Multi-agent system control method with saturation constraint and time delay

Abstract

The invention provides a multi-agent system control method under saturation constraint and time delay, which relates to the technical field of intelligent control, and comprises the following steps: establishing a multi-agent system model, establishing a virtual leader between a leader agent and a follower agent, communicating the follower with the virtual leader, communicating the virtual leader with the leader, and establishing a multi-agent system model between the leader agent and the follower agent; on the basis, a controller is designed based on saturation constraint and communication time delay, an error system between a follower agent and a leader is constructed, a consistency condition is established, and a multi-agent system is controlled to realize leader following consistency. Aiming at the problem of different dimensions between the leader and the follower in the model, the virtual leader is established between the leader and follower agents, and the communication between the actual leader and follower is completed. In addition, aiming at the actual situation that the inherent attributes of the intelligent agent are limited, a control protocol is adjusted based on saturation constraint information and communication time lag, and leader following consistency of the system is achieved.

Description

Technical Field

[0001] The present invention relates to the field of intelligent control technology, and in particular to a multi-agent system control method under saturation constraints and time delays. Background Art

[0002] The collective intelligence of multi-agent systems (MAS) is usually reflected in cluster behavior. The cooperative control of multi-agent systems has attracted widespread attention in recent years due to its broad application prospects, such as multi-UAV cluster coverage, robot cluster formation, and unmanned vehicle cluster encirclement. The consistency tracking problem of multi-agent systems has attracted the research of many scholars as an important issue in the field of cooperative control of multi-agent systems. Multi-agent systems can not only overcome the limitations of individual agents in terms of load, coverage, and fault tolerance, but also improve the execution efficiency of cooperative tasks and the survivability of the entire system. The leader-follower consistency control problem is a basic problem of cooperative control of multi-agent systems and has been widely studied. Leader-follower consistency control refers to that all followers track the trajectory of the leader.

[0003] However, the state dimensions between leaders and followers are different, and it is not feasible to directly use the relative information between leaders and followers to design control protocols. In addition, communication saturation constraints and communication delays may occur in practical applications, which will have an adverse impact on consistency tracking. Summary of the invention

[0004] The purpose of the present invention is to solve the problem of poor control effect between leaders and followers in current multi-agent systems. The present invention provides a multi-agent system control method under saturation constraints and time delays.

[0005] The technical solution of the embodiment of the present application is implemented as follows:

[0006] A first aspect of an embodiment of the present application provides a multi-agent system control method under saturation constraints and time delay, comprising:

[0007] S110, establish a multi-agent system model;

[0008] Consider a heterogeneous multi-agent system consisting of x followers and 1 leader, whose dynamic equation is as follows:

[0009]

[0010] Among them, ρ a (t)∈Rp,Θ a (t) respectively represent the state and control input of the ith follower, ρ0(t)∈R q , Θ0(t) is the leader state and control input, and p≠q, κ a∈R p×p and κ0∈R q×q is a preset parameter matrix, at least one follower gets information from the leader, and there is a matrix ω a Make ω a κ0=κ a ω a ,a={1,2,…,χ};

[0011] A virtual leader is established between the leader and follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader; the dynamic equation of the virtual leader is as follows:

[0012]

[0013] S120, design controller;

[0014] The control protocol is adjusted based on saturation constraints and communication delays. The control protocol is as follows:

[0015]

[0016] Among them, α a , β a is the parameter of the control protocol, v is the delay time, s ab , σ a Determined by the topology map of HMAS. i} is a set of pulse time series, satisfying 0<t i <t i+1 and

[0017] S130, constructing an error system between the follower agent and the leader;

[0018] The error between the follower and the virtual leader is ψ a (t) = ρ a (t)-ω a Ψ a (t), the error between the virtual leader and the actual leader is φ a (t) = Ψ a (t)-ρ0(t), from which we can get:

[0019]

[0020] Among them, ψ(t)=[ψ1(t), ψ2(t), ..., ψ χ (t)] T ,φ(t)=[φ1(t),φ2(t),...,φ χ (t)] T,κ=diag[κ1,κ2,...,κ χ ], κ0=diag[κ0, κ0,...,κ0], ω=diag[ω1, ω2,...,ω χ ],σ=diag[σ1,σ2,...,σ χ ],α=diag[α1,α2,...,α χ ], β=diag[β1, β2,...,β χ ],

[0021] S140. Establish consistency conditions when the following inequalities are met:

[0022]

[0023] The multi-agent system is controlled to achieve leader-follower consistency.

[0024] Optionally, a virtual leader is established between the leader and the follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader, including:

[0025] At least one virtual leader is set for each follower, and a first connection channel is established between the follower and the corresponding virtual leader, and a second connection channel is established between each virtual leader and the leader.

[0026] Optionally, the method further includes: using graph theory knowledge to establish information interaction characteristics between the leader and the virtual leader and between the virtual leader and the followers.

[0027] A second aspect of the embodiment of the present application provides a multi-agent system control device under saturation constraints and time delay, comprising: a model building module, a control design module, an error system construction module and a consistency control module, wherein:

[0028] The model building module is configured to build a multi-agent system model;

[0029] Consider a heterogeneous multi-agent system consisting of x followers and 1 leader, whose dynamic equation is as follows:

[0030]

[0031] Among them, ρ a (t)∈R p , Θ a (t) respectively represent the state and control input of the ith follower, ρ0(t)∈R q , Θ0(t) is the leader state and control input, and p≠q, κa ∈R p×p and κ0∈R q×q is a preset parameter matrix, at least one follower gets information from the leader, and there is a matrix ω a Make ω a κ0=κ a ω a ,a={1,2,…,χ};

[0032] A virtual leader is established between the leader and follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader; the dynamic equation of the virtual leader is as follows:

[0033]

[0034] The control design module is configured to design a controller;

[0035] The control protocol is adjusted based on saturation constraints and communication delays. The control protocol is as follows:

[0036]

[0037] Among them, α a , β a is the parameter of the control protocol, v is the delay time, s ab , σ a Determined by the topology map of HMAS. i} is a set of pulse time series, satisfying 0<t i <t i+1 and

[0038] The error system building module is configured to build an error system between the follower agent and the leader;

[0039] The error between the follower and the virtual leader is ψ a (t) = ρ a (t)-ω a Ψ a (t), the error between the virtual leader and the actual leader is φ a (t) = Ψ a (t)-ρ0(t), from which we can get:

[0040]

[0041] Among them, ψ(t)=[ψ1(t), ψ2(t), ..., ψ χ (t)] T ,φ(t)=[φ1(t),φ2(t),...,φχ (t)] T ,κ=diag[κ1,κ2,...,κ χ ], κ0=diag[κ0, κ0,...,κ0], ω=diag[ω1, ω2,...,ω χ ],σ=diag[σ1,σ2,...,σ χ ],α=diag[α1,α2,...,α χ ], β=diag[β1, β2,...,β χ ],

[0042] The consistency control module is configured to establish a consistency condition when the following inequality is satisfied:

[0043]

[0044] The multi-agent system is controlled to achieve leader-follower consistency.

[0045] A third aspect of an embodiment of the present application provides an electronic device, comprising a processor and a memory; the memory stores a computer program, wherein the computer program, when executed by the processor, implements the multi-agent system control method under saturation constraints and delays described in the first aspect.

[0046] A fourth aspect of an embodiment of the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0047] Compared with the prior art, the technical solution provided by this application has the following beneficial effects:

[0048] The present invention provides a method and device for controlling a multi-agent system under saturation constraints and time delays. By establishing a multi-agent system model, at least one virtual leader is set between the leader and the follower, the follower communicates with the virtual leader, and the virtual leader communicates with the actual leader. On this basis, a controller is designed based on saturation constraints and communication time delays, an error system between the follower agent and the leader is constructed, and consistency conditions are established to control the multi-agent system to achieve leader-follower consistency. By constructing a virtual leader between the leader and the follower, the communication between the actual leader and the follower is completed. In addition, in view of the actual situation where the inherent attributes of the agent are limited, the control protocol is adjusted based on saturation constraint information and communication time delay, so that the system achieves leader-follower consistency, thereby improving the consistency tracking accuracy of the multi-agent system. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1A flow chart of a multi-agent system control method under saturation constraints and time delay provided in an embodiment of the present application;

[0050] Figure 2 A schematic diagram of the structure of a multi-agent system control device with saturation constraints and time delay provided in an embodiment of the present application;

[0051] Figure 3 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0052] Below, embodiments of the present application will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present application. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present application. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concepts of the present application.

[0053] The terms used herein are only for describing specific embodiments and are not intended to limit the present application. The terms "include", "comprising", etc. used herein indicate the existence of the features, steps, operations and / or components, but do not exclude the existence or addition of one or more other features, steps, operations or components.

[0054] All terms (including technical and scientific terms) used herein have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification, and should not be interpreted in an idealized or overly rigid manner.

[0055] Some block diagrams and / or flow charts are shown in the accompanying drawings. It should be understood that some blocks or combinations thereof in the block diagrams and / or flow charts may be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that these instructions, when executed by the processor, may create a device for implementing the functions / operations described in these block diagrams and / or flow charts.

[0056] In some embodiments, see Figure 1 , Figure 1 A flow chart of a multi-agent system control method under saturation constraints and time delay provided in an embodiment of the present application; a multi-agent system control method under saturation constraints and time delay provided in an embodiment of the present application includes:

[0057] S110, establish a multi-agent system model;

[0058] Consider a heterogeneous multi-agent system consisting of x followers and 1 leader, whose dynamic equation is as follows:

[0059]

[0060] Among them, ρ a (t)∈R p , Θ a (t) respectively represent the state and control input of the ith follower, ρ0(t)∈R q , Θ0(t) is the leader state and control input, and p≠q, κ a ∈R p×p and κ0∈R q×q is a preset parameter matrix, at least one follower gets information from the leader, and there is a matrix ω a Make ω a κ0=κ a ω a ,a={1,2,…,χ};

[0061] A virtual leader is established between the leader and follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader; the dynamic equation of the virtual leader is as follows:

[0062]

[0063] S120, design controller;

[0064] The control protocol is adjusted based on saturation constraints and communication delays. The control protocol is as follows:

[0065]

[0066] Among them, α a , β a is the parameter of the control protocol, v is the delay time, s ab , σ a Determined by the topology map of HMAS. i} is a set of pulse time series, satisfying 0<t i <t i+1 and

[0067] S130, constructing an error system between the follower agent and the leader;

[0068] The error between the follower and the virtual leader is ψ a (t) = ρ a (t)-ω a Ψ a(t), the error between the virtual leader and the actual leader is φ a (t) = Ψ a (t)-ρ0(t), from which we can get:

[0069]

[0070] Among them, ψ(t)=[ψ1(t), ψ2(t), ..., ψ χ (t)] T ,φ(t)=[φ1(t),φ2(t),...,φ χ (t)] T ,κ=diag[κ1,κ2,...,κ χ ], κ0=diag[κ0, κ0,...,κ0], ω=diag[ω1, ω2,...,ω χ ],σ=diag[σ1,σ2,...,σ χ ],α=diag[α1,α2,...,α χ ], β=diag[β1, β2,...,β χ ],

[0071] S140. Establish consistency conditions when the following inequalities are met:

[0072]

[0073] Controlling multi-agent systems to achieve leader-follower consensus.

[0074] In some embodiments, the Lyapunov function is constructed When t≠t i hour:

[0075]

[0076] Can get ; When t = t i hour:

[0077]

[0078] At this point, we can get:

[0079]

[0080] When t∈[t0,t1], Further deduction shows that when t∈(t i , t i+1 ]hour,

[0081]

[0082] Define the maximum value d of the pulse interval max ≥t i -t i-1 , Can get

[0083]

[0084] If the above conditions are met, the system can achieve consistency.

[0085] In some embodiments, a virtual leader is established between a leader and a follower agent, the follower communicates with the virtual leader, and the virtual leader communicates with the leader, including:

[0086] At least one virtual leader is set for each follower, and a first connection channel is established between the follower and the corresponding virtual leader, and a second connection channel is established between each virtual leader and the leader.

[0087] In this embodiment, the virtual leader acts as an intermediate layer between the actual leader and the followers, and becomes an intermediary for communication and coordination. The leader, the virtual leader and the followers are connected through different connection channels. The virtual leader can simplify the complex instructions of the actual leader into a form that is easy for the followers to understand and execute, and then transmit it to the followers. It can also monitor the status of the followers and feedback to the actual leader to make necessary adjustments. Exemplarily, in a robot formation task, one or more actual leaders are responsible for overall task planning, while the virtual leader is responsible for assigning complex tasks to each robot (follower) and monitoring their execution. In a distributed system, the actual leader can be a master node, responsible for overall scheduling and resource allocation. The virtual leader, as a child node or agent, is responsible for assigning tasks to each computing unit (follower) and collecting their execution results. In a large network, the actual leader can be a network control center, and the virtual leader can be a regional router or switch, responsible for conveying the instructions of the network control center to each network node (follower) and monitoring the network status. The virtual leader can adjust the communication strategy with the followers according to the actual situation to optimize the system performance.

[0088] In some embodiments, it also includes: using graph theory knowledge to establish information interaction characteristics between the leader and the virtual leader and between the virtual leader and the followers.

[0089] When using graph theory to establish the information interaction characteristics between leaders, virtual leaders, and followers, the system can be viewed as a directed graph. In this graph, nodes represent different entities (leaders, virtual leaders, and followers), and directed edges represent the direction of information flow. Information starts from the leader node, passes through the virtual leader node, and finally reaches the follower node, forming a hierarchical information transmission structure. This hierarchy helps reduce the direct communication burden between the leader and a large number of followers, thereby improving the scalability of the system.

[0090] The embodiment of the present application establishes a multi-agent system model, sets at least one virtual leader between the leader and the follower, the follower communicates with the virtual leader, and the virtual leader communicates with the actual leader. On this basis, a controller is designed based on saturation constraints and communication time delays, an error system between the follower agent and the leader is constructed, and consistency conditions are established to control the multi-agent system to achieve leader-follow consistency. By constructing a virtual leader between the leader and the follower, the communication between the actual leader and the follower is completed. In addition, in view of the actual situation where the inherent properties of the agent are limited, the control protocol is adjusted based on saturation constraint information and communication time delay, so that the system achieves leader-follow consistency, thereby improving the consistency tracking accuracy of the multi-agent system.

[0091] In some embodiments, see Figure 2 , Figure 2 The schematic diagram of the structure of a multi-agent system control device under saturation constraints and time delay provided in an embodiment of the present application. The multi-agent system control device 200 under saturation constraints and time delay provided in an embodiment of the present application includes: a model building module 210, a control design module 220, an error system construction module 230 and a consistency control module 240, wherein:

[0092] A model building module 210, configured to build a multi-agent system model;

[0093] Consider a heterogeneous multi-agent system consisting of x followers and 1 leader, whose dynamic equation is as follows:

[0094]

[0095] Among them, ρ a (t)∈R p , Θ a (t) respectively represent the state and control input of the ith follower, ρ0(t)∈R q , Θ0(t) is the leader state and control input, and p≠q, κ a ∈R p×p and κ0∈R q×qis a preset parameter matrix, at least one follower gets information from the leader, and there is a matrix ω a Make ω a κ0=κ a ω a ,a={1,2,…,χ};

[0096] A virtual leader is established between the leader and follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader; the dynamic equation of the virtual leader is as follows:

[0097]

[0098] A control design module 220 configured to design a controller;

[0099] The control protocol is adjusted based on saturation constraints and communication delays. The control protocol is as follows:

[0100]

[0101] Among them, α a , β a is the parameter of the control protocol, v is the delay time, s ab , σ a Determined by the topology map of HMAS. i} is a set of pulse time series, satisfying 0<t i <t i+1 and

[0102] an error system building module 230, configured to build an error system between the follower agent and the leader;

[0103] The error between the follower and the virtual leader is ψ a (t) = ρ a (t)-ω a Ψ a (t), the error between the virtual leader and the actual leader is φ a (t) = Ψ a (t)-ρ0(t), from which we can get:

[0104]

[0105] Among them, ψ(t)=[ψ1(t), ψ2(t), ..., ψ χ (t)] T ,φ(t)=[φ1(t),φ2(t),...,φ χ (t)] T ,κ=diag[κ1,κ2,...,κχ ], κ0=diag[κ0, κ0,...,κ0], ω=diag[ω1, ω2,...,ω χ ],σ=diag[σ1,σ2,...,σ χ ],α=diag[α1,α2,...,β χ ], β=diag[β1, β2,...,β χ ],

[0106] The consistency control module 240 is configured to establish a consistency condition when the following inequality is satisfied:

[0107]

[0108] Controlling multi-agent systems to achieve leader-follower consensus.

[0109] In some embodiments, the model building module 210 is specifically configured as follows:

[0110] At least one virtual leader is set for each follower, and a first connection channel is established between the follower and the corresponding virtual leader, and a second connection channel is established between each virtual leader and the leader.

[0111] In some embodiments, the model building module 210 is further specifically configured to: use graph theory knowledge to establish information interaction characteristics between the leader and the virtual leader, and between the virtual leader and the followers.

[0112] The multi-agent system control device under saturation constraints and time delay provided in the embodiment of the present application can implement the various processes in the embodiments corresponding to the above-mentioned multi-agent system control method under saturation constraints and time delay. To avoid repetition, they will not be repeated here.

[0113] It should be noted that the multi-agent system control device under saturation constraints and time delays provided in the embodiment of the present application and the multi-agent system control method under saturation constraints and time delays provided in the embodiment of the present application are based on the same application concept. Therefore, the specific implementation of this embodiment can refer to the implementation of the aforementioned multi-agent system control method under saturation constraints and time delays, and the repeated parts will not be repeated.

[0114] In some embodiments, see Figure 3 , Figure 3 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. An electronic device 300 provided in an embodiment of the present application includes a processor 310 and a memory 320; the memory 320 stores a computer program, wherein the computer program implements the above-mentioned multi-agent system control method under saturation constraints and delay when executed by the processor.

[0115] Specifically, the processor 310 may include, for example, a general-purpose microprocessor, an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), etc. The processor 310 may also include an onboard memory for cache purposes. The processor 310 may be a single processing unit or multiple processing units for executing different actions of the method flow according to the embodiment of the present application.

[0116] The memory 320 may be any medium capable of containing, storing, conveying, propagating or transmitting instructions. For example, the memory 320 may include, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared or semiconductor system, device, component or propagation medium. Specific examples of the memory 320 include: a magnetic storage device, such as a magnetic tape or a hard disk (HDD); an optical storage device, such as a compact disk (CD-ROM); a random access memory (RAM) or flash memory; and / or a wired / wireless communication link.

[0117] The present application also provides a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned multi-agent system control method under saturation constraints and delays. The computer-readable medium may be included in the device / apparatus / system described in the above-mentioned embodiments; or it may exist independently without being assembled into the device / apparatus / system. The above-mentioned computer-readable medium carries one or more programs, and when the above-mentioned one or more programs are executed, the method according to the embodiment of the present application is implemented.

[0118] According to an embodiment of the present application, a computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. A computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that may be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, wherein a computer-readable program code is carried. Such propagated data signals may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wired, optical cable, radio frequency signal, etc., or any suitable combination of the above.

[0119] Those skilled in the art will appreciate that the features described in the various embodiments and / or claims of the present application may be combined and / or combined in a variety of ways, even if such combinations or combinations are not explicitly described in the present application. In particular, without departing from the spirit and teachings of the present application, the features described in the various embodiments and / or claims of the present application may be combined and / or combined in a variety of ways. All of these combinations and / or combinations fall within the scope of the present application. Therefore, the scope of the present application should not be limited to the above-described embodiments, but should be determined not only by the appended claims, but also by the equivalents of the appended claims.

Claims

1. A control method for a multi-agent system with saturation constraints and time delay, characterized in that: include: S110, establish a multi-agent system model; Consider a heterogeneous multi-agent system consisting of x followers and 1 leader, whose dynamic equation is as follows: Among them, ρ a (t)∈R p , Θ a (t) respectively represent the state and control input of the ith follower, ρ0(t)∈R q , Θ0(t) is the leader state and control input, and p≠q, κ a ∈R p×p and κ0∈R q×q is a preset parameter matrix, at least one follower gets information from the leader, and there is a matrix ω a Make ω a κ0=κ a ω a , a={1,2,…,χ}; A virtual leader is established between the leader and follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader; the dynamic equation of the virtual leader is as follows: S120, design controller; The control protocol is adjusted based on saturation constraints and communication delays. The control protocol is as follows: Among them, α a , β a is the parameter of the control protocol, v is the delay time, s ab , σ a Determined by the topology map of HMAS. i } is a set of pulse time series, satisfying 0 <t i <t i+1 and S130, constructing an error system between the follower agent and the leader; The error between the follower and the virtual leader is ψ a (t) = ρ a (t)-ω a ψ a (t), the error between the virtual leader and the actual leader is φ a (t) = ψ a (t)-ρ0(t), from which we can get: Where, ψ(t) = [ψ1(t), ψ2(t),..., ψ χ (t)] T ,φ(t)=[φ1(t),φ2(t),…,φ χ (t)] T ,κ=diag[κ1,κ2,…,κ χ ], κ0 = diag[κ0, κ0,…, κ0], ω = diag[ω1, ω2,…, ω χ ],σ=diag[σ1,σ2,...,σ χ ], α=diag[α1, α2,..., α χ ], β=diag[β1, β2,..., β χ ], S140. Establish consistency conditions when the following inequalities are met: The multi-agent system is controlled to achieve leader-follower consistency.

2. The multi-agent system control method under saturation constraints and time delay according to claim 1, characterized in that: The step of establishing a virtual leader between a leader and a follower agent, wherein the follower communicates with the virtual leader, and the virtual leader communicates with the leader, comprises: At least one virtual leader is set for each follower, and a first connection channel is established between the follower and the corresponding virtual leader, and a second connection channel is established between each virtual leader and the leader.

3. The multi-agent system control method under saturation constraints and time delay according to claim 1, characterized in that: Also includes: The information interaction characteristics between the leader and the virtual leader and between the virtual leader and the followers are established by using graph theory knowledge.

4. A multi-agent system control device under saturation constraints and time delay, characterized in that: include: Model building module, control design module, error system building module and consistency control module, among which, The model building module is configured to build a multi-agent system model; Consider a heterogeneous multi-agent system consisting of x followers and 1 leader, whose dynamic equation is as follows: Among them, ρ a (t)∈R p , Θ a (t) respectively represent the state and control input of the ith follower, ρ0(t)∈R q , Θ0(t) is the leader state and control input, and p≠q, κ a ∈R p×p and κ0∈R q×q is a preset parameter matrix, at least one follower gets information from the leader, and there is a matrix ω a Make ω a κ0=κ a ω a , a={1,2,…,χ}; A virtual leader is established between the leader and follower agents, the followers communicate with the virtual leader, and the virtual leader communicates with the leader; the dynamic equation of the virtual leader is as follows: The control design module is configured to design a controller; The control protocol is adjusted based on saturation constraints and communication delays. The control protocol is as follows: Among them, α a , β a is the parameter of the control protocol, v is the delay time, s ab , σ a Determined by the topology map of HMAS. i } is a set of pulse time series, satisfying 0 <t i <t i+1 and The error system building module is configured to build an error system between the follower agent and the leader; The error between the follower and the virtual leader is ψ a ( t )=ρ a (t)-ω a ψ a (t), the error between the virtual leader and the actual leader is φ a (t) = ψ a (t)-ρ0(t), from which we can get: Where, ψ(t) = [ψ1(t), ψ2(t),..., ψ χ (t)] T ,φ(t)=[φ1(t),φ2(t),…,φ χ (t)] T ,κ=diag[κ1,κ2,…,κ χ ], κ0 = diag[κ0, κ0,…, κ0], ω = diag[ω1, ω2,…, ω χ ],σ=diag[σ1,σ2,...,σ χ ], α=diag[α1, α2,..., α χ ], β=diag[β1, β2,..., β χ ], The consistency control module is configured to establish a consistency condition when the following inequality is satisfied: The multi-agent system is controlled to achieve leader-follower consistency.

5. An electronic device comprising a processor and a memory; the memory stores a computer program, wherein: When the computer program is executed by the processor, the computer program implements the multi-agent system control method under saturation constraints and delays according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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