4.7m]T，x3(0)＝[4.2m,-3.5m]TAnd x4(0)＝[-4.7m,-5.2m]T. Each agent has an inequality constraint parameter A1＝[0.3,0.9]T，A2＝[1.1,0.7]T，A3＝[0.2,0.4]T，A4＝[1.1,0.5]T，b＝[b1,b2,b3,b4]T＝[1,6.5,6,5]T. Let the Lagrange multiplier λ, μ and the auxiliary variable z have zero initial values. Simulation step length of tp0.1s, 8000 steps and 319.1 s.
The track change of the multi-agent system along with the motion of time under the driving of the control protocol obtained by the multi-agent system consistency control method provided by the invention is shown in fig. 3. System state
Figure GDA0003530551890000171
And
Figure GDA0003530551890000172
the track change of (2) is shown in fig. 4 and 5. Fig. 6 shows the trajectory variation of the global cost function f (x). FIG. 7 illustrates the non-smooth inequality constraints imposed on individual agents
Figure GDA0003530551890000173
The trajectory of i ∈ {1,2,3,4} over time. As can be seen from fig. 3 to 7, the state of the multi-agent system eventually converges to the optimal point satisfying the non-smooth inequality constraint, and the agreement is reached. Lagrange multiplier
Figure GDA0003530551890000174
λiThe trajectory of i e {1,2,3,4} over time is shown in FIGS. 8-10, while demonstrating the boundedness and convergence of the overall state of the multi-agent system.
In summary, the embodiment provides a method for controlling consistency of a multi-agent system, which constructs an interactive topology of the multi-agent system according to a communication relationship between agents in the multi-agent system, further constructs a consistency control model of the multi-agent system according to an interactive topology, sets constraints of the model including consistency condition constraints and non-smooth inequality constraints, designs an optimal decoupling terminal of the consistency control model, and determines a control protocol of the multi-agent system according to the optimal decoupling terminal, so that the multi-agent system can simultaneously satisfy the consistency condition constraints and the non-smooth inequality constraints.
It should be understood that, although the steps in the flowcharts shown in the figures of the present specification are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in the flowchart may include multiple sub-steps or multiple stages, which are not necessarily performed at the same time, but may be performed at different times, and the order of performing the sub-steps or stages is not necessarily sequential, but may be performed alternately or alternately with other steps or at least a portion of the sub-steps or stages of other steps.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, databases, or other media used in embodiments provided herein may include non-volatile and/or volatile memory. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
Example two
Based on the above embodiments, the present invention further provides a terminal, as shown in fig. 11, where the terminal includes a processor 10 and a memory 20. Fig. 11 shows only some of the components of the terminal, but it is to be understood that not all of the shown components are required to be implemented, and that more or fewer components may be implemented instead.
The memory 20 may in some embodiments be an internal storage unit of the terminal, such as a hard disk or a memory of the terminal. The memory 20 may also be an external storage device of the terminal in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like provided on the terminal. Further, the memory 20 may also include both an internal storage unit and an external storage device of the terminal. The memory 20 is used for storing application software installed in the terminal and various data. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, the memory 20 stores a multi-agent system consistency control program 30, and the multi-agent system consistency control program 30 can be executed by the processor 10, so as to implement the multi-agent system consistency control method of the present application.
The processor 10 may be, in some embodiments, a Central Processing Unit (CPU), microprocessor or other chip for running program codes stored in the memory 20 or Processing data, such as executing the multi-agent system consistency control method.
EXAMPLE III
The present invention also provides a storage medium having one or more programs stored thereon that are executable by one or more processors to implement the steps of the multi-agent system consistency control method as described above.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (8)

1. A multi-agent system consistency control method, characterized in that the method comprises:
acquiring communication relations among all agents in a multi-agent system, and constructing an interactive topology of the multi-agent system according to the communication relations;
constructing a consistency control model of the multi-agent system according to the interaction topology, wherein constraints of the consistency control model comprise consistency condition constraints and non-smooth inequality constraints;
designing a decoupling operator of an optimal solution of the consistency control model;
determining a control protocol of the multi-agent system according to a decoupling operator of the optimal solution, so that each agent in the multi-agent system controls its own motion according to the control protocol;
the kinematic model of the agent in the multi-agent system is:
Figure FDA0003539155690000011
wherein u isi(t) is the speed control quantity of agent i at time t,
Figure FDA0003539155690000012
is the position state of agent i, which is a q-dimensional vector;
the building a consistency control model of the multi-agent system according to the interaction topology includes:
obtaining cost functions and non-smooth inequality constraint information of each agent in the multi-agent system, and constructing a consistency control model of the multi-agent system according to the interactive topology and the kinematics model as follows:
Figure FDA0003539155690000013
Figure FDA0003539155690000014
wherein the content of the first and second substances,
Figure FDA0003539155690000015
n is the number of agents in the multi-agent system, fi(xi)＝fi 0(xi)+fi 1(xi)，fi 0、fi 1Two local cost functions, f, for agent ii 0Is a smooth convex function, fi 1Is a non-smooth convex function of the image,
and is
Figure FDA0003539155690000017
0nqIs a zero vector of the nq-dimension,
Figure FDA0003539155690000018
is a matrix LnAnd IqKronecker product of LnIs a Laplace matrix of the interaction topology, IqIs a q-dimensional unit matrix and is,
Figure FDA0003539155690000021
is a non-smooth inequality constraint for agent i,
Figure FDA0003539155690000022
is a non-smooth convex function that can be approximated,
Figure FDA0003539155690000023
and
Figure FDA0003539155690000024
are respectively
Figure FDA0003539155690000025
-Liphoxitz in continuous with
Figure FDA0003539155690000026
-Liphoz continuous.
2. The multi-agent system consistency control method as recited in claim 1, wherein said constructing an interaction topology of the multi-agent system according to the communication relationships comprises:
the laplacian matrix of the interaction topology is: l isnD-a, wherein the matrix
Figure FDA0003539155690000027
Associated with agent i
Figure FDA0003539155690000028
Agent j and agent i via information interaction edge e as diagonal matrix of diagonal elementsijE belongs to E connection and information interaction edge EijE represents that the agent i and the agent j can exchange information in two directions, if the information exchange is carried out, EijE, then aij＝aji> 0, otherwise aij＝0，
Figure FDA0003539155690000029
Is a weighted adjacency matrix.
3. The multi-agent system consistency control method of claim 1, wherein said designing a decoupling operator of an optimal solution for said consistency control model comprises:
the decoupling operator for designing the optimal solution of the consistency control model is as follows:
Figure FDA00035391556900000210
Figure FDA00035391556900000211
wherein x is*And is the optimal solution of the state of the multi-agent system, lambda and mu are Lagrange multipliers,
Figure FDA00035391556900000212
for introducing parameters, alpha and beta are preset parameters, for any
Figure FDA00035391556900000213
Figure FDA00035391556900000214
All have:
Figure FDA00035391556900000215
z*satisfies the following conditions:
Figure FDA00035391556900000216
and is
Figure FDA00035391556900000217
Figure FDA00035391556900000218
4. A multi-agent system consistency control method according to claim 3, characterized in that the control protocol of the multi-agent system is:
Figure FDA0003539155690000031
Figure FDA0003539155690000032
Figure FDA0003539155690000033
Figure FDA0003539155690000034
wherein beta is more than 0 and less than 1/Lambdamax(L),0＜γ＜1-βΛmax(L),
Figure FDA0003539155690000035
Figure FDA0003539155690000036
0＜α＜mink＝1,2,3[οk]C is a constant, t is a time variable, Λmax(L) is the maximum eigenvalue of L,
Figure FDA0003539155690000037
5. the multi-agent system consistency control method of claim 1, wherein said designing an optimal solution for the consistency control model comprises:
the decoupling operator for designing the optimal solution of the consistency control model is as follows:
Figure FDA0003539155690000038
Figure FDA0003539155690000039
wherein x is*And is the optimal solution of the state of the multi-agent system, lambda and mu are Lagrange multipliers,
Figure FDA00035391556900000310
for introducing parameters, alpha and beta are preset parameters, for any
Figure FDA00035391556900000311
Figure FDA00035391556900000312
All have:
Figure FDA00035391556900000313
z*satisfies the following conditions:
Figure FDA00035391556900000314
and is
Figure FDA00035391556900000315
Figure FDA00035391556900000316
6. The multi-agent system consistency control method according to claim 5, wherein the control protocol of the multi-agent system is:
Figure FDA0003539155690000041
Figure FDA0003539155690000042
Figure FDA0003539155690000043
Figure FDA0003539155690000044
wherein beta is more than 0 and less than 1/Lambdamax(L),0＜γ＜1-βΛmax(L),
Figure FDA0003539155690000045
Figure FDA0003539155690000046
0＜α＜mink＝1,2,3[οk]C is a constant, t is a time variable, Λmax(L) is the maximum eigenvalue of L,
Figure FDA0003539155690000047
7. a terminal, characterized in that the terminal comprises: a processor, a storage medium communicatively connected to the processor, the storage medium adapted to store a plurality of instructions, the processor adapted to invoke the instructions in the storage medium to perform the steps of implementing the multi-agent system consistency control method of any of the preceding claims 1-6.
8. A storage medium storing one or more programs, the one or more programs being executable by one or more processors to implement the steps of the multi-agent system consistency control method as claimed in any one of claims 1 to 6.
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