CN114935931B - 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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CN114935931B
CN114935931B CN202210492964.7A CN202210492964A CN114935931B CN 114935931 B CN114935931 B CN 114935931B CN 202210492964 A CN202210492964 A CN 202210492964A CN 114935931 B CN114935931 B CN 114935931B
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CN114935931A (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
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    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
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    • 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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
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Abstract

The invention discloses a time-varying heterogeneous multi-agent consistency control method and a system, comprising the following steps: establishing an input-output relation model and a connection topological graph of the multi-agent system; creating a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model to obtain state estimation information of the intelligent agent under any sensor; setting an optimal information fusion criterion, and carrying out 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; and setting a consistency control protocol according to the optimal state estimation information of the intelligent agents, and carrying out consistency control on the multiple intelligent agents. The invention realizes consistency control on time-varying heterogeneous multi-agent under the condition of multiple 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 study, the situation is considered too simple, and the situation containing random noise and time-varying variation is rarely considered. Most studies do not consider the situation of time-varying isomerism at the same time, like [ 1 ] only studying the consistency in the time-varying case, and [ 2 ] only studying the consistency in the isomerism case. This will lead to a poor range of applications and poor applicability. Moreover, the existing multi-agent is usually researched under the condition of a single sensor, and when the sensor fails, the state of the system 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 method and a system for controlling consistency of time-varying heterogeneous multi-agent, which can realize consistency control of the time-varying heterogeneous multi-agent under the condition of multiple sensors.
In order to solve the technical problems, 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 a multi-agent system, wherein each agent in the input-output relation model is provided with a plurality of sensors and contains random noise;
s2, creating a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model to obtain state estimation information of the intelligent agent under any sensor;
s3, setting an optimal information fusion criterion, and carrying out 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 to take the minimum covariance matrix of the state estimation information of any sensor and the other sensor of the intelligent agent as a weighting matrix of linear weighting;
s4, setting a consistency control protocol according to the optimal state estimation information of the intelligent agents, and carrying out consistency control on the plurality of intelligent agents, wherein a state feedback gain in the consistency control protocol is calculated by adopting a least square method.
As a further improvement of the invention, the multi-agent system has N agents, and the ith agent has N i The input-output relation model of the ith sensor for the ith intelligent agent and 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)
wherein ,xi (t)∈R n Representing the system state of the ith agent, u i (t)∈R k System input representing the ith agent, y i j (t)∈R p Representing a measurable input of a j-th sensor of an i-th agent, R n 、R k， 、R p N-dimensional, k-dimensional and p-dimensional vectors representing the system, respectively; w (w) i(t) and is an independent zero-mean noise sequence; matrix->The system state matrix, the system input matrix and the system observation matrix are respectively adopted.
As a further improvement of the invention, the connection topology wherein ,representing a set of nodes in the graph, +.>Representing a set of edges connecting nodes in the graph,an adjacency weight matrix representing the graph and having a ii ＝0；
When (i, j) ∈ε, a ij > 0, node i may receive node j's information, otherwise a ij ＝0；
Representing a set of all neighboring points of the node i; the degree of ingress of node i is defined asLet d=diag (D (1), D (2), …, D (N)), diag denote the diagonal block matrix, then the laplace matrix of the figure is +.>
As a further improvement of the present invention, the step S2 specifically includes: creating a kalman observer for the j observer of the i single agent:
wherein ,representing the state estimate of agent i at sensor j,/>Representing post state estimates,/->Representing the pre-state estimation value, P i j (t+ 1|t) represents a pre-covariance matrix, P i j (t+1|t+1) represents the post covariance matrix, ++>For Kalman gain, Q i (t) is w i (k) Covariance of->Is->Is a covariance of (c).
As a further improvement of the present invention, the optimal state estimation information of agent i:
wherein ,representing a matrix of state estimation gain coefficients,P i jk (t) is the covariance matrix of the estimated values of the jth sensor and the kth sensor of the ith agent at the moment t,/v->Representing a state estimation matrix; i n Is an n x n-dimensional identity matrix,/a>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, then a T Denoted as transpose of a.
As a further improvement of the present invention, the obtaining the optimal state estimation information of the agent in step S3 specifically includes:
order theAccording to P i jk The following steps are:
when (when)When the fusion estimation value is minimum, the Kalman observer of the intelligent agent i obtains the optimal fusion estimation value;
order theΛ i In order to be a lagrangian operator,
thenWhen L i (t) minimum, i.e. +.>
I.e.
Solving to obtain:
the final state estimation value of the intelligent agent i is obtained as follows:
wherein ,
as a further improvement of the present invention, the step S4 specifically includes the steps of:
order theu(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 ，
Delta (t) represents the synchronization error and,representing the average value of the states, if a certain matrix or vector a is written as a T Form, then a T A transpose denoted a; t (T) i (t) is an input gain matrix;
according to the least square method, letThe multi-agent realizes consistency control, wherein S is an arbitrary matrix, and +represents pseudo-inverse.
As a further improvement of the present invention, the state feedback gain T (T) is obtained, specifically including:
based on the synchronization error δ (t), there are:
wherein E is a mean square error matrix,
will beApproximately x (t), then:
order the
Then
When A (T) -B (T) T (T) L N When=0, i.eAnd the multi-agent realizes consistency control.
A time-varying heterogeneous multi-agent consistency control system adopts a time-varying heterogeneous multi-agent consistency control method to control multi-agent consistency.
As a further improvement of the invention, the multi-agent system has N agents, and the ith agent has N i The input-output relation model of the ith sensor for the ith intelligent agent and 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)
wherein ,xi (t)∈R n Representing the system state of the ith agent, u i (t)∈R k Representing the system input of the ith agent,representing a measurable input of a j-th sensor of an i-th agent, R n ，R k， ，R p ； w i(k) and />Is an independent zero-mean noise sequence; matrix->The system state matrix, the system input matrix and the system observation matrix are respectively adopted.
The invention has the beneficial effects that: when the multi-agent system contains random noise and time-varying variation of the system structure, the invention aims to realize consistency control on the multi-agent system under the condition of multiple sensors: the invention provides an optimal information fusion criterion in the sense of linear weighting, adopts the optimal information fusion criterion of matrix weighting in the sense of linear minimum variance, is applied to a multi-agent system under the condition of multiple sensors, and finally provides a multi-agent consistency control algorithm under the condition of multiple sensors, wherein the calculation method is simpler and has less calculation amount.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a topology of a vehicle fleet in accordance with a first embodiment of the present invention;
FIG. 3 is a vehicle alignment track diagram of a first embodiment of the present invention;
FIG. 4 is a vehicle alignment state diagram of a first embodiment of the present invention;
fig. 5 shows actual values, estimated values and fusion estimated values of the vehicle 1 according to the first embodiment of the present invention;
fig. 6 shows actual values, estimated values and fusion estimated values of the vehicle 2 according to the first embodiment of the present invention;
fig. 7 shows actual values, estimated values and fusion estimated values of the vehicle 3 according to the first embodiment of the present invention;
fig. 8 shows actual values, estimated values and fusion estimated values of the vehicle 4 according to the first embodiment of the present invention;
fig. 9 shows actual values, estimated values and fusion estimated values of the vehicle 5 according to the first embodiment of the present invention;
fig. 10 shows actual values, estimated values and fusion 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 according to a second embodiment of the present invention;
FIG. 13 shows actual, estimated and fused estimates of agent1 according to a second embodiment of the present invention;
FIG. 14 is a diagram showing actual, estimated, and fusion estimates of agent 2 according to a second embodiment of the present invention;
FIG. 15 shows actual, estimated and fused estimates of agent 3 according to a second embodiment of the present invention;
fig. 16 shows actual values, estimated values and fusion estimated values of the agent 4 according to the second embodiment of the present invention.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
Referring to fig. 1, 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 a multi-agent system, wherein each agent in the input-output relation model is provided with a plurality of sensors and contains random noise;
s2, creating a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model to obtain state estimation information of the intelligent agent under any sensor;
s3, setting an optimal information fusion criterion, and carrying out 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 to take the minimum covariance matrix of the state estimation information of any sensor and the other sensor of the intelligent agent as a weighting matrix of linear weighting;
s4, setting a consistency control protocol according to the optimal state estimation information of the intelligent agents, and carrying out consistency control on the plurality of intelligent agents, wherein a state feedback gain in the consistency control protocol is calculated by adopting a least square method.
The optimal information fusion criterion provided by the invention is an optimal information fusion criterion weighted by a matrix in the sense of linear minimum variance 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.
The method specifically comprises the following steps:
(1) Establishing an input-output relation 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 ith sensor, for the ith agent and the jth time model of the jth sensor of the agent is:
x i (t)＝A i (t-1)x i (t-1)+B i (t-1)u i (t-1)+w i (t-1)
wherein ：xi (t)∈R n ，u i (t)∈R k ，Respectively represent the system state, the system input, the measurable output, w i(k) and />Are independent zero-mean noise sequences with covariance Q i and />Matrix->The system state matrix is a system input matrix and a system observation matrix;
representing m x k block matrices, each matrix being an n x n identity matrix;
for intelligent body undirected topology graphRepresentation of->Representing a set of nodes in the graph, +.>Represents the set of edges of the connection node in the diagram, +.>An adjacency weight matrix representing the graph and having a ii =0; when (i, j) ∈ε, a ij > 0, meaning that node i can receive node j's information, otherwise a ij ＝0；/>Representing a set of all neighboring points of the node i; the degree of ingress of node i is defined asLet d=d=diag (D (1), D (2), …, D (N)), diag representing a diagonal block matrix, the laplace matrix of the figure is +.>
(2) According to the input-output equation of step (1), we create a Kalman observer for the j observer of the i single agent:
wherein ：estimated value representing the state of agent i under the j sensor, +.>The post-estimation is represented by a representation,representing the pre-estimation, P i j (t+ 1|t) represents a pre-covariance matrix, P i j (t+1|t+1) represents the post covariance matrix, ++>Is Kalman gain
(3) Obtaining estimated information of the agent observer from the step (2), and enabling the final estimation of the ith agent to beThe most fusion criterion is set according to the unbiased principle:
order the
Then there are:
order the
P i jk Covariance matrix of the j sensor and the k sensor estimation value of the i-th agent
When (when)At the minimum, the observer obtains the optimal fusion estimation;
order theΛ i For Lagrangian operator, then +.>At the time, the minimum value is obtained
I.e.
I.e.
Obtaining
The final estimate of agent i is:
wherein
(4) According to the estimated information, a consistency control protocol is set so that a plurality of agents realize consistency control:
order the
A＝diag[A 1 … A N ] T ，B＝diag[B 1 … B N ] T ，T＝diag[T 1 … T N ] T
Delta represents the synchronization error and is used to determine,
then there is
wherein ,
since the estimation obtained in the step (3) is an unbiased estimation, the methodApproximately regarded as x, can be obtained
Then
Order the
Then
When A (T) -B (T) T (T) L N When=0, i.eWhen the multi-agent realizes consistency control, wherein S is an arbitrary matrix, and +represents pseudo-inverse.
Example 1
As shown in fig. 2, the present embodiment provides a homogeneous vehicle formation system controlled by a time-varying multi-agent consistency control method as described above, where a leader of the vehicle formation system knows destination information and moves toward a destination (destination), and a follower follows the movement, and their position information is monitored by three satellites (satellites) on the sky. Moving the leader along y=5sin (0.2 x), then:
the motion model of the ith vehicle at the kth moment is that
x i Is a four-dimensional column vector, wherein,for the x-direction position at time k->Is the y-direction displacement at time k. />For the average input speed in x-direction, +.>For the average input speed in the y-direction, +.>Observing the information of the ith vehicle position for the jth satellite, and when the sampling interval is deltat, the equation is:
wherein ,
simulation study was performed for the above cases:
as a result, as shown in fig. 3, the vehicles 1-6 (agents 1-6) move in a train along a predetermined trajectory; the vehicle alignment state diagram of fig. 4 can see that the vehicles 1-6 eventually converge to a close state, thereby achieving good consistency control, and fig. 5-10 show the actual state value (actual) and the estimated value (estimate) of the vehicles 1-6, respectively, and can see that the estimated value is extremely close to the actual value. Since the agents of fig. 5 and 6 have only one sensor, they have only one estimated value, and the agents of fig. 7 to 10 are equipped with a plurality of sensors, it can be seen from the figures that the estimated value (sensor) made from the sensors is not accurate in fusion estimation (fusion), showing the superiority of the algorithm proposed in this patent.
Example two
Establishing a heterogeneous abstract system topology as shown in fig. 11, wherein a box represents Sensors (Sensors), a round box represents agents (agents), and various parameters are as follows:
Q 1 …Q 4 ＝0.05 2 *I 3 ，
simulation study was performed for the above cases:
as fig. 12 shows a multi-agent system state diagram, it can be seen that agents 1-4 eventually converge to a near state, thereby achieving good consistency control;
as shown in fig. 13-16, which show the actual values and the estimated values of the states of the intelligent agents 1-4 of the multi-intelligent agent system, 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 accuracy of the invention can be controlled within the error range of 0.05 noise standard deviation; as can be seen from the figure, the estimation value (sensor) made from the sensor is not accurate in fusion estimation (fusion), showing the superiority of the proposed algorithm of this patent.
In the invention, the least square has good data fusion estimation effect under the condition of multiple sensors through mathematical reasoning, and then, for a 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 multiple agents is realized under the interference of random noise.
The above-described embodiments are merely preferred embodiments for fully explaining the present invention, and the scope of the present invention is not limited thereto. Equivalent substitutions and modifications will occur to those skilled in the art based on the present invention, and are intended to be within the scope of the present 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 in that: the method comprises the following steps:
s1, establishing an input-output relation model and a connection topological graph of a multi-agent system, wherein each agent in the input-output relation model is provided with a plurality of sensors and contains random noise;
s2, creating a Kalman observer for any sensor in a single intelligent agent according to the input-output relation model to obtain state estimation information of the intelligent agent under any sensor;
s3, setting an optimal information fusion criterion, and carrying out 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 to take the minimum covariance matrix of the state estimation information of any sensor and the other sensor of the intelligent agent as a weighting matrix of linear weighting;
s4, setting a consistency control protocol according to the optimal state estimation information of the intelligent agents, and carrying out consistency control on the plurality of intelligent agents, wherein a state feedback gain in the consistency control protocol is calculated by adopting a least square method.
2. The time-varying heterogeneous multi-agent consistency control method of claim 1, wherein: the multi-agent system has N agents, and the ith agent has N i The input-output relation model of the ith sensor for the ith intelligent agent and 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)
wherein ,xi (t)∈R n Representing the system state of the ith agent, u i (t)∈R k Representing the system input of the ith agent,representing a measurable input of a j-th sensor of an i-th agent, R n 、R k， 、R p N-dimensional, k-dimensional and p-dimensional vectors representing the system, respectively; w (w) i(t) and />Is an independent zero-mean noise sequence; matrix->The system state matrix, the system input matrix and the system observation matrix are respectively adopted.
3. The time-varying heterogeneous multi-agent consistency control method of claim 1, wherein: the connection topology map wherein ,/>Representing a set of nodes in the graph, +.>Represents the set of edges of the connection node in the diagram, +.>An adjacency weight matrix representing the graph and having a ii ＝0；
When (i, j) ∈ε, a ij > 0, node i may receive node j's information, otherwise a ij ＝0；
Representing a set of all neighboring points of the node i; the degree of ingress of node i is defined asLet d=diag (D (1), D (2), …, D (N)), diag denote the diagonal block matrix, then the laplace matrix of the figure is +.>
4. The time-varying heterogeneous multi-agent consistency control method of claim 2, wherein: the step S2 specifically includes: creating a kalman observer for the j observer of the i single agent:
wherein ,representing the state estimate of agent i at sensor j,/>Representing the post-state estimate value,representing the pre-state estimation value, P i j (t+ 1|t) represents a pre-covariance matrix, P i j (t+1|t+1) represents the post covariance matrix, ++>For Kalman gain, Q i (t) is w i (k) Covariance of->Is->Is a covariance of (c).
5. The method for controlling the consistency of a time-varying heterogeneous multi-agent according to claim 4, wherein: optimal state estimation information for agent i:
wherein ,representing a matrix of state estimation gain coefficients,P i jk (t) is the covariance matrix of the estimated values of the jth sensor and the kth sensor of the ith agent at the moment t,/v->Representing a state estimation matrix; i n Is an n x n-dimensional identity matrix,/a>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, then a T Denoted as transpose of a.
6. The time-varying heterogeneous multi-agent consistency control method of claim 5, wherein: the step S3 of obtaining the optimal state estimation information of the agent specifically includes:
order theAccording to P i jk The following steps are:
when (when)When the fusion estimation value is minimum, the Kalman observer of the intelligent agent i obtains the optimal fusion estimation value;
order theΛ i In order to be a lagrangian operator,
thenWhen L i (t) minimum, i.e. +.>
I.e.
Solving to obtain:
the final state estimation value of the intelligent agent i is obtained as follows:
wherein ,
7. the time-varying heterogeneous multi-agent consistency control method of claim 2, wherein: the step S4 specifically includes the following steps:
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 ，
delta (t) represents the synchronization error and,representing the average value of the states, if a certain matrix or vector a is written as a T Form, then a T A transpose denoted a; t (T) i (t) is an input gain matrix;
according to the least square method, letThe multi-agent realizes consistency control, wherein S is an arbitrary matrix, and +represents pseudo-inverse.
8. The time-varying heterogeneous multi-agent consistency control method of claim 2, wherein: obtaining the state feedback gain T (T), specifically including:
based on the synchronization error δ (t), there are:
wherein E is a mean square error matrix,
will beApproximately x (t), then:
order the
Then
When A (T) -B (T) T (T) L N When=0, i.eAnd the multi-agent realizes consistency control.
9. A time-varying heterogeneous multi-agent consistency control system, characterized by: multi-agent consistency control using a time-varying heterogeneous multi-agent consistency control method according to any of claims 1-8.
10. The time-varying heterogeneous multi-agent coherence control system of claim 9, wherein: the multi-agent system has N agents, and the ith agent has N i A sensor for the ith agentAnd the input-output relation model of the jth moment of the jth sensor of the intelligent body is as follows:
wherein ,xi (t)∈R n Representing the system state of the ith agent, u i (t)∈R k Representing the system input of the ith agent,representing a measurable input of a j-th sensor of an i-th agent, R n ,R k, ,R p ；w i(k) and />Is an independent zero-mean noise sequence; matrix->The system state matrix, the system input matrix and the system observation matrix are respectively adopted.
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