A nonlinear second-order multi-agent system including a control method and a system

Abstract

The present invention discloses a second-order nonlinear multi-agent system inclusion control method and system, including: establishing a nonlinear second-order multi-agent system; setting a compensator for the nonlinear second-order multi-agent system; setting an inclusion control strategy for the nonlinear second-order multi-agent system based on a distributed compensator time-delay control algorithm; and verifying the stability of the nonlinear second-order multi-agent system. Through the intelligent adjustment and time-delay processing of the compensator, the follower agent can gradually tend to the trajectory within the convex hull formed by the leader agent, thereby achieving collaborative work and inclusion control; through the analysis and verification of Lyapunov stability theory and nonlinear dynamic systems, the effectiveness and feasibility of the proposed control protocol are proved. Compared with traditional methods, the present invention has better robustness and can handle nonlinear effects and inherent time delays in the system, thereby improving the performance and stability of the system.

Description

Technical Field

[0001] The present invention relates to the field of nonlinear second-order multi-agent system inclusion control, in particular to a nonlinear second-order multi-agent system inclusion control method based on a compensator and containing inherent time delay; Background Art

[0002] With the rapid development of today's intelligent and autonomous systems, multi-agent systems have also been widely used in various fields, such as robot collaboration, social networks, traffic flow control, etc.; these systems are composed of multiple agents that work together to complete various complex tasks; however, a common challenge facing multi-agent systems is how to achieve efficient coordination and inclusive control to ensure system stability and optimal performance.

[0003] In multi-agent systems, communication and coordination between agents play a vital role; effective communication and coordination are key factors to ensure the smooth operation of the system; however, multi-agent systems are often affected by a series of challenges:

[0004] 1. Communication instability: The communication channel may be disturbed or unstable, resulting in unreliable information transmission, thus affecting the stability of the system; 2. Bandwidth limitation: The communication bandwidth is limited, which may limit the speed and capacity of information exchange between intelligent agents and limit the performance of the system; 3. Packet loss: During the communication process, data packets may be lost, which may lead to incomplete information and interfere with the decision-making and control of the system.

[0005] To meet these challenges, researchers have been seeking innovative control methods and communication strategies; adaptive control methods allow the system to adjust the control strategy according to environmental changes and uncertainties to maintain system stability and performance; on the other hand, intermittent communication strategies reduce the impact of communication delays on the system by reducing the communication frequency and burden.

[0006] Traditional multi-agent systems usually rely on continuous communication to exchange information; however, in some cases, continuous communication may lead to excessive communication burden, reduce system efficiency and increase energy consumption; therefore, researchers introduced the concept of intermittent communication, that is, agents communicate with each other regularly, and during the communication intervals, the agents can perform tasks and make decisions independently to reduce the communication burden.

[0007] Although intermittent communication solves the problem of communication burden to a certain extent, it may still lead to system performance degradation in some complex tasks and highly coordinated situations; therefore, an innovative control method is needed that can maintain the stability and efficiency of the multi-agent system while taking intermittent communication into account. Summary of the invention

[0008] In view of the shortcomings of the prior art mentioned above, the present invention provides a nonlinear second-order multi-agent system inclusion control method and system, which uses compensator control to solve the inclusion control problem; by introducing a controller with optimized design and using a directed topological structure to construct the Laplace matrix, a monotonic convergence characteristic and a faster convergence speed are obtained, thereby improving the dynamic performance of the system.

[0009] A second-order nonlinear multi-agent system inclusive control method based on compensator and inherent time delay is proposed to cope with the communication and coordination challenges in multi-agent systems. This method combines compensator design with inherent time delay processing to improve the stability and performance of the system, enabling the system to adapt to changes in the external environment and time delay problems, thereby completing various collaborative tasks more effectively. This technological innovation is expected to play an important role in various application fields of multi-agent systems.

[0010] The technical solution of the present invention is as follows:

[0011] In a first aspect, the present invention provides a second-order nonlinear multi-agent system control method, comprising:

[0012] Step 1: Establish a nonlinear second-order multi-agent system;

[0013] Step 2: Set up a compensator for the nonlinear second-order multi-agent system;

[0014] Step 3: Based on the distributed compensator time-delay control algorithm, set the inclusive control strategy of the nonlinear second-order multi-agent system;

[0015] Step 4: Verify the stability of the nonlinear second-order multi-agent system.

[0016] In a second aspect, the present invention provides a second-order nonlinear multi-agent system including a control system, comprising:

[0017] System building module, used to build nonlinear second-order multi-agent systems;

[0018] The compensator setting module is used to set the compensator for the nonlinear second-order multi-agent system;

[0019] The included control strategy setting module is used to set the included control strategy of the nonlinear second-order multi-agent system based on the distributed compensator time-delay control algorithm;

[0020] Stability verification module, used to verify the stability of nonlinear second-order multi-agent systems.

[0021] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0022] Enhanced system stability: By setting a fixed compensator for the nonlinear second-order multi-agent system and setting an inclusive control strategy for the nonlinear second-order multi-agent system based on the distributed compensator time-delay control algorithm, the stability of the nonlinear second-order multi-agent system can be effectively improved; the intelligent adjustment and time-delay processing of the compensator help to alleviate the adverse effects of time delay on system performance, thereby reducing the system's oscillations and instability, allowing the system to remain stable in the face of external disturbances and uncertainties.

[0023] Reduced communication burden: Taking into account the characteristics of communication, the communication burden between agents is effectively reduced through the design of the compensator; it helps to reduce communication delays, improve communication efficiency, and reduce competition for communication bandwidth, thereby making the system's communication interaction more efficient and sustainable.

[0024] Enhanced adaptability: The compensator design can not only handle inherent time delays, but also has adaptability to external environments; enabling the multi-agent system to adapt to different environmental conditions and task requirements, adaptively adjust control strategies and compensator parameters, and ensure that the system remains stable and efficient in various scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a flow chart of the method of the present invention;

[0026] Figure 2 It is a model block diagram of a multi-agent system including control;

[0027] Figure 3 It is a communication topology diagram;

[0028] Figure 4a is a state trajectory diagram under the control protocol of this application;

[0029] Figure 4b is the controller state trajectory diagram in this application;

[0030] Figure 5 is the relative position error trajectory diagram in this application;

[0031] Figure 6 is the relative velocity error trajectory diagram in this application;

[0032] Figure 7 It is the compensator state trajectory diagram in this application. DETAILED DESCRIPTION

[0033] Example

[0034] This embodiment proposes a nonlinear second-order multi-agent system inclusion control method. Figure 1 ,include:

[0035] Step 1: Establish a nonlinear second-order multi-agent system;

[0036] Step 2: Set a fixed compensator for the nonlinear second-order multi-agent system. Through this compensator-based design, the control method can better adapt to changes in the external environment and inherent time lags, thereby improving the performance and stability of the system and making it widely applicable in various application fields.

[0037] Step 3: Based on the distributed compensator time-delay control algorithm, set the inclusive control strategy of the nonlinear second-order multi-agent system;

[0038] Step 4: Verify the stability of the nonlinear second-order multi-agent system.

[0039] The present invention aims to deal with the problem of inclusion control in a multi-agent system; by introducing a compensator design and a strategy for dealing with inherent time delays, an innovative control protocol is proposed to achieve coordinated motion and inclusion control of agents in the system; the control method enables the follower agent to gradually tend to the trajectory within the convex hull formed by the leader agent through intelligent adjustment of the compensator and time delay processing, thereby achieving collaborative work and inclusion control. In the present invention, the effectiveness and feasibility of the proposed control protocol are proved through the analysis and verification of Lyapunov stability theory and nonlinear dynamic systems. Compared with traditional methods, the present invention has better robustness and can deal with nonlinear effects and inherent time delays in the system, thereby improving the performance and stability of the system; simulation experiments further verify the excellent performance and feasibility of the control method of the present invention in a multi-agent system.

[0040] The present invention is not only suitable for multi-agent collaborative tasks, but can also play a key role in many fields such as robot collaboration, social networks, traffic flow control, and autonomous driving fleets. By innovatively integrating compensator design and inherent time-delay processing strategies, it provides a more reliable and efficient solution for the collaboration and control of multi-agent systems in practical applications, which has practical value for improving system performance and promoting applications.

[0041] As a preferred technical solution, in this embodiment, step 1 is specifically as follows:

[0042] Modeling of nonlinear second-order multi-agent systems, considering the dynamic interactions and coordination relationships between agents; describing the position and velocity changes of agents by establishing a nonlinear second-order dynamic model, so as to facilitate subsequent control design and analysis;

[0043] Set up a A nonlinear second-order multi-agent system with agents, where the followers have , leaders have ; define the follower agent as , the leader agent is ; The follower set and leader set are defined as and ;

[0044] Followers The model is described as:

[0045]

[0046] in, Respectively represent The position, velocity and control input of each agent, is a nonlinear term and a continuous function, is the delay time;

[0047] Leaders The model is described as:

[0048]

[0049] in, Respectively represent The position and speed of each agent; since the leader has no neighbors, the Laplacian matrix is ​​decomposed into:

[0050]

[0051] In the formula, L1 is The matrix related to the information flow of followers is is with Leaders to The matrix related to the information flow of followers is In the present invention, the Laplacian matrix is ​​given by Figure 3 The communication topology diagram is obtained.

[0052] As a preferred technical solution, in this embodiment, step 2 is specifically as follows:

[0053] Design a compensator. Through this compensator-based design, the control method can better adapt to changes in the external environment and inherent time lags, thereby improving the performance and stability of the system and making it widely applicable in various application fields:

[0054] The first The error of a follower is defined as:

[0055]

[0056] In the formula, j Indicates followers j ;

[0057] To achieve inclusive control, unknown state estimation and information transfer lag, a fixed compensator is used to design the controller;

[0058] For Agent, the fixed compensator is designed as:

[0059]

[0060] in, is the state variable of formula (5), is an appropriate constant.

[0061] As a preferred technical solution, in this embodiment, step 3 is specifically as follows:

[0062] A control protocol based on compensator and inherent time delay is proposed to realize the inclusive control strategy of the system;

[0063] The time-delay control algorithm based on distributed compensator is as follows:

[0064]

[0065] in, To control the parameters, is a constant;

[0066] No. Each agent uses a distributed compensator time-delay control algorithm to achieve inclusive control of the leader and the follower, namely:

[0067]

[0068] in, ;

[0069] From formula (5), we get:

[0070]

[0071]

[0072]

[0073] From formula (6), we get:

[0074]

[0075]

[0076] Defining vectors ,according to Definition , ;

[0077] According to formula (1), (2), (7) The derivative is:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] definition ;

[0086] From formula (7), we know:

[0087]

[0088] Further simplified to:

[0089]

[0090] in, ;

[0091] Similarly simplified ,Right now:

[0092]

[0093] definition , from formula (8) and formula (9), we know:

[0094]

[0095]

[0096] in, , ,

[0097] Depend on Definition, combining (1), (2), and (4) we get:

[0098]

[0099] in, ;

[0100] According to formula (10), we have:

[0101]

[0102] in, , .

[0103] As a preferred technical solution, in this embodiment, step 4 is specifically as follows:

[0104] Prove the stability of the system through Lyapunov function:

[0105] Consider the Lyapunov candidate function as:

[0106] ,

[0107] According to formula (10), Taking the derivative, we get:

[0108]

[0109]

[0110] in, is the Hurwitz matrix, by choosing a suitable ,get ;

[0111] therefore, ,and ,have to:

[0112]

[0113]

[0114]

[0115]

[0116] in, , ;

[0117] After sorting, we get:

[0118]

[0119]

[0120] (11)

[0121] Similarly,

[0122]

[0123] (12)

[0124] By introducing equations (11) and (12), we can get:

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] in, , ;

[0135] Right now

[0136] in, ;

[0137] Right now

[0138]

[0139] in, ,and ;

[0140] and ,Right now for the lower world;

[0141] Arranged

[0142] therefore, ,Right now , similarly ;

[0143] Also verify:

[0144]

[0145]

[0146] Right now , , at this time the nonlinear second-order multi-agent system is stable.

[0147] The second-order nonlinear multi-agent system including the control system provided in an embodiment of the present invention is introduced below. The second-order nonlinear multi-agent system including the control system described below and the second-order nonlinear multi-agent system including the control method described above can be cross-referenced.

[0148] The second-order nonlinear multi-agent system provided by the embodiment of the present invention includes a control system, including:

[0149] System building module, used to build nonlinear second-order multi-agent systems;

[0150] The compensator setting module is used to set the compensator for the nonlinear second-order multi-agent system;

[0151] The included control strategy setting module is used to set the included control strategy of the nonlinear second-order multi-agent system based on the distributed compensator time-delay control algorithm;

[0152] Stability verification module, used to verify the stability of nonlinear second-order multi-agent systems.

[0153] according to Figure 2 The multi-agent system includes a control model block diagram; first set the initial state of each agent , , , , in the initial state, each agent already has a time delay. When the simulation time is less than the deadline, the controller and other agents will deduce the relative error to update the compensator according to the state of each agent at the previous moment, and then update the controller; this process is repeated until the simulation deadline is reached;

[0154] Figure 3 The figure is a communication topology diagram with three leaders and five followers. The arrows indicate the direction of communication, i.e., information is transmitted from the node pointed to by the arrow to the node where the arrow starts. The communication relationship is: leader 1 communicates with follower 3, leader 2 communicates with follower 4, leader 3 communicates with follower 1, follower 1 communicates with follower 2, follower 4, and follower 5, follower 2 communicates with follower 1 and follower 3, and follower 4 communicates with follower 1. Each leader communicates with its corresponding follower, and there are also communication connections between followers, forming a complex communication network.

[0155] Figure 4aIt is the state trajectory diagram under the control protocol; the X-axis is the horizontal coordinate of each agent, the Y-axis is the vertical coordinate of each agent, and the Z-axis is time; each agent updates its state according to time, and it can be seen that the controller quickly guides the five agents into the convex hull formed by the three leader states; in the following time, each follower state has been maintained in the convex hull, and is updated synchronously with the leader position and speed, the position remains relatively static, and the speed is the same; and from the local enlarged diagram, it can be seen that it still has the inclusion control effect after convergence, which shows that the inclusion control method adopted has significant effectiveness and excellent stability in this nonlinear second-order multi-agent system;

[0156] Figure 4b This is the evolution diagram of the control input under the control protocol; the control input of each follower gradually converges and stabilizes, and remains at 0, indicating that the control protocol adopted by the inclusive control can achieve its control target;

[0157] Figure 5 is the relative position error trajectory diagram; the X-axis and Y-axis represent the relative running time (unit: s) of each agent and the relative position of each agent respectively; it can be seen that the relative position of each agent reaches 0 within 5s, indicating that the controller can meet the experimental expectations and the position state of each follower can always be maintained in the convex hull formed by the leader;

[0158] Figure 6 is the relative speed error trajectory diagram; the X-axis and Y-axis represent the relative running time (unit: s) of each agent and the relative position of each agent respectively; it can be seen that the relative speed of each agent reaches 0 within 5s, indicating that the leaders and followers are After that, it can remain relatively static and meet the control requirements;

[0159] Figure 7 is the state trajectory diagram of the compensator; the compensators of the five follower agents all converged and stabilized within 5 seconds, indicating that the compensator control method can handle the inclusion control problem of nonlinear second-order multi-agent systems.

[0160] Figure 2 The model block diagram of the multi-agent system including control is shown; each agent is given an initial state with time delay , , , , No. k After the batch compensator is updated, the controller u i , update its state and act on the state of each agent , When the simulation time is less than the deadline, the relative error is obtained according to the state of each agent at the previous moment, and then the corresponding compensator and controller are updated. u i , and then update the state of each agent k+1 times , , to implement the included control strategy; and so on until the simulation deadline is reached.

[0161] against Figure 2 The communication topology structure diagram and the nonlinear second-order multi-agent system shown in formula (1) are set as follows:

[0162] The nonlinear second-order multi-agent system consists of five followers and three leaders, denoted as 1-5 as followers and 6-8 as leaders;

[0163] The initial states of the five followers and three leaders are set as:

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172] The nonlinear term of the design is:

[0173]

[0174] Laplacian Matrix , They are designed as follows:

[0175]

[0176] Communication topology such as Figure 2As shown, nodes 1-4 correspond to followers and nodes 5-7 represent leaders; the values ​​of ρ1, ρ2, and ρ3 are determined based on assumptions 2 and 3, and the results are ρ1 = 0.28, ρ2 = 0.008, ρ3 = 0.0032; the parameters k1, k2, γ1, and γ2 can be selected as follows: k1 = 0.4, k2 = 0.3, γ1 = 2, γ2 = 1; the initial values ​​of the compensator components are shown below:

[0177]

[0178] The system simulation time is set to , the sampling time is set to .

[0179] The present invention considers time lag on the basis of the compensator, and the state of the compensator is updated according to the local state information; the controller adopts a control scheme of a fixed compensator, which not only ensures the realization of inclusive control, but also has a certain robustness and a more perfect control effect; through the analysis and proof of the Lyapunov method and matrix inequality, it is proved that when the proposed control scheme is used, the states of all followers can converge to the convex hull formed by the leader; finally, the reliability of the proposed control strategy is verified by a simulation example.

[0180] The above is only a preferred embodiment of the present application, and the present invention is not limited to the above embodiments. It can be understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present invention should be considered to be included in the scope of protection of the present invention.

Claims

1. A second-order nonlinear multi-agent system includes a control method, characterized in that: Including: Step 1: Establish a non - linear second - order multi - agent system; Specifically, Step 1 is as follows: Set up a non - linear second - order multi - agent system with N agents, where there are M followers with M < N and N - M leaders; define the follower agents as 1, …, M and the leader agents as M + 1, …, N; the follower set and the leader set are defined as F = {1, …, M} and L = {M + 1, …, N} respectively; The model of follower i is expressed as: Among them, x i (t),v i (t),u i (t) represents the position, velocity and control input of the ith agent, respectively. f, g are nonlinear terms and continuous functions. τ is the delay time. The model of leader k is expressed as: Among them, x k (t),v k (t) represents the position and speed of the kth agent respectively; since the leader has no neighbors, the Laplacian matrix is ​​decomposed into: Where L1 is the matrix associated with the information flow of M followers, L1∈R M×M , L2 is the matrix associated with the information flow from NM leaders to M followers, L2∈R M×(N-M) ; Step 2: Set a compensator for the non - linear second - order multi - agent system; Specifically, Step 2 is as follows: Define the error of the i - th follower as: where j represents follower j; To achieve containment control, unknown state estimation, and information transfer delay, use a fixed compensator to design a controller; For the i - th agent, the fixed compensator is designed as: Among them, φ i (t) = [φ i1 (t) T ,φ i2 (t) T ] T ∈R 2n is the state variable of formula (5), γ1, γ2 are appropriate constants; Step 3: Based on the distributed compensator time - delay control algorithm, set the containment control strategy of the non - linear second - order multi - agent system; Specifically, Step 3 is as follows: Propose a control protocol based on the compensator and the inherent time - delay to achieve the containment control strategy of the system; The distributed compensator time - delay control algorithm is as follows: u i (t)=-Kφ i (t),i=1,…,M (6) in, is the control parameter, k1, k2 are constants; The i - th agent adopts the distributed compensator time - delay control algorithm to achieve the containment control between the leader and the followers, that is: in, From equation (5), we get: From equation (6), we get: Defining vectors According to φ i ,φ i Definition According to equations (1), (2), and (7), φ i The derivative is: definition From formula (7), we know that: Further simplified to: in, k=[k1,k2], c = [1,0]; Similarly simplified Right now: definition From formula (8) and formula (9), we know: in, By φ i ,φ i Definition, combining (1), (2), and (4) we get: in, According to equation (10), we have: in, Step 4: Verify the stability of the non - linear second - order multi - agent system.

2. The second-order nonlinear multi-agent system control method according to claim 1, characterized in that: In Step 4, verify the stability of the non - linear second - order multi - agent system through the Lyapunov function.

3. The second-order nonlinear multi-agent system control method according to claim 2, characterized in that: Specifically, Step 4 is as follows: Prove the system stability through the Lyapunov function: Consider the Lyapunov candidate function as: V(t)=ψ T (t)Pψ(t), Take the derivative of V(t) according to equation (10) to get: in, is the Hurwitz matrix. By selecting appropriate k and γ, we can get therefore, and have to: in, After sorting, we get: Similarly, Introduce equations (11) and (12) and organize to get: in, Right now Among them, β1=1-2ω, That is Among them, |V(0)| τ =max -τ≤s≤0 V(s), and and Right now is the lower bound of V1; Arranged therefore, That is lim t→∞ ‖φ i ‖=0, similarly At the same time, verify: Right now At this time, the nonlinear second-order multi-agent system is stable.

4. A second-order nonlinear multi-agent system including a control system, using the second-order nonlinear multi-agent system including a control method according to any one of claims 1 to 3, characterized in that: Including: A system establishment module for establishing a non - linear second - order multi - agent system; Specifically: Set up a non - linear second - order multi - agent system with N agents, where there are M followers with M < N and N - M leaders; define the follower agents as 1, …, M and the leader agents as M + 1, …, N; the follower set and the leader set are defined as F = {1, …, M} and L = {M + 1, …, N} respectively; The model of follower i is expressed as: Among them, x i (t),v i (t),u i (t) represents the position, velocity and control input of the ith agent, respectively. f, g are nonlinear terms and continuous functions. τ is the delay time. The model of leader k is expressed as: Among them, x k (t),v k (t) represents the position and speed of the kth agent respectively; since the leader has no neighbors, the Laplacian matrix is ​​decomposed into: Where L1 is the matrix associated with the information flow of M followers, L1∈R M×M , L2 is the matrix associated with the information flow from NM leaders to M followers, L2∈R M×(N-M) ; A compensator setting module for setting a compensator for the non - linear second - order multi - agent system; Specifically: Define the error of the i - th follower as: where j represents follower j; To achieve containment control, unknown state estimation, and information transfer delay, use a fixed compensator to design a controller; For the i - th agent, the fixed compensator is designed as: Among them, φ i (t) = [φ i1 (t) T ,φ i2 (t) T ] T ∈R 2n is the state variable of formula (5), γ1, γ2 are appropriate constants; An inclusion control strategy setting module for setting the inclusion control strategy of the non - linear second - order multi - agent system based on the distributed compensator time - delay control algorithm; Specifically: Propose a control protocol based on the compensator and the inherent time - delay to achieve the containment control strategy of the system; The distributed compensator time - delay control algorithm is as follows: u i (t)=-Kφ i (t),i=1,…,M (6) in, is the control parameter, k1, k2 are constants; The i - th agent adopts the distributed compensator time - delay control algorithm to achieve the containment control between the leader and the followers, that is: in, From equation (5), we get: From equation (6), we get: Defining vectors According to φ i ,φ i Definition According to equations (1), (2), and (7), φ i The derivative is: definition From formula (7), we know that: Further simplified to: in, k=[k1,k2], c = [1,0]; Similarly simplified Right now: definition From formula (8) and formula (9), we know: in, By φ i ,φ i Definition, combining (1), (2), and (4) we get: in, According to formula (10), we have: in, Stability verification module, used to verify the stability of nonlinear second-order multi-agent systems.

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