CN110597109B - Multi-agent consistency control method based on event triggering - Google Patents

Multi-agent consistency control method based on event triggering Download PDF

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CN110597109B
CN110597109B CN201910788559.8A CN201910788559A CN110597109B CN 110597109 B CN110597109 B CN 110597109B CN 201910788559 A CN201910788559 A CN 201910788559A CN 110597109 B CN110597109 B CN 110597109B
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王祝萍
张皓
吴永辉
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Tongji Institute Of Artificial Intelligence Suzhou Co ltd
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Abstract

The invention relates to a multi-agent consistency control method based on event triggering, which comprises the following steps: establishing a general linear multi-agent dynamic model, and designing a distributed controller according to the information of agent nodes and the information of neighbor agent nodes to ensure the consistency of the multi-agent; communication strategies based on event triggering are designed to ensure that communication between agents is intermittent. The invention realizes the consistency control of the multi-agent system, solves the problem of larger network communication load caused by continuous information exchange between agents, reduces the updating load of a system controller and prolongs the service life of the agent system.

Description

Multi-agent consistency control method based on event triggering
Technical Field
The invention belongs to the technical field of intelligent cooperative control, and particularly relates to a multi-agent consistency control method based on event triggering.
Background
Cooperative consistency control among multiple agents is a basic problem of intelligent cooperative control neighborhood. By realizing multi-agent consistency control, complex cooperative tasks such as distributed optimization, distributed formation, distributed filtering and the like can be completed. By triggering the cooperative control algorithm through events among the agents, the cooperative capability among the agents can be effectively improved, and the energy consumption of the multi-agent system is reduced.
The distributed control method is used for multi-agent consistency control, so that the use of global information can be better avoided, the stability and the robustness of intelligent agent cooperative control are improved, and the distributed control method is widely applied to the consistency problem of a large-scale intelligent agent system. Agent consistency control is enormous in terms of energy consumed by communication, and frequent data communication between existing agents causes a lot of unnecessary data transmission, resulting in waste of resources. Therefore, an event trigger mechanism is introduced, so that the communication load among the intelligent agents can be reduced; meanwhile, the controller is continuously updated, so that the updating load of the controller is increased, and the service life of the intelligent system is shortened.
Disclosure of Invention
The invention aims to provide a multi-agent consistency control method based on event triggering, which realizes the consistency control of multi-agents through a distributed controller under the framework of a system formed by the multi-agents, introduces an event triggering mechanism to reduce the communication load and the updating times of the controller and improves the utilization rate of system resources.
In order to achieve the purpose, the invention adopts the technical scheme that:
a multi-agent consistency control method based on event triggering, comprising:
s1, establishing a general linear multi-agent dynamic model, and designing a distributed controller according to the information of agent nodes and the information of neighbor agent nodes to ensure the consistency of the multi-agent;
and S2, designing a communication strategy based on event triggering to ensure that the communication between the intelligent agents is discontinuous.
Preferably, in S1: establishing a general linear multi-agent dynamic model comprises the following steps: assuming that there are N agents, then the ith agent dynamics model is:
Figure GDA0002265415710000021
wherein: x is the number ofi(t)∈Rn，ui(t)∈RmRepresenting state and control inputs of agents, A ∈ R, respectivelyn×n，B∈Rn×mIs a constant system matrix.
Further preferably, when ensuring the multi-agent coherence, for any initial state:
Figure GDA0002265415710000022
preferably, in S1: the communication network of the agent is a directed strong connection graph, and the geometric connection degree a (L) of the directed strong connection graph is defined as follows:
Figure GDA0002265415710000023
wherein:
Figure GDA0002265415710000024
Figure GDA00022654157100000213
l is communicationThe laplacian matrix of the network,
the geometric connectivity is calculated according to the following formula:
Figure GDA0002265415710000025
wherein
Figure GDA0002265415710000026
Further preferably, in S2: designing an event trigger-based communication strategy, comprising:
defining state estimation variables
Figure GDA0002265415710000027
Figure GDA0002265415710000028
Wherein:
Figure GDA0002265415710000029
is a communication time sequence of agents i, determined by a communication event triggered control strategy, each agent i defining variables to design the communication event triggered control strategy, i 1.
Defining event trigger threshold variables
Figure GDA00022654157100000210
Figure GDA00022654157100000211
Wherein:
Figure GDA00022654157100000212
ni is the set of neighbor agents for agent i,
defining a communication state measurement error ei(t)，
Figure GDA0002265415710000031
The event-triggered control strategy for communication is designed as follows:
Figure GDA0002265415710000032
wherein:
Figure GDA0002265415710000033
is an event trigger function, which is designed as follows:
Figure GDA0002265415710000034
wherein: c. Ci1> 0 is the control parameter to be designed.
Further preferably, the controller update strategy triggered by the agent event includes:
defining controller measurement error for agent i:
Figure GDA0002265415710000035
Figure GDA0002265415710000036
wherein:
Figure GDA0002265415710000037
is the update time sequence of the controller, which is determined by the introduced event trigger mechanism,
Figure GDA0002265415710000038
designing an event trigger function:
Figure GDA0002265415710000039
wherein: c. Ci2> 0 is the control parameter to be designed,
according to the event-triggered control mechanism, the controller of agent i is designed to:
Figure GDA00022654157100000310
wherein: matrix K is a state feedback matrix, c > 0 is a coupling gain,
in the event trigger system (3), (4) and (5), the control parameters are selected as follows:
feedback matrix
Figure GDA00022654157100000311
P is an algebraic Riccati equation positive solution matrix:
PA+ATP-cμPBBTp ═ Q, (6) wherein: matrix Q is a negative definite matrix, 0 < mu. ltoreq. a (L),
the mathematical notation defining the following determines the control parameters, the matrix:
Figure GDA00022654157100000312
Figure GDA0002265415710000041
Figure GDA0002265415710000042
wherein: c. Ci1＞0，ci2Is greater than 0, and satisfies:
Figure GDA0002265415710000043
preferably, said constant system matrix (a, B) is assumed to be stable.
Preferably: in S1: the generally linear multi-agent dynamics model includes a second order model.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages and effects:
the invention realizes the consistency control of the multi-agent system, solves the problem of larger network communication load caused by continuous information exchange between agents, reduces the updating load of a system controller and prolongs the service life of the agent system.
Drawings
FIG. 1 is a diagram of a multi-agent communication topology in this embodiment;
FIG. 2 is a diagram illustrating the state response of the multi-agent in the control algorithm in this embodiment;
figure 3 shows the communication and controller update times and time intervals for agent number 1 under the control algorithm.
Detailed Description
The invention is further described below with reference to the accompanying drawings and embodiments:
a multi-agent consistency control method based on event triggering, comprising:
s1, establishing a general linear multi-agent dynamic model, and designing a distributed controller through the information of an agent node and the information of a neighbor agent node (through a communication network protocol) to ensure the consistency of the multi-agent.
Establishing a general linear multi-agent dynamic model comprises the following steps: assuming that there are N agents, then the ith agent dynamics model is:
Figure GDA0002265415710000044
wherein: xi（t）∈Rn，ui(t)∈RmRespectively representing the state of the agent and the control input,
A∈Rn×n，B∈Rn×mis a constant system matrix. In this embodiment: the general linear multi-agent dynamics model comprises a second order model, and the constant system matrices (a, B) are assumed to be stable.
The distributed control strategy designed in this embodiment ensures that the intelligent system implementation is consistent, i.e. for any initial state:
Figure GDA0002265415710000051
the communication network of the agent is a directed strong connection graph, and the geometric connection degree a (L) of the directed strong connection graph is defined as follows:
Figure GDA0002265415710000052
wherein:
Figure GDA0002265415710000053
Figure GDA0002265415710000054
l is the laplacian matrix of the communication network,
the geometric connectivity is calculated according to the following formula:
Figure GDA0002265415710000055
wherein
Figure GDA0002265415710000056
And S2, designing a communication strategy based on event triggering to ensure that the communication between the intelligent agents is discontinuous.
Designing an event-triggered communication strategy between agents, comprising:
defining state estimation variables
Figure GDA0002265415710000057
Figure GDA0002265415710000058
Wherein:
Figure GDA0002265415710000059
is a communication time sequence of agents i, determined by a communication event triggered control strategy, each agent i defining variables to design the communication event triggered control strategy, i 1.
Defining event trigger threshold variables
Figure GDA00022654157100000510
Figure GDA00022654157100000511
Wherein:
Figure GDA00022654157100000512
ni is the set of neighbor agents for agent i because the state is estimated
Figure GDA00022654157100000513
Only the actual state values at the moment of communication are utilized and therefore there is no need to continuously communicate with the neighbour agent to form the state threshold.
Defining a communication state measurement error ei(t)，
Figure GDA00022654157100000514
The event-triggered control strategy for communication is designed as follows:
Figure GDA0002265415710000061
wherein:
Figure GDA0002265415710000062
is an event trigger function, which is designed as follows:
Figure GDA0002265415710000063
wherein: c. Ci1> 0 is the control parameter to be designed.
The event trigger mechanism (3) is designed to get rid of the dependence on continuous communication between the intelligent agents, so that a large amount of communication energy is saved.
An agent event triggered controller update policy comprising:
defining controller measurement error for agent i:
Figure GDA0002265415710000064
Figure GDA0002265415710000065
wherein:
Figure GDA0002265415710000066
is the update time sequence of the controller, which is determined by the introduced event trigger mechanism,
Figure GDA0002265415710000067
designing an event trigger function:
Figure GDA0002265415710000068
wherein: c. Ci2> 0 is the control parameter to be designed.
According to the event-triggered control mechanism, the controller of agent i is designed to:
Figure GDA0002265415710000069
wherein: matrix K is a state feedback matrix, c > 0 is a coupling gain,
in the event trigger mechanism systems (3), (4) and (5), the intelligent agent finally achieves consistent state through the communication of local discontinuous information. The control parameters are selected as follows:
feedback matrix
Figure GDA00022654157100000610
P is an algebraic Riccati equation positive solution matrix:
PA+ATP-cμPBBTP＝Q，， (6)
wherein: matrix Q is a negative definite matrix, 0 < mu. ltoreq. a (L),
the mathematical notation defining the following determines the control parameters, the matrix:
Figure GDA00022654157100000611
Figure GDA0002265415710000071
Figure GDA0002265415710000072
wherein: c. Ci1＞0，ci2Is greater than 0, and satisfies:
Figure GDA0002265415710000073
in this embodiment, the system matrix is as follows:
Figure GDA0002265415710000074
wherein:
Figure GDA0002265415710000075
I3being a three-dimensional identity matrix, omega0＝0.001。
The system state can be written as:
Figure GDA0002265415710000076
wherein:
Figure GDA0002265415710000077
respectively, represent the velocity in the X-Y-Z direction.
Figure GDA0002265415710000078
Respectively, represent the distances in the X-Y-Z direction from the target point. A communication network consisting of six agents, as shown in figure 1.
The specific parameters are selected as the geometric connectivity a (L) 0.7939, Q-4I of the communication network6，
Figure GDA0002265415710000079
ξ＝[0.25000.10710.10710.21430.17860.1429]Feedback matrix:
Figure GDA00022654157100000710
the matrix P is an algebraic Riccati equation positive solution matrix. It can be seen from fig. 2 that the speeds of the agents tend to be consistent and the positions reach the specified positions individually, i.e. the algorithm can achieve consistent control. The communication time and controller update time of agent numbered 1, and the time interval between adjacent trigger times are presented as in fig. 3. Thus, the control algorithm can ensure that communication between agents and controller updates are intermittent.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims (7)

1. A multi-agent consistency control method based on event triggering is characterized in that: the method comprises the following steps:
s1, establishing a general linear multi-agent dynamic model, designing a distributed controller through the information of agent nodes and the information of neighbor agent nodes to ensure the consistency of the multi-agents, wherein the communication network of the agents is a directed strong connection graph, and the geometric connectivity a (L) of the directed strong connection graph is defined as follows:
Figure FDA0002614564150000011
wherein:
Figure FDA0002614564150000012
Figure FDA0002614564150000013
l is the laplacian matrix of the communication network,
the geometric connectivity is calculated according to the following formula:
Figure FDA0002614564150000014
wherein
Figure FDA0002614564150000015
And S2, designing a communication strategy based on event triggering to ensure that the communication between the intelligent agents is discontinuous.
2. The event-triggered multi-agent consistency control method as claimed in claim 1, wherein: in S1: establishing a general linear multi-agent dynamic model comprises the following steps: assuming that there are N agents, then the ith agent dynamics model is:
Figure FDA0002614564150000016
wherein: x is the number ofi(t)∈Rn，ui(t)∈RmRepresenting state and control inputs of agents, respectively, A ∈ En×n，B∈Rn×mIs a constant system matrix.
3. The event-triggered multi-agent consistency control method as claimed in claim 2, wherein: to ensure multi-agent consistency, for any initial state:
Figure 1
。
4. the event-triggered multi-agent consistency control method as claimed in claim 2, wherein: in S2: designing an event trigger-based communication strategy, comprising:
defining state estimation variables
Figure FDA0002614564150000018
Figure FDA0002614564150000019
Wherein:
Figure FDA0002614564150000021
is a communication time sequence of agents i, determined by a communication event triggered control strategy, each agent i defining variables to design the communication event triggered control strategy, i 1.
Defining event trigger threshold variables
Figure FDA0002614564150000022
Figure FDA0002614564150000023
Wherein:
Figure FDA0002614564150000024
ni is the set of neighbor agents for agent i,
defining a communication state measurement error ei(t)，
Figure FDA0002614564150000025
The event-triggered control strategy for communication is designed as follows:
Figure FDA0002614564150000026
wherein:
Figure FDA0002614564150000027
is an event trigger function, which is designed as follows:
Figure FDA0002614564150000028
wherein: c. Ci1> 0 is the control parameter to be designed.
5. The event-triggered multi-agent consistency control method as claimed in claim 4, wherein: an agent event triggered controller update policy comprising:
defining controller measurement error for agent i:
Figure FDA0002614564150000029
Figure FDA00026145641500000210
wherein:
Figure FDA00026145641500000211
is the update time sequence of the controller, which is determined by the introduced event trigger mechanism,
Figure FDA00026145641500000212
designing an event trigger function:
Figure FDA00026145641500000213
wherein: c. Ci2> 0 is the control parameter to be designed,
according to the event-triggered control mechanism, the controller of agent i is designed to:
wherein: matrix K is a state feedback matrix, c > 0 is a coupling gain,
in the event trigger system (3), (4) and (5), the control parameters are selected as follows:
feedback matrix
Figure FDA00026145641500000215
P is an algebraic Riccati equation positive solution matrix:
PA+ATP-cμPBBTP＝Q， (6)
wherein: matrix Q is a negative definite matrix, 0 < mu. ltoreq. a (L),
the mathematical notation defining the following determines the control parameters, the matrix:
M＝(IN-1NξT)，
Figure FDA0002614564150000031
Figure FDA0002614564150000032
Figure FDA0002614564150000033
wherein: c. Ci1＞0，ci2Is greater than 0, and satisfies:
Figure FDA0002614564150000034
6. the event-triggered multi-agent consistency control method as claimed in claim 2, wherein: the constant system matrix (a, B) is assumed to be stable.
7. The event-triggered multi-agent consistency control method as claimed in claim 1, wherein: in S1: the generally linear multi-agent dynamics model includes a second order model.
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