CN114935931A - Time-varying heterogeneous multi-agent consistency control method and system - Google Patents

Time-varying heterogeneous multi-agent consistency control method and system Download PDF

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CN114935931A
CN114935931A CN202210492964.7A CN202210492964A CN114935931A CN 114935931 A CN114935931 A CN 114935931A CN 202210492964 A CN202210492964 A CN 202210492964A CN 114935931 A CN114935931 A CN 114935931A
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CN114935931B (en
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郭胜辉
相国梁
唐明珠
尤任阳
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Suzhou University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

The invention discloses a method and a system for controlling consistency of time-varying heterogeneous multi-agent, which comprises the following steps: establishing an input-output relation model and a connection topological graph of the multi-agent system; according to the input-output relation model, a Kalman observer is established for any sensor in a single intelligent agent, and state estimation information of the intelligent agent under any sensor is obtained; setting an optimal information fusion criterion, and performing linear weighted fusion on state estimation information of all sensors under the intelligent agent to obtain optimal state estimation information of the intelligent agent; and setting a consistency control protocol according to the optimal state estimation information of the intelligent agent, and performing consistency control on the multi-intelligent agent. The invention realizes the consistency control of time varying structure multi-agent under the condition of multi-sensors.

Description

Time-varying heterogeneous multi-agent consistency control method and system
Technical Field
The invention relates to the technical field of multi-agent control, in particular to a time-varying heterogeneous multi-agent consistency control method and system.
Background
In the multi-agent consistency control research, the considered situation is too simple, and the situation containing random noise and time-varying isomerism is rarely considered. Most studies do not simultaneously consider the situation of time-varying isomerism, such as [ 1 ] study of coherence only in time-varying situations and [ 2 ] study of coherence only in heterogeneous situations. This results in a less versatile and less applicable application. In addition, the existing multi-agent is generally researched under the condition of a single sensor, and when the sensor fails, the system state is difficult to estimate, so that effective control is performed.
[1]J.H.Jiang and Y.Y.Jiang，”Leader-following consensus of linear time-varying multi-agent systems under fixed and switching topologies，”Automatica， vol.113，Mar 2020，Art no.108804.
[2]Z.Gao，H.Zhang，Y.Wang and Y.Mu，”Time-varying output formation-containment control for homogeneous/heterogeneous descrip-tor fractional-order multi-agent systems，”Information Sciences，vol.567，pp.146-166， Aug 2021.
Disclosure of Invention
The invention aims to provide a time-varying heterogeneous multi-agent consistency control method and a time-varying heterogeneous multi-agent consistency control system, which are used for realizing consistency control on time-varying heterogeneous multi-agents under the condition of multiple sensors.
In order to solve the technical problem, the invention provides a time-varying heterogeneous multi-agent consistency control method, which comprises the following steps:
s1, establishing an input-output relation model and a connection topological graph of the multi-agent system, wherein each agent in the input-output relation model is provided with a plurality of sensors and contains random noise;
s2, establishing a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model, and obtaining state estimation information of the intelligent agent under any sensor;
s3, setting an optimal information fusion criterion, and performing linear weighted fusion on the state estimation information of all the sensors under the intelligent agent to obtain the optimal state estimation information of the intelligent agent; the optimal information fusion criterion is that a minimum covariance matrix of state estimation information of any sensor and another sensor of the intelligent agent is taken as a weighting matrix of linear weighting;
and S4, setting a consistency control protocol according to the optimal state estimation information of the agents, and performing consistency control on the multiple agents, wherein the state feedback gain in the consistency control protocol is calculated by adopting a least square method.
As a further improvement of the invention, there are N agents in the multi-agent system, and the ith agent has N i The sensor, for the ith agent and the jth sensor of the agent, the input-output relation model at the tth moment is as follows:
x i (t)＝A i (t-1)x i (t-1)+B i (t-1)u i (t-1)+w i (t-1)
Figure BDA0003632257340000021
wherein ,xi (t)∈R n Indicating the system state of the ith agent, u i (t)∈R k Representing the system input, y, of the ith agent i j (t)∈R p Indicating measurable input from jth sensor of ith agent, R n 、R k， 、R p Respectively representing n-dimensional, k-dimensional and p-dimensional vectors of the system; w is a i(t) and
Figure BDA0003632257340000022
is an independent zero mean noise sequence; matrix of
Figure BDA0003632257340000023
Respectively a system state matrix, a system input matrix and a system observation matrix.
As a further development of the invention, the connection topology is
Figure BDA0003632257340000024
wherein ,
Figure BDA00036322573400000317
a collection of nodes in the graph is represented,
Figure BDA0003632257340000031
representing a set of edges connecting the nodes in the diagram,
Figure BDA0003632257340000032
an adjacent weight matrix representing the graph and having a ii ＝0；
When (i, j) ∈ ε, a ij If the number of the nodes is more than 0, the node i can receive the information of the node j, otherwise, a ij ＝0；
Figure BDA0003632257340000033
Representing the set of all adjacent points of the node i; the degree of entry of node i is defined as
Figure BDA0003632257340000034
Let D be diag (D (1), D (2), …, D (n)), diag representing the diagonal block matrix, the laplacian matrix of the figure is
Figure BDA0003632257340000035
As a further improvement of the present invention, the step S2 specifically includes: creating a Kalman observer for the jth observer of the ith single agent:
Figure BDA0003632257340000036
Figure BDA0003632257340000037
Figure BDA0003632257340000038
Figure BDA0003632257340000039
Figure BDA00036322573400000310
wherein ,
Figure BDA00036322573400000311
representing the state estimate of agent i at sensor j,
Figure BDA00036322573400000312
the post-state estimation value is represented,
Figure BDA00036322573400000313
representing the estimated value of the preamble state, P i j (t +1| t) denotes a pre-covariance matrix, P i j (t +1| t +1) represents a post covariance matrix,
Figure BDA00036322573400000314
for Kalman gain, Q i (t) is w i (k) The covariance of (a) of (b),
Figure BDA00036322573400000315
is composed of
Figure BDA00036322573400000316
The covariance of (a).
As a further improvement of the present invention, the optimal state estimation information of agent i:
Figure BDA0003632257340000041
Figure BDA0003632257340000042
wherein ,
Figure BDA0003632257340000043
a matrix of state estimation gain coefficients is represented,
Figure BDA0003632257340000044
P i jk (t) is a covariance matrix of the j sensor of the ith agent and the estimated value of the k sensor at time t,
Figure BDA0003632257340000045
representing a state estimation matrix; i is n Is an n x n dimensional unit matrix,
Figure BDA0003632257340000046
is N i ×N i Wherein each block is an n × n dimensional identity matrix; if a certain matrix or vector a is written as a T Form a of T Denoted as transpose of a.
As a further improvement of the present invention, the obtaining of the optimal state estimation information of the agent in step S3 specifically includes:
order to
Figure BDA0003632257340000047
According to P i jk Then, there are:
Figure BDA0003632257340000048
when in use
Figure BDA0003632257340000049
When the minimum value is reached, a Kalman observer of the agent i obtains an optimal fusion estimation value;
order to
Figure BDA00036322573400000410
Λ i In order to be a lagrange operator, the lagrange operator,
then
Figure BDA00036322573400000411
When, L i (t) taking the minimum value, i.e.
Figure BDA00036322573400000412
Namely, it is
Figure BDA0003632257340000051
Solving to obtain:
Figure BDA0003632257340000052
the final state estimation value of the agent i is obtained as follows:
Figure BDA0003632257340000053
wherein ,
Figure BDA0003632257340000054
as a further improvement of the present invention, the step S4 specifically includes the following steps:
order to
Figure BDA0003632257340000055
u(t)＝[u 1 (t) T … u N (t) T ] T ，w(t)＝[w 1 (t) T … w N (t) T ] T ， A(t)＝diag[A 1 (t) … A N (t)]，B(t)＝diag[B 1 (t) … B N (t)]，T(t)＝diag[T 1 (t) … T N (t)]；
x(t)＝[x 1 (t) T … x N (t) T ] T ，
Figure BDA0003632257340000056
δ (t) represents the synchronization error,
Figure BDA0003632257340000058
representing the mean value of the state if a certain matrix or vector a is written as a T Form a of T Transpose denoted as a; t is i (t) is an input gain matrix;
according to the least square method, let
Figure BDA0003632257340000057
The multi-agent implements coherence control, where S is an arbitrary matrix and + represents the pseudo-inverse.
As a further improvement of the present invention, obtaining the state feedback gain t (t) specifically includes:
according to the synchronization error δ (t), there are:
Figure BDA0003632257340000061
wherein E is a mean square error matrix,
Figure BDA0003632257340000062
will be provided with
Figure BDA0003632257340000063
Approximately x (t), then:
Figure BDA0003632257340000064
Figure BDA0003632257340000065
order to
Figure BDA0003632257340000066
Then
Figure BDA0003632257340000067
When A (t) -B (t) T (t) L N When equal to 0, i.e.
Figure BDA0003632257340000068
And meanwhile, the multi-agent realizes consistency control.
A time-varying heterogeneous multi-agent consistency control system adopts the time-varying heterogeneous multi-agent consistency control method to carry out multi-agent consistency control.
As a further improvement of the present invention, there are N agents in the multi-agent system, and the ith agent has N i The sensor, the I intelligent agent and the I/O relation model of the intelligent agent at the jth moment of the jth sensor are as follows:
x i (t)＝A i (t-1)x i (t-1)+B i (t-1)u i (t-1)+w i (t-1)
Figure BDA0003632257340000071
wherein ,xi (t)∈R n Indicating the system state of the ith agent, u i (t)∈R k Representing the system input of the ith agent,
Figure BDA0003632257340000072
indicating measurable input from jth sensor of ith agent, R n ，R k， ，R p ； w i(k) and
Figure BDA0003632257340000073
is an independent zero mean noise sequence; matrix array
Figure BDA0003632257340000074
Respectively a system state matrix, a system input matrix and a system observation matrix.
The invention has the beneficial effects that: when the multi-agent system contains random noise and the system structure is time-varying and heterogeneous, the invention aims to realize consistency control on the multi-agent system under the condition of multiple sensors: the optimal information fusion criterion is the optimal information fusion criterion of matrix weighting in the linear minimum variance meaning in the linear weighting meaning, and is applied to a multi-agent system under the multi-sensor condition, and finally, a multi-agent consistency control algorithm under the multi-sensor condition is provided, so that the calculation method is simpler and the calculated amount is less.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a topological diagram of a vehicle formation according to a first embodiment of the present invention;
FIG. 3 is a diagram of a vehicle formation track according to a first embodiment of the present invention;
FIG. 4 is a state diagram of a vehicle formation according to a first embodiment of the present invention;
fig. 5 shows the actual value, estimated value and fusion estimated value of the vehicle 1 according to the first embodiment of the present invention;
fig. 6 shows the actual, estimated and fused estimated values of the vehicle 2 according to the first embodiment of the present invention;
fig. 7 shows the actual, estimated and fused estimated values of the vehicle 3 according to the first embodiment of the present invention;
FIG. 8 shows the actual, estimated and fused estimated values of the vehicle 4 according to the first embodiment of the present invention;
FIG. 9 shows the actual, estimated and fused estimated values of the vehicle 5 according to the first embodiment of the present invention;
FIG. 10 shows the actual, estimated and fused estimated values of the vehicle 6 according to the first embodiment of the present invention;
FIG. 11 is a multi-agent topology of a second embodiment of the present invention;
FIG. 12 is a state diagram of a multi-agent system in accordance with a second embodiment of the invention;
fig. 13 shows the actual value, estimated value, and fusion estimated value of agent1 according to the second embodiment of the present invention;
FIG. 14 shows the actual, estimated and fusion estimated values of agent 2 according to the second embodiment of the present invention;
fig. 15 shows the actual value, estimated value and fusion estimated value of agent 3 according to the second embodiment of the present invention;
fig. 16 shows the actual value, estimated value and fusion estimated value of agent 4 according to the second embodiment of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
Referring to fig. 1, the present invention provides a method for controlling consistency of time-varying heterogeneous multi-agent, comprising the following steps:
s1, establishing an input-output relation model and a connection topological graph of the multi-agent system, wherein each agent in the input-output relation model is provided with a plurality of sensors and contains random noise;
s2, establishing a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model, and obtaining state estimation information of the intelligent agent under any sensor;
s3, setting an optimal information fusion criterion, and performing linear weighted fusion on the state estimation information of all sensors under the intelligent agent to obtain the optimal state estimation information of the intelligent agent; the optimal information fusion criterion is that a minimum covariance matrix of state estimation information of any sensor and another sensor of the intelligent agent is taken as a weighting matrix of linear weighting;
and S4, setting a consistency control protocol according to the optimal state estimation information of the agents, and performing consistency control on the multiple agents, wherein the state feedback gain in the consistency control protocol is calculated by adopting a least square method.
The invention provides an optimal information fusion criterion, which is based on linear weighting, adopts a matrix weighting optimal information fusion criterion based on linear minimum variance, and is applied to a multi-agent system under the condition of the multi-sensor, and finally provides a multi-agent consistency control algorithm under the condition of the multi-sensor.
The method comprises the following steps:
(1) establishing an input-output relationship model and a connection topological graph for describing the multi-agent system;
the model is as follows:
there are N agents, the ith agent has N i The model of the ith intelligent agent and the jth moment of the jth sensor of the intelligent agent is as follows:
x i (t)＝A i (t-1)x i (t-1)+B i (t-1)u i (t-1)+w i (t-1)
Figure BDA0003632257340000091
wherein ：xi (t)∈R n ，u i (t)∈R k ，
Figure BDA0003632257340000092
Respectively representing system state, system input, measurable output, w i(k) and
Figure BDA0003632257340000093
are independent zero mean noise sequences with their covariances Q i And
Figure BDA0003632257340000094
matrix array
Figure BDA0003632257340000095
A system state matrix, a system input matrix and a system observation matrix;
Figure BDA0003632257340000096
representing m × k block matrices, each matrix being an n × n identity matrix;
for undirected topological graph of intelligent agent
Figure BDA0003632257340000097
Is shown in which
Figure BDA00036322573400000911
A collection of nodes in the graph is represented,
Figure BDA0003632257340000098
a set of edges connecting the nodes in the diagram is represented,
Figure BDA0003632257340000099
an adjacent weight matrix representing the graph and having a ii 0; when (i, j) ∈ ε, a ij > 0, meaning that node i can receive information from node j, otherwise a ij ＝0；
Figure BDA00036322573400000910
Representing the set of all adjacent points of the node i; the degree of entry of node i is defined as
Figure BDA0003632257340000101
Let D be diag (D (1), D (2), …, D (n)), diag denote the diagonal block matrix, and the laplacian matrix of the figure is
Figure BDA0003632257340000102
(2) From the input-output equation of step (1), we create a Kalman observer for the jth observer of the ith single agent:
Figure BDA0003632257340000103
Figure BDA0003632257340000104
Figure BDA0003632257340000105
Figure BDA0003632257340000106
Figure BDA0003632257340000107
wherein ：
Figure BDA0003632257340000108
an estimate representing the state of agent i at sensor j,
Figure BDA0003632257340000109
it is indicated that the post-estimation,
Figure BDA00036322573400001010
denotes a preamble estimate, P i j (t +1| t) denotes a pre-covariance matrix, P i j (t +1| t +1) represents a post covariance matrix,
Figure BDA00036322573400001011
is a Kalman gain
(3) Obtaining the estimation information of the observer of the intelligent agent by the step (2), and making the final estimation of the ith intelligent agent be
Figure BDA00036322573400001012
Setting the most fusion criterion according to the unbiased principle:
order to
Figure BDA00036322573400001013
Then there are:
Figure BDA00036322573400001014
order to
Figure BDA0003632257340000111
P i jk Is the covariance matrix of the jth sensor and the estimated value of the kth sensor of the ith agent
Figure BDA0003632257340000112
When in use
Figure BDA0003632257340000113
When the minimum, the observer obtains the optimal fusion estimation;
order to
Figure BDA0003632257340000114
Λ i Is Lagrangian, then
Figure BDA0003632257340000115
When it is, take the minimum value
Namely, it is
Figure BDA0003632257340000116
Namely, it is
Figure BDA0003632257340000117
Obtain the result
Figure BDA0003632257340000118
The final estimate of agent i is then:
Figure BDA0003632257340000119
wherein
Figure BDA00036322573400001110
(4) According to the estimation information, setting a consistency control protocol to enable the multi-agent to realize consistency control:
order to
Figure BDA00036322573400001111
A＝diag[A 1 … A N ] T ，B＝diag[B 1 … B N ] T ，T＝diag[T 1 … T N ] T
Figure BDA0003632257340000121
Delta represents the error in the synchronization and is,
then there is
Figure BDA0003632257340000122
wherein ,
Figure BDA0003632257340000123
since the estimation obtained in step (3) is an unbiased estimation, will
Figure BDA0003632257340000129
Approximately looking at x, one can obtain
Figure BDA0003632257340000124
Then the
Figure BDA0003632257340000125
Order to
Figure BDA0003632257340000126
Then
Figure BDA0003632257340000127
When A (t) -B (t) T (t) L N When equal to 0, i.e.
Figure BDA0003632257340000128
And then, the multi-agent realizes consistency control, wherein S is an arbitrary matrix, and + represents a pseudo inverse.
Example one
As shown in fig. 2, this embodiment provides a homogeneous vehicle formation system, which uses a time-varying heterogeneous multi-agent consistency control method as described above for control, the leader of the vehicle formation system knows the destination information and moves towards the destination (destination), the follower follows the destination, and their location information is monitored by three satellites (satellites) on the sky. The leader moves along y-5 sin (0.2x), then:
the motion model of the ith vehicle at the kth moment is
Figure BDA0003632257340000131
Figure BDA0003632257340000132
x i Is a four-dimensional column vector in which,
Figure BDA0003632257340000133
for the x-direction position at the time k,
Figure BDA0003632257340000134
is the y-direction displacement at time k.
Figure BDA0003632257340000135
Is the average input speed in the x-direction,
Figure BDA0003632257340000136
is the average input speed in the y-direction,
Figure BDA0003632257340000137
observing the information of the ith vehicle position for the jth satellite, and when the sampling interval is delta t, the equation is:
Figure BDA0003632257340000138
wherein ,
Figure BDA0003632257340000139
simulation studies were performed for the above cases:
as a result, as shown in FIG. 3, the vehicles are grouped into tracks, and the vehicles 1-6(Agent1-6) move along the tracks; the vehicle formation state diagram of fig. 4 shows that the vehicles 1-6 finally converge to a close state, thereby achieving good consistency control, and fig. 5-10 show the actual value (actual) and the estimated value (estimate) of the states of the vehicles 1-6, respectively, and it can be seen that the estimated values are extremely close to the actual values. Since the agents of fig. 5 and 6 have only one sensor and therefore only one estimation value, and the agents of fig. 7-10 are equipped with a plurality of sensors, it can be seen that the advantages of the algorithm proposed by the present patent are shown in terms of the estimation values (sensors) made by the sensors being less accurate than the fusion estimation (fusion).
Example two
A heterogeneous abstract system topology as shown in fig. 11 is established, a box represents a sensor (Sensors), a round box represents an Agent (Agent), and various parameters are as follows:
Figure BDA0003632257340000141
Figure BDA0003632257340000142
Figure BDA0003632257340000143
Figure BDA0003632257340000144
Q 1 …Q 4 ＝0.05 2 *I 3 ，
Figure BDA0003632257340000145
Figure BDA0003632257340000146
Figure BDA0003632257340000147
Figure BDA0003632257340000148
Figure BDA0003632257340000149
simulation studies were performed for the above cases:
as shown in FIG. 12, which illustrates a multi-agent system state diagram, it can be seen that agents 1-4 eventually converge to a close state, thereby achieving good consistency control;
as the actual values and the estimated values of the states of the agents 1 to 4 of the multi-agent system are shown in fig. 13 to 16, it can be seen that the estimated values are extremely close to the actual values, and the actual values cannot be completely and accurately estimated due to the influence of random noise, but the estimation precision of the invention can be controlled within the error range of 0.05 noise standard deviation; it can be seen from the figure that the estimation value (sensor) made by the sensor is not accurate from the fusion estimation (fusion), showing the superiority of the algorithm proposed by the patent.
In the invention, the least square under the condition of multiple sensors is proved to have good data fusion estimation effect through mathematical reasoning, then aiming at the multi-agent system under the condition of multiple sensors, a consistency control protocol design method based on an observer is provided, and the consistency control of the multiple agents is realized under the interference of random noise.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (10)

1. A time-varying heterogeneous multi-agent consistency control method is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing an input-output relation model and a connection topological graph of the multi-agent system, wherein each agent in the input-output relation model is provided with a plurality of sensors and contains random noise;
s2, establishing a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model, and obtaining state estimation information of the intelligent agent under any sensor;
s3, setting an optimal information fusion criterion, and performing linear weighted fusion on the state estimation information of all sensors under the intelligent agent to obtain the optimal state estimation information of the intelligent agent; the optimal information fusion criterion is that a minimum covariance matrix of state estimation information of any sensor and another sensor of the intelligent agent is taken as a weighting matrix of linear weighting;
and S4, setting a consistency control protocol according to the optimal state estimation information of the agent, and performing consistency control on the multi-agent, wherein the state feedback gain in the consistency control protocol is calculated by adopting a least square method.
2. As claimed in claim1, the consistency control method of the time-varying heterogeneous multi-agent is characterized in that: there are N agents in the multi-agent system, and the ith agent has N i The sensor, for the ith agent and the jth sensor of the agent, the input-output relation model at the tth moment is as follows:
x i (t)＝A i (t-1)x i (t-1)+B i (t-1)u i (t-1)+w i (t-1)
Figure FDA0003632257330000011
wherein ,xi (t)∈R n Represents the system state of the ith agent, u i (t)∈R k Representing the system input of the ith agent,
Figure FDA0003632257330000012
indicating measurable input from jth sensor of ith agent, R n 、R k， 、R p Respectively representing n-dimensional, k-dimensional and p-dimensional vectors of the system; w is a i(t) and
Figure FDA0003632257330000013
is an independent zero mean noise sequence; matrix A i ，B i ，
Figure FDA0003632257330000014
Respectively a system state matrix, a system input matrix and a system observation matrix.
3. A time-varying heterogeneous multi-agent coherence control method as claimed in claim 1, wherein: the connection topology
Figure FDA0003632257330000021
wherein ,
Figure FDA0003632257330000022
a collection of nodes in the graph is represented,
Figure FDA0003632257330000023
representing a set of edges connecting the nodes in the diagram,
Figure FDA0003632257330000024
an adjacent weight matrix representing the graph and having a ii ＝0；
When (i, j) ∈ epsilon,
Figure FDA0003632257330000025
the node i can receive the information of the node j, otherwise
Figure FDA0003632257330000026
Figure FDA0003632257330000027
Representing the set of all adjacent points of the node i; the degree of entry of node i is defined as
Figure FDA0003632257330000028
Let D be diag (D (1), D (2), …, D (n)), diag representing the diagonal block matrix, the laplacian matrix of the figure is
Figure FDA0003632257330000029
4. A time-varying heterogeneous multi-agent coherence control method as claimed in claim 2, wherein: the step S2 specifically includes: creating a Kalman observer for the jth observer of the ith single agent:
Figure FDA00036322573300000210
Figure FDA00036322573300000211
Figure FDA00036322573300000212
Figure FDA00036322573300000213
Figure FDA00036322573300000214
wherein ,
Figure FDA00036322573300000215
representing the state estimate of agent i at sensor j,
Figure FDA00036322573300000216
the post-state estimation value is represented,
Figure FDA00036322573300000217
representing the estimated value of the preamble state, P i j (t +1| t) denotes a pre-covariance matrix, P i j (t +1| t +1) represents a post covariance matrix,
Figure FDA0003632257330000031
for Kalman gain, Q i (t) is w i (k) The covariance of (a) of (b),
Figure FDA0003632257330000032
is composed of
Figure FDA0003632257330000033
The covariance of (a).
5. The method of time-varying heterogeneous multi-agent coherence control of claim 4, wherein: optimal state estimation information of agent i:
Figure FDA0003632257330000034
Figure FDA0003632257330000035
wherein ,
Figure FDA0003632257330000036
a matrix of state estimation gain coefficients is represented,
Figure FDA0003632257330000037
P i jk (t) is a covariance matrix of the j sensor of the ith agent and the estimated value of the k sensor at time t,
Figure FDA0003632257330000038
representing a state estimation matrix; i is n Is an n x n dimensional identity matrix,
Figure FDA0003632257330000039
is N i ×N i Wherein each block is an n × n dimensional identity matrix; if a certain matrix or vector a is written as a T Form a of T Denoted as transpose of a.
6. The method of time-varying heterogeneous multi-agent coherence control of claim 5, wherein: the obtaining of the optimal state estimation information of the agent in step S3 specifically includes:
order to
Figure FDA00036322573300000310
According to P i jk Then, there are:
Figure FDA00036322573300000311
when in use
Figure FDA00036322573300000312
When the minimum time is reached, a Kalman observer of the agent i obtains an optimal fusion estimation value;
order to
Figure FDA0003632257330000041
Λ i In order to be a lagrange operator, the lagrange operator,
then
Figure FDA0003632257330000042
When L is i (t) taking the minimum value, i.e.
Figure FDA0003632257330000043
Namely, it is
Figure FDA0003632257330000044
Solving to obtain:
Figure FDA0003632257330000045
the final state estimation value of the agent i is obtained as follows:
Figure FDA0003632257330000046
wherein ,
Figure FDA0003632257330000047
7. a time-varying heterogeneous multi-agent coherence control method as claimed in claim 1, wherein: the step S4 specifically includes the following steps:
order to
Figure FDA0003632257330000048
u(t)＝[u 1 (t) T … u N (t) T ] T ，w(t)＝[w 1 (t) T … w N (t) T ] T ，A(t)＝diag[A 1 (t) … A N (t)]，B(t)＝diag[B 1 (t) … B N (t)]，T(t)＝diag[T 1 (t) … T N (t)]；
x(t)＝[x 1 (t) T … x N (t) T ] T ，
Figure FDA0003632257330000051
δ (t) represents the synchronization error,
Figure FDA0003632257330000052
representing the mean value of the state if a certain matrix or vector a is written as a T Form, then a T Transpose denoted as a; t is i (t) is an input gain matrix;
according to the least square method, let
Figure FDA0003632257330000053
The multi-agent implements coherency control, where S is an arbitrary matrix and + represents the pseudo-inverse.
8. A time-varying heterogeneous multi-agent coherence control method as claimed in claim 1, wherein: obtaining the state feedback gain t (t), which specifically includes:
according to the synchronization error δ (t), there are:
Figure FDA0003632257330000054
wherein E is a mean square error matrix,
Figure FDA0003632257330000055
will be provided with
Figure FDA00036322573300000511
Approximately x (t), then:
Figure FDA0003632257330000056
Figure FDA0003632257330000057
order to
Figure FDA0003632257330000058
Then
Figure FDA0003632257330000059
When A (t) -B (t) T (t) L N When equal to 0, i.e.
Figure FDA00036322573300000510
And meanwhile, the multi-agent realizes consistency control.
9. A time-varying heterogeneous multi-agent consistency control system is characterized in that: multi-agent consistency control using a time varying heterogeneous multi-agent consistency control method as claimed in any one of claims 1 to 8.
10. Such asA time-varying heterogeneous multi-agent coherence control system of claim 9, wherein: there are N agents in the multi-agent system, and the ith agent has N i The sensor, for the ith agent and the jth sensor of the agent, the input-output relation model at the tth moment is as follows:
x i (t)＝A i (t-1)x i (t-1)+B i (t-1)u i (t-1)+w i (t-1)
Figure FDA0003632257330000061
wherein ,xi (t)∈R n Indicating the system state of the ith agent, u i (t)∈R k Representing the system input of the ith agent,
Figure FDA0003632257330000062
indicating measurable input from jth sensor of ith agent, R n ，R k， ，R p ；w i(k) and
Figure FDA0003632257330000063
is an independent zero mean noise sequence; matrix A i ，B i ，
Figure FDA0003632257330000064
Respectively a system state matrix, a system input matrix and a system observation matrix.
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