CN117093006A - Self-adaptive fixed-time affine formation control method for multi-agent cluster system - Google Patents
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Abstract
The invention discloses a self-adaptive fixed-time affine formation control method for a multi-agent cluster system, and relates to the technical field of formation control of the multi-agent cluster system. The method comprises the steps of setting affine formation time and a class of time functions, and constructing a class of time function gains; determining a distributed self-adaptive fixed-time affine formation control rate according to the gain of a time function, the communication relationship among agents in the multi-agent cluster system and the target formation configuration; and performing formation control on the multi-agent cluster system by using the distributed self-adaptive fixed-time affine formation control rate. The method and the system can improve the formation efficiency and robustness of the multi-agent cluster system, and simultaneously can form the cluster intelligent system more rapidly and accurately.
Description
Technical Field
The invention relates to the technical field of multi-agent cluster system formation control, in particular to a self-adaptive fixed-time affine formation control method for a multi-agent cluster system.
Background
A multi-agent cluster system is a complex network system consisting of multiple agents that can interact and cooperate with each other to accomplish a task or achieve a goal. In a cluster system, information transfer and resource sharing can be performed among various agents through communication, so that distributed processing and decision making are realized. These agents may be different types of equipment such as unmanned aerial vehicles, robots, sensors, etc. that cooperate to accomplish efficient data collection, processing, and control tasks in a particular environment. Due to high expandability, self-adaption and robustness, the multi-agent cluster system is widely applied to daily life, such as unmanned automobiles, aviation flight control, medical diagnosis, environmental monitoring and the like.
In the control task of the multi-agent cluster system, formation control is always popular in the research of the field, wherein affine formation control problem is novel in recent years, and formation control can enable the unknown state of agents to be changed continuously by selecting proper communication network topology to realize information interaction of the system, so that a formation configuration which is actually needed is formed. In addition, the convergence speed is also an important evaluation index in the formation control algorithm. A fixed time queuing control algorithm may be more popular than an unpredictable steady time control algorithm because such an algorithm is more practical. The fixed time formation control algorithm also has the defect that global information under a meeting topology structure cannot be easily obtained, and how to overcome the defect makes the design of a controller of the problem worth being broken.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a self-adaptive fixed-time affine formation control method for a multi-agent cluster system, which combines affine formation control technology with a self-adaptive algorithm and a fixed-time algorithm to solve the problems that the robustness is insufficient and the reliability is difficult to guarantee in the formation process of the cluster intelligent system in the prior art, thereby improving the formation efficiency and the robustness of the multi-agent cluster system and simultaneously being capable of forming the cluster intelligent system more rapidly and accurately.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
a multi-agent cluster system self-adaptive fixed time affine formation control method comprises the following steps:
s1, setting affine formation time and a class of time functions, and constructing a class of time function gains;
s2, determining a distributed self-adaptive fixed-time affine formation control rate according to a time function gain, a communication relation among agents in the multi-agent cluster system and a target formation configuration;
s3, performing formation control on the multi-agent cluster system by using the distributed self-adaptive fixed-time affine formation control rate.
Further, the time function set in step S1 is specifically:
wherein,tin order to be able to take time,t f for affine formation time set according to different formation task requirements,is a kind of time function->Is of the initial value of->And->Respectively are a kind of time functions intTime of day and time of dayt f The right derivative of time.
Further, the time function gains constructed in step S1 are specifically:
wherein,gain for a class of time functions->Is constant.
Further, step S2 specifically includes:
and determining the distributed self-adaptive fixed-time affine formation control rate of the leader system according to the gain of the time function, the communication relation among the agents in the multi-agent cluster system and the target formation configuration.
Further, the distributed self-adaptive fixed-time affine formation control rate of the leader system is specifically:
wherein,is the firstiControl input of individual agent,/->Gain for a class of time functions->For adaptively controlling gain->For the number of agents in the multi-agent cluster system, < ->Is the first in the multi-agent cluster systemiPersonal agent and the firstjCommunication weight between the individual agents, +.>And->Respectively the firstiPersonal agent and the firstjStatus of individual agent->For manually setting parameters->Gain +.>Rate of change of->Is the square of the two norms.
Further, step S2 specifically includes:
and determining the distributed self-adaptive fixed-time affine formation control rate of the Leader-follower system according to the time function gains, the communication relations among the agents in the multi-agent cluster system and the target formation configuration.
Further, the distributed self-adaptive fixed-time affine formation control rate of the Leader-follower system is specifically:
wherein,is the firstiControl input of individual agent,/->Gain for a class of time functions->And->Are all self-adaptive control gains->For the number of agents in the multi-agent cluster system, < ->Is the first in the multi-agent cluster systemiPersonal agent and the firstjCommunication weight between the individual agents, +.>And->Respectively the firstiPersonal agent and the firstjStatus of individual agent->To set parameters +.>And->Adaptive control gain respectively>And->Rate of change of->Is two norms>Is the square of the two norms,N i is the firstiThe neighbor set of the individual agents, sgn, is a sign function.
The invention has the following beneficial effects:
the affine formation control method and the affine formation control system solve the affine formation control problem of the leader-follower system and the leader-follower system of two main branches in formation by combining affine formation control with the self-adaptive technology and the fixed time technology. Compared with the traditional formation control method, the method improves the formation efficiency and robustness of the multi-agent cluster system, can form the cluster intelligent system more rapidly and accurately, and is more beneficial to solving the formation control problem.
Drawings
FIG. 1 is a flow chart of a method for controlling adaptive fixed time affine formation of a multi-agent cluster system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a target formation configuration to be formed in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a motion trail of each agent in a target formation process for a leader multi-agent cluster system according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a motion trail of each agent in a target formation process for a leader-follower multi-agent cluster system according to an embodiment of the present invention;
FIG. 5 shows the adaptive control gain according to an embodiment of the present inventionA change condition diagram in the process of forming a target formation by a leader system;
FIG. 6 is a diagram of adaptive control gain in an embodiment of the present inventionA change condition diagram in the process of forming a target formation by a leader-follower system;
FIG. 7 is a diagram of adaptive control gain in an embodiment of the present inventionSchematic of the change in the leader-follower system forming the target formation.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, the embodiment of the invention provides a multi-agent cluster system adaptive fixed-time affine formation control method, which comprises the following steps S1 to S3:
s1, setting affine formation time and a class of time functions, and constructing a class of time function gains;
in an alternative embodiment of the present invention, the multi-agent cluster system to which the present embodiment is directed is a system composed of a plurality of agents with a first order integrator as a kinetic model.
In this embodiment, the time function set in step S1 is specifically:
wherein,tin order to be able to take time,t f for affine formation time set according to different formation task requirements, according toIs designed to be suitable for the value of TBG function +.>，/>Is a kind of time function->Is of the initial value of->And->Respectively are a kind of time functions intTime of day and time of dayt f The right derivative of time.
In this embodiment, when forming an agent, a determination criterion for forming a formation is needed, and first, a formation error and a tracking error are defined:
the enqueue error is defined as:
wherein,for formation errors, ++>Stress matrix corresponding to multi-agent cluster system>Is the state of the agent.
For the Leader-follower system, the tracking error of the follower is defined as:
wherein,for tracking error of follower +.>Is a stress matrix corresponding to the multi-agent cluster system,and->States of follower and leader in agent, respectively, +.>And->Respectively sub-matrices after dividing the stress matrix.
When the formation task is successful, the following conditions are satisfied:
or->
In this embodiment, the time function gains constructed in step S1 are specifically:
wherein,gain for a class of time functions->Is constant (I)>，/>Is a very small constant value and containsIn order to ensure that +.>The TBG gain denominator is not zero later.
Specifically, according to a specific formation task requirement, the TBG function is set as follows:
wherein,TBG function designed for demands of formation tasks, < - > for the purpose of the TBG function>For time (I)>5s.
The corresponding TBG gain design is as follows:
。
s2, determining a distributed self-adaptive fixed-time affine formation control rate according to a time function gain, a communication relation among agents in the multi-agent cluster system and a target formation configuration;
in an alternative embodiment of the present invention, the target formation configuration of the present embodiment is specifically designed by analyzing different actual formation task requirements. For the leader system, the communication relationship of the multi-agent cluster system is that each agent only performs communication interaction with a specific agent. For the leader-follower system, the communication relationship of the multi-agent cluster system is specifically: the leader only sends information without receiving information, and the follower not only sends own information but also receives information sent by a specific intelligent agent.
In this embodiment, determining the distributed adaptive fixed time affine formation control rate of the leader system according to a time function gain, a communication relationship among agents in the multi-agent cluster system, and a target formation configuration specifically includes:
wherein,is the firstiControl input of individual agent,/->Gain for a class of time functions->For adaptively controlling gain->For the number of agents in the multi-agent cluster system, < ->Is the first in the multi-agent cluster systemiPersonal agent and the firstjCommunication weight between the individual agents, +.>And->Respectively the firstiPersonal agent and the firstjStatus of individual agent->To set parameters, satisfy->，/>Gain +.>Rate of change of->Is the square of the two norms.
In this embodiment, determining the distributed adaptive fixed-time affine formation control rate of the Leader-follower system according to a time function gain, a communication relationship among the agents in the multi-agent cluster system, and a target formation configuration specifically includes:
wherein,is the firstiControl input of individual agent,/->Gain for a class of time functions->And->Are all self-adaptive control gains->For the number of agents in the multi-agent cluster system, < ->Is the first in the multi-agent cluster systemiPersonal agent and the firstjCommunication weight between the individual agents, +.>And->Respectively the firstiPersonal agent and the firstjStatus of individual agent->To set parameters, satisfy->，/>And->Adaptive control gain respectively>And->Rate of change of->Is two norms>Is the square of the two norms,N i is the firstiThe neighbor set of the individual agents, sgn, is a sign function.
S3, performing formation control on the multi-agent cluster system by using the distributed self-adaptive fixed-time affine formation control rate.
In order to verify the adaptive fixed-time affine formation control method for the multi-agent cluster system provided by the embodiment, feasibility analysis of the embodiment is performed in a specific application scene.
Firstly, analyzing a leaderless system, and constructing a Lyapunov function as follows:
wherein,is a Lyapunov function, ++>Transpose of the vector composed for all agent states, < >>Is stress matrix->Is adaptive parameter->Is a term for errors in the error.
The control rate for the leader system can be used to obtainIs a solution set of (a):
wherein,is Lyapunov function->Is the initial value of (a).
The formation error can then be found as follows:
wherein,is the firstiTeam error of individual agents, +.>Is the firstiAbsolute value of the formation error of the individual agents,nfor intelligent number->To take maximum value->Is the non-zero minimum eigenvalue of the stress matrix.
When the parameters are to be takenFor a sufficiently small design, the end result of the formation error can be obtained:
next, the leader-follower system is analyzed to construct the lyapunov function as follows:
wherein,is a Lyapunov function, ++>For transposition of tracking error +.>For the submatrix representing the follower and follower in the stress matrix, < >>In order to track the error in the tracking,N f for follower set, ->Is an adaptive parameter.
The controller for the leader-follower system can be obtainedIs a solution set of (a):
wherein,is Lyapunov function->Is the initial value of (a).
The tracking error can then be found by the following expression:
wherein,is a two-norm of the tracking error, +.>For a constant which can be set, +.>And decomposing the minimum non-zero eigenvalue of the sub-matrix of the interaction between the follower and the follower for the stress matrix.
When the parameters are to be takenFor a sufficiently small design, the end result of tracking error can be obtained:
an example simulation is performed below for the controller designed in this embodiment to verify the effectiveness of the controller in the present invention.
(1) Crowd control system and formation configuration setting:
using a multi-agent cluster system of 6 agents as an example, a simulation was performed to perform a fixed time queuing task in two dimensions with the desired nominal configuration shown in fig. 2.
Initial positions of the respective agents in the leader system are as follows in table 1:
TABLE 1
Initial locations of the respective agents in the Leader-follower system are shown in table 2 below:
TABLE 2
Given a fixed time of task demandAt the same time set +.>Making it small enough.
As in fig. 3 and 4, where x (m) represents position information in the x direction, y (m) represents position information in the y direction, and Time(s) represents Time; as can be seen from fig. 3 and 4, the controller of this embodiment can be used to implement a formation task for a multi-agent cluster system composed of 6 agents in a fixed time, both for the leader system and the leader-follower system. As can be further seen from fig. 4, the control method can not only achieve formation within a fixed time, but also maintain the target formation after a fixed time.
Fig. 5, 6 and 7 describe adaptive control gainAnd->The solid line represents the trend of the adaptive control gain of the agent 1 over time. The dash-dot line represents the trend of the adaptive control gain of the agent 2 over time. The dashed line represents the trend of the adaptive control gain of the agent 3 over time. The double-dashed line represents the adaptive control gain trend of the agent 4 over time. The double-lined and pentagram-marked line represents the adaptive control gain trend of the agent 5 over time. The double-lined and circled line represents the adaptive control gain trend of the agent 6 over time. Since the agents 1, 2, 3 are not controlled by the leader, the adaptive control gain trend curves with time overlap in fig. 6 and 7. As can be seen from fig. 5, 6 and 7, the present invention achieves efficient adaptive control. Simulation of a leader system and a leader-follower system verifies the practicability and effectiveness of the distributed self-adaptive fixed-time affine formation control method.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (7)
1. The self-adaptive fixed-time affine formation control method for the multi-agent cluster system is characterized by comprising the following steps of:
s1, setting affine formation time and a class of time functions, and constructing a class of time function gains;
s2, determining a distributed self-adaptive fixed-time affine formation control rate according to a time function gain, a communication relation among agents in the multi-agent cluster system and a target formation configuration;
s3, performing formation control on the multi-agent cluster system by using the distributed self-adaptive fixed-time affine formation control rate.
2. The method for controlling adaptive fixed-time affine formation of multi-agent cluster system according to claim 1, wherein a class of time functions set in step S1 is specifically:
wherein,tin order to be able to take time,t f for affine formation time set according to different formation task requirements,is a kind of time function->Is of the initial value of->And->Respectively are a kind of time functions intTime of day and time of dayt f The right derivative of time.
3. The adaptive fixed-time affine formation control method of a multi-agent cluster system according to claim 2, wherein the time function gains constructed in step S1 are specifically:
wherein,gain for a class of time functions->Is constant.
4. The method for controlling adaptive fixed-time affine formation of a multi-agent cluster system according to claim 1, wherein step S2 specifically comprises:
and determining the distributed self-adaptive fixed-time affine formation control rate of the leader system according to the gain of the time function, the communication relation among the agents in the multi-agent cluster system and the target formation configuration.
5. The method for controlling adaptive fixed-time affine formation of multi-agent cluster system according to claim 4, wherein the control rate of the distributed adaptive fixed-time affine formation of the leader system is specifically as follows:
wherein,is the firstiControl input of individual agent,/->Gain for a class of time functions->For adaptively controlling gain->For the number of agents in the multi-agent cluster system, < ->Is the first in the multi-agent cluster systemiPersonal agent and the firstjCommunication weight between the individual agents, +.>And->Respectively the firstiPersonal agent and the firstjStatus of individual agent->To set parameters +.>Gain +.>Rate of change of->Is the square of the two norms.
6. The method for controlling adaptive fixed-time affine formation of a multi-agent cluster system according to claim 1, wherein step S2 specifically comprises:
and determining the distributed self-adaptive fixed-time affine formation control rate of the Leader-follower system according to the time function gains, the communication relations among the agents in the multi-agent cluster system and the target formation configuration.
7. The method for controlling adaptive fixed-time affine formation of a multi-agent cluster system according to claim 6, wherein the distributed adaptive fixed-time affine formation control rate of the Leader-follower system is specifically:
wherein,is the firstiControl input of individual agent,/->Gain for a class of time functions->And->Are all self-adaptive control gains->For the number of agents in the multi-agent cluster system, < ->Is the first in the multi-agent cluster systemiPersonal agent and the firstjCommunication weight between the individual agents, +.>And->Respectively the firstiPersonal agent and the firstjShape of individual agentStatus of->For manually setting parameters->And->Adaptive control gain respectively>And->Rate of change of->Is two norms>Is the square of the two norms,N i is the firstiThe neighbor set of the individual agents, sgn, is a sign function.
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