Second-order linear multi-agent system adaptive inclusion control method, system, equipment and medium

Abstract

The invention relates to the technical field of multi-agent system control, and discloses a second-order linear multi-agent system adaptive inclusion control method, system, device and medium, and the method comprises the steps: S1, constructing a second-order linear multi-agent system model comprising a follower and a leader; s2, acquiring states of a follower and a leader; s3, generating a control signal by using a controller; s4, external interference is introduced, the second-order linear multi-agent system model is updated according to the control signal and the external interference, and the updated states of the follower and the leader are obtained; s5, judging whether the simulation time is greater than or equal to the deadline, if so, ending, and if not, executing S6; and S6, according to the updated states of the follower and the leader, adjusting the controller to generate a new control input signal by using a preset adaptive law, and skipping to execute the step S4. According to the method, the robustness, the control precision and the environmental adaptability of a multi-agent system control technology are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent system control technology, and more specifically, to a second-order linear multi-agent system adaptive control method, system, device and medium. Background Art

[0002] With the vigorous development of modern science and technology, multi-agent systems have become a research hotspot in scientific research and engineering due to their wide applications in many fields such as robot formation, intelligent transportation network, and distributed energy management. Multi-agent systems have the ability to complete complex tasks through the collaborative cooperation between multiple agents, which is difficult for a single agent to achieve. However, in actual application scenarios, multi-agent systems face many severe challenges. Among them, achieving stable inclusive control under complex environments and interference conditions has become a key problem that hinders the further development and widespread application of multi-agent systems. During the operation of multi-agent systems, the robustness of communication and control plays a decisive role in the performance and stability of the system. However, external interference, such as random noise, sudden interference, and uncertainty in system parameters, always affects the normal operation of the system, greatly reducing the robustness and stability of the system. At the same time, the complex dynamic coupling between agents is more prominent in nonlinear second-order systems, which greatly increases the difficulty of designing control strategies. In addition, when executing tasks, agents need to communicate and coordinate with neighbors based on local information to approach the target state, and the existence of external interference and complex network topology makes this coordination extremely difficult.

[0003] In recent years, researchers have conducted a lot of exploration and proposed a variety of solutions. For example, the adaptive control method improves the robustness of the system to a certain extent by dynamically adjusting the control gain according to environmental changes; the algorithm based on distributed control uses local information exchange to achieve global goals, reducing communication costs while improving system performance. Although these methods have achieved certain results, in the face of complex and changeable interference, complex nonlinear dynamic characteristics and the growing demand for high-precision control, the existing technology still has obvious deficiencies in system robustness, control accuracy and environmental adaptability, and cannot meet the needs of practical applications. Summary of the invention

[0004] In order to improve the robustness, control accuracy and environmental adaptability of multi-agent system control technology, the present invention proposes the following technical solutions:

[0005] In a first aspect, the present invention proposes a second-order linear multi-agent system adaptive inclusion control method, comprising:

[0006] S1: Construct a second-order linear multi-agent system model including followers and leaders;

[0007] S2: Get the status of followers and leaders;

[0008] S3: Generate a control signal using a controller;

[0009] S4: introducing external interference, updating the second-order linear multi-agent system model according to the control signal and the external interference, and obtaining updated states of followers and leaders;

[0010] S5: Determine whether the simulation time is greater than or equal to the deadline, if so, end, if not, execute S6;

[0011] S6: According to the updated states of the follower and the leader, the controller is adjusted to generate a new control input signal using the preset adaptive law, and the process jumps to S4.

[0012] As a preferred technical solution, the second-order linear multi-agent system model includes a dynamic model of the follower and a dynamic model of the leader;

[0013] The expression of the follower's dynamic model is as follows:

[0014]

[0015] In the formula, x i (t) represents the position of the ith agent, v i (t) represents the speed of the ith agent, u i (t) represents the control input signal of the ith agent, and F = {M+1,…,N} is the set of followers;

[0016] The expression of the follower's dynamic model is as follows:

[0017]

[0018] In the formula, x i (t) represents the position of the kth agent, v i (t) represents the speed of the kth agent, and L = {1,…,M} is the leader set.

[0019] As a preferred technical solution, the method further includes designing the second-order linear multi-agent system model as a graph And decompose the Laplacian matrix of graph g into:

[0020]

[0021] Connect, G FL ∈R (N-M)×M is the matrix related to the information flow from M leaders to NM followers, G F ∈R(N -M)×(N-M) is the matrix related to the information flow of NM followers.

[0022] As a preferred technical solution, the expression of the preset adaptive law is as follows:

[0023]

[0024] Where c(t) is the adaptive gain; is an exponential term, a1 is a preset parameter, t is a time constant; ρ is a preset parameter; e(t) is an error term, including the velocity error e of the i-th follower at time t v (t) and the position error e of the ith follower at time t x (t).

[0025] As a preferred technical solution, the position error e x (t) is defined as:

[0026]

[0027] In the formula, i is the number of the follower, N is the total number of agents, M is the number of leaders, NM is the number of followers, and a ij represents the connection relationship between the ith follower and the jth follower, a il represents the connection relationship between the i-th follower and the j-th leader, x i (t) represents the position of the ith follower at time t, x j (t) represents the position of the jth follower at time t, x l (t) represents the position of the lth leader at time t;

[0028] The speed error e v (t) is defined as:

[0029]

[0030] In the formula, v i (t) represents the speed of the ith follower at time t, v j (t) represents the speed of the jth follower at time t, v l (t) represents the speed of the lth leader at time t.

[0031] As a preferred technical solution, the controller is adjusted to generate a new control input signal u using a preset adaptive law. i (t), whose expression is as follows:

[0032]

[0033] Among them, α1,α 2, β1 and β2 are preset real number parameters, and 0<α1<1, sgn(·) represents the sign function.

[0034] As a preferred technical solution, when updating the second-order linear multi-agent system model, the method also includes using a Lyapunov function to monitor the stability of the second-order linear multi-agent system model in real time.

[0035] In a second aspect, the present invention further proposes a second-order linear multi-agent system adaptive inclusion control system, which is applied to the second-order linear multi-agent system adaptive inclusion control method as described in any solution of the first aspect, comprising:

[0036] Building blocks for constructing second-order linear multi-agent system models consisting of followers and leaders;

[0037] The acquisition module is used to obtain the status of followers and leaders;

[0038] A generating module, used for generating a control signal using a controller;

[0039] An updating module, used for introducing external interference, updating the second-order linear multi-agent system model according to the control signal and the external interference, and obtaining the updated states of the follower and the leader;

[0040] A judgment module is used to judge whether the simulation time is greater than or equal to the deadline. If so, the simulation ends. If not, the execution adjustment module is called;

[0041] The adjustment module is used to adjust the controller to generate a new control input signal according to the updated states of the follower and the leader using a preset adaptive law, and call the execution update module.

[0042] In the third aspect, the present invention further proposes an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the operations performed by the adaptive control method for the second-order linear multi-agent system as described in any of the schemes in the first aspect are implemented.

[0043] In a fourth aspect, the present invention further proposes a computer-readable storage medium having a program stored thereon, wherein the program is executed by a processor to include the operations performed by the adaptive control method for a second-order linear multi-agent system as described in any of the schemes in the first aspect.

[0044] The beneficial effects of the present invention include at least:

[0045] The present invention can comprehensively describe the motion state and mutual relationship of each agent in the system by constructing a second-order linear multi-agent system model including followers and leaders. During the operation of the system, the states of the followers and leaders are continuously obtained, the control signals are generated by the controller, external interference is introduced and the system model is updated accordingly, the updated state is obtained, and then the controller is adjusted according to the updated state and the preset adaptive law to generate a new control input signal, and this cycle is repeated. This allows the system to adjust in real time according to external interference and changes in the state of the agent. When facing external interference such as random noise and sudden disturbances, the adaptive law can adjust the controller parameters to ensure stable operation of the system, thereby significantly improving the robustness of the system; because the control input can be adjusted in real time according to the state, the follower can follow the leader more accurately, improving the control accuracy; and under different environmental interferences, the adaptive law can play a role, adjust the control input, and make the system adapt to environmental changes, thereby enhancing environmental adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A flow chart of the adaptive control method for a second-order linear multi-agent system provided in an embodiment of the present invention.

[0047] Figure 2 The second-order linear multi-agent system model provided in the embodiment of the present invention includes a control block diagram.

[0048] Figure 3 A communication topology diagram of the second-order linear multi-agent system model provided in an embodiment of the present invention.

[0049] Figure 4 A state trajectory diagram of an intelligent agent that performs control under sinusoidal signal interference provided by an embodiment of the present invention.

[0050] Figure 5 This is an evolution diagram of the control input signal provided by an embodiment of the present invention.

[0051] Figure 6 This is an adaptive response curve diagram provided by an embodiment of the present invention.

[0052] Figure 7 A schematic diagram of the speed state of an intelligent agent under various interferences provided by an embodiment of the present invention.

[0053] Figure 8 An adaptive response trajectory diagram under various interferences provided by an embodiment of the present invention.

[0054] Fig. 9 An architecture diagram of the second-order linear multi-agent system adaptive control system provided in an embodiment of the present invention.

[0055] Fig.10 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following will describe the embodiments of the present invention with reference to the accompanying drawings and preferred technical solutions. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred technical solutions are only for illustrating the present invention, not for limiting the scope of protection of the present invention.

[0057] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0058] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.

[0059] Example 1

[0060] This embodiment proposes a second-order linear multi-agent system adaptive inclusion control method, such as Figure 1 As shown, Figure 1 A schematic flow chart of a second-order linear multi-agent system adaptive control method provided in this embodiment, the method comprising the following steps:

[0061] S1: Construct a second-order linear multi-agent system model including followers and leaders;

[0062] S2: Get the status of followers and leaders;

[0063] S3: Generate a control signal using a controller;

[0064] S4: introducing external interference, updating the second-order linear multi-agent system model according to the control signal and the external interference, and obtaining updated states of followers and leaders;

[0065] S5: Determine whether the simulation time is greater than or equal to the deadline, if so, end, if not, execute S6;

[0066] S6: According to the updated states of the follower and the leader, the controller is adjusted to generate a new control input signal using the preset adaptive law, and the process jumps to S4.

[0067] As an example, let's take the robot collaborative handling scenario as an example. Suppose there is a group of robots, some of which are leader robots responsible for planning paths and guiding directions, and the rest are follower robots that perform specific handling tasks. Before starting collaborative handling, a second-order linear multi-agent system model is first constructed to define the motion rules of the leader robot and the follower robot, respectively. For example, the leader sets a fixed travel speed and route, and the follower adjusts its movement based on the leader's state and its own state. After that, the various sensors equipped on the robot are used to obtain the status information of each robot, such as the position and speed. Then, the controller in the central control system generates control signals based on these status information to guide the actions of the follower robots.

[0068] During the handling process, external interferences such as uneven ground and obstacles may occur. At this time, the robot collaboration system model is updated according to the control signal and these external interference factors, and the updated state of each robot is recalculated. Subsequently, it is determined whether the set time of the handling task has ended. If not, the controller is adjusted according to the updated state using the preset adaptive law to generate a new control input signal, so that the robot adjusts its actions according to the new signal, and the system model is updated again according to the new signal and interference. This process is continuously repeated to ensure that the handling task can be completed efficiently and stably under complex circumstances.

[0069] It can be understood that by constructing a second-order linear multi-agent system model including followers and leaders, the motion state and mutual relationship of each agent in the system can be fully described. During the operation of the system, the states of the followers and leaders are continuously obtained, the control signals are generated by the controller, external interference is introduced and the system model is updated accordingly, the updated state is obtained, and then the controller is adjusted according to the updated state and the preset adaptive law to generate a new control input signal, and so on. This allows the system to adjust in real time according to external interference and changes in the state of the agent. When facing external interference such as random noise and sudden disturbances, the adaptive law can adjust the controller parameters to ensure stable operation of the system, thereby significantly improving the robustness of the system; because the control input can be adjusted in real time according to the state, the follower can follow the leader more accurately, improving the control accuracy; and under different environmental interferences, the adaptive law can play a role, adjust the control input, and make the system adapt to environmental changes, enhancing environmental adaptability.

[0070] Example 2

[0071] This embodiment makes improvements on the basis of the second-order linear multi-agent system adaptive containment control method proposed in Embodiment 1.

[0072] In this embodiment, a second-order linear multi-agent system model with N agents is proposed, where there are M (M < N) leaders and N - M followers. The follower agents are defined as 1, …, N - M, and the leader agents are defined as 1, …, M. The leader set and the follower set are defined as L = {1, …, M} and F = {M + 1, …, N}, respectively.

[0073] Among them, the expression of the dynamic model of the followers is as follows:

[0074]

[0075] In the formula, x i (t) represents the position of the i-th agent, v i (t) represents the velocity of the i-th agent, u i (t) represents the control input signal of the i-th agent, and F = {M + 1, …, N} is the follower set;

[0076] Considering the case of static leaders, that is, the expression of the dynamic model of the followers is as follows:

[0077]

[0078] In the formula, x i (t) represents the position of the k-th agent, v i (t) represents the velocity of the k-th agent, and L = {1, …, M} is the leader set.

[0079] In this embodiment, the second-order linear multi-agent system model is designed as a graph g = (V, E). Since the leaders have no neighbors, the Laplacian matrix of the graph G is decomposed into:

[0080]

[0081] Connection, G FL ∈R (N-M)×M is a matrix related to the information flow from M leaders to N - M followers, and G F ∈R (N -M)×(N-M) is a matrix related to the information flow of N - M followers.

[0082] In this embodiment, by designing an adaptive law, this design based on dynamic adaptive gain enables the control method to better adapt to changes in the external environment, thereby improving the performance and stability of the system and making it widely applicable in various application fields.

[0083] The expression of the adaptive law is as follows:

[0084]

[0085] Where c(t) is the adaptive gain; is an exponential term, a1 is a preset parameter, t is a time constant; ρ is a preset parameter; e(t) is an error term, including the velocity error e of the i-th follower at time t v (t) and the position error e of the ith follower at time t x (t).

[0086] In this embodiment, the position error e x (t) is defined as:

[0087]

[0088] In the formula, i is the number of the follower, N is the total number of agents, M is the number of leaders, NM is the number of followers, and a ij represents the connection relationship between the ith follower and the jth follower, a il represents the connection relationship between the i-th follower and the j-th leader, x i (t) represents the position of the ith follower at time t, x j (t) represents the position of the jth follower at time t, x l (t) represents the position of the lth leader at time t;

[0089] The speed error e v (t) is defined as:

[0090]

[0091] In the formula, v i (t) represents the speed of the ith follower at time t, v j (t) represents the speed of the jth follower at time t, v l (t) represents the speed of the lth leader at time t.

[0092] In this embodiment, a control protocol based on an adaptive law is used to implement an inclusive control strategy of the system.

[0093] The control algorithm based on the adaptive law is as follows:

[0094]

[0095] Among them, α1,α 2, β1 and β2 are preset real number parameters, and 0<α1<1, sig α (x)=|x| α sgn(x), sgn(·) denote sign functions.

[0096] The i-th agent can achieve inclusive control of the leader and the follower by adopting an adaptive control algorithm, and its expression is as follows:

[0097]

[0098] in,

[0099] Depend on and We can get:

[0100] e x (t) = G F x F (t)+G FL x G (t)

[0101] e v (t) = G F v F (t)+G FL v G (t)

[0102] In summary, further control protocol u i It is expressed as:

[0103]

[0104] In this embodiment, when the second-order linear multi-agent system model is updated, the method further includes using a Lyapunov function to monitor the stability of the second-order linear multi-agent system model in real time.

[0105] Consider the Lyapunov candidate function V(t), which is expressed as V(t)=V1(t)+V2(t), where:

[0106]

[0107] V1(t) is based on the velocity error e of the follower v (t) and the matrix G F Build.

[0108]

[0109] V2(t) combines, among other things, the integral term associated with the position error.

[0110] Next, we take the derivative of V1(t) and V3(t) respectively:

[0111] Taking the derivative of V1(t) we get:

[0112]

[0113] Select

[0114]

[0115] Considering And α2<1,

[0116]

[0117] Taking the derivative of V2(t) we get:

[0118]

[0119] In summary, we can get:

[0120]

[0121] because And V(t) is bounded, so we can know that the adaptive gain c(t) converges, and c(t) increases monotonically, that is, c(t) will gradually converge to a constant. Only at the equilibrium point If and only if e v (t) = 0. According to LaSalle's invariance principle, Available and Therefore, and Complete the demonstration of system stability.

[0122] When the system has no external interference w(t), that is, w(t) = 0. The proof method is similar to the proof method with external interference.

[0123] Consider the Lyapunov candidate function V(t) = V1(t) + V2(t). V1(t) and V2(t) refer to the above expressions.

[0124]

[0125] In summary, we can get:

[0126]

[0127] Therefore, and Complete the demonstration of system stability.

[0128] It is understandable that in the operation of a multi-agent system, external interference is often a key factor affecting its performance. The present invention innovatively introduces an adaptive mechanism and interference suppression strategy, which can effectively resist various interferences such as random noise, sudden disturbances, and system parameter uncertainty. The control algorithm can adaptively adjust the control gain according to the interference situation to ensure that the system can still operate stably in a complex interference environment, thereby greatly improving the robustness and anti-interference ability of the multi-agent system.

[0129] In order to achieve high-precision control effects, the present invention uses the constructed Lyapunov function to conduct a rigorous analysis of the closed-loop system, fully proving the global stability of the system. At the same time, through the carefully designed distributed control strategy, the followers can quickly approach the leader's dynamic convex hull, significantly improving the control accuracy and convergence speed of the system. Even in a complex dynamic environment, fast and efficient containment control can be achieved.

[0130] In addition, the present invention has a unique advantage, which is that it can adaptively adjust control parameters according to environmental changes and external interference, without making precise assumptions about the interference model. Whether facing dynamic topology, complex interference, or time-varying network, the control strategy can be adaptively adjusted to effectively ensure the stability and performance of the system, showing stronger environmental adaptability and task flexibility.

[0131] From the perspective of practical application, the control method of the present invention has wide applicability and can be applied to various scenarios of multi-agent systems such as drone formation, robot collaboration, intelligent transportation network, and distributed energy management. Its innovative adaptive inclusive control design provides efficient and reliable technical support for collaboration and coordination in complex tasks, and has broad application prospects and extremely high promotion value.

[0132] Example 4

[0133] This embodiment is based on the adaptive inclusive control method of the second-order linear multi-agent system proposed in Example 3 and is explained in combination with specific experiments.

[0134] like Figure 2 As shown, Figure 2 The control block diagram of the second-order linear multi-agent system model provided by the embodiment of the present invention includes the initial state x given by each agent. F ,x L ,v F ,v L , and then the controller u i , update its state, acting on the state x of each agent i , v i 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 adaptive law and the controller u are updated.i , and then update the next state x of each agent i , v i , to achieve the included control strategy. This process continues until the simulation deadline is reached.

[0135] like Figure 3 As shown, Figure 3 The communication topology structure diagram of the second-order linear multi-agent system model provided in the embodiment of the present invention includes three leaders and five followers. The arrow indicates the communication direction, that is, the information is transmitted from the starting node of the arrow to the node pointed by the arrow. The communication relationship is: the leader communicates with the corresponding followers respectively, and there is also a communication relationship between the followers. For example, leader 1 communicates with follower 4, and follower 5 communicates with followers 4 and 6, forming a complex communication network structure. This communication topology provides a network foundation for controller design.

[0136] against Figure 3 The communication topology diagram and the designed second-order linear multi-agent system model are shown, and the variable parameters are set as follows:

[0137] Figure 3 In the example, there are five followers and three leaders, 1-3 are leaders, 4-8 are followers. The initial states of the five followers and three leaders are set as:

[0138] x F (0) = [2; 4; 5; 1; 3]

[0139] v F (0) = [2; 3; 6; 8; 10]

[0140] x G (0) = [8; 3; 2]

[0141] Laplacian matrix G FL , G F Designed for

[0142]

[0143] Nodes 4-8 correspond to followers, and nodes 1-3 represent leaders. The parameters involved in the controller are selected as α1=0.8, α2=0.8889, β1=9, and β2=4. The parameters involved in the adaptive law are a1=0.04 and ρ=0.01. The system simulation time is set to t=30s, and the sampling time is set to T s =0.01s.

[0144] like Figure 4 As shown, Figure 4The state trajectory diagram of the intelligent agent under the interference of sinusoidal signals provided by the embodiment of the present invention is included. The X and Y axes determine the plane position of the intelligent agent, and the Z axis reflects the change of its state over time. Under the action of the control protocol, each follower has a different initial position, but can quickly enter the convex hull dynamically formed by the leader, reflecting the high efficiency of the control protocol in information transmission and state coordination, so that the followers can respond quickly to system goals. In the subsequent process, even if there is sinusoidal signal interference, the followers still remain stably in the convex hull, showing the strong anti-interference ability of the control protocol, ensuring the reliability of the multi-agent system in practical applications.

[0145] At the same time, the controller successfully guides the followers to synchronize their positions and speeds with the leaders, which is the key to achieving the control objectives. This indicates that the control method can effectively coordinate the behaviors of the agents and improve the efficiency and coordination of the system. In summary, the control method of the present invention is effective and stable, and is expected to provide reliable support for the efficient operation of multi-agent systems in complex environments, which is of great value.

[0146] like Figure 5 As shown, Figure 5 This is an evolution diagram of the control input signal provided by an embodiment of the present invention. The horizontal axis is time, and the vertical axis is the control input signal of different followers. Initially, the control inputs of each follower are very different and the values ​​are considerable, indicating that the system startup phase requires a large number of instructions to adjust the state. But as time goes on, they converge rapidly, tend to 0 in about 10-15 seconds and remain stable. This shows that the control protocol can adjust the control input according to the system state and target to balance the system. Stability at 0 means that the follower and leader states match, and no additional adjustment is required, that is, the control target is achieved, which reflects the effectiveness and stability of the protocol.

[0147] like Figure 6 As shown, Figure 6 The adaptive response curve diagram provided by the embodiment of the present invention, in which the horizontal axis represents time and the vertical axis presents the dynamic changes of the adaptive control gain parameters, presents the evolution trajectory of the adaptive parameters of the five follower agents. In the initial stage, the adaptive parameters of each follower are adjusted rapidly, reflecting the system's agile response ability when facing interference and changes in its own state. In a short period of time, these parameters converge to stable values, which not only reflects the high efficiency of the adaptive mechanism, but also shows that it can quickly adapt to external interference and system state changes to optimize the control effect. This characteristic of rapid response and stable convergence provides strong support for the multi-agent system to achieve efficient control in complex environments, ensuring that the system can operate stably and reliably.

[0148] like Figure 7 As shown, Figure 7This is a schematic diagram of the speed state of an intelligent agent under various interferences provided by an embodiment of the present invention. The horizontal axis records the time process and the vertical axis shows the speed state of the intelligent agent. The figure covers the speed evolution of the leader and the follower under various interference scenarios such as sinusoidal interference, random noise interference, and exponential decay interference. Under sinusoidal interference, although the follower speed is affected by fluctuations, it still quickly adjusts to the leader speed; in the face of random noise interference, its speed does not deviate significantly and still converges stably; during exponential decay interference, the follower can also quickly adapt to interference changes. Under different interference conditions, the follower speed converges quickly and remains consistent with the leader, which fully verifies that the proposed control method has excellent robustness and anti-interference ability, and can effectively maintain the speed synchronization of the multi-agent system in a complex and changeable interference environment to ensure stable operation of the system.

[0149] like Figure 8 As shown, Figure 8 The adaptive response trajectory diagram under various interferences provided by the embodiment of the present invention, the horizontal axis is time, the vertical axis presents the change of the adaptive control gain parameter, and the five curves correspond to the responses of the five follower agents under different interferences. In the sinusoidal interference (c-sin) scenario, the adaptive parameters start to adjust quickly and quickly tend to the stable value; in the face of exponential decay interference (c-exp), it can also respond in time and stabilize quickly; in the case of random noise interference (c-randn), although the interference is uncertain, the parameters are still not affected too much and converge quickly to a stable state; under square wave interference (c-square) and mixed interference (c-mixed) conditions, it also shows fast and stable characteristics. The adaptive parameters can quickly reach stable values ​​under different interferences, which fully reflects the strong adaptability of the parameters to various complex interferences, and further verifies that the adaptive control strategy has excellent effectiveness and robustness in a dynamically changing and diverse interference environment, and can provide reliable guarantee for the stable operation of the multi-agent system.

[0150] It can be understood that the present invention innovatively proposes a linear second-order multi-agent system inclusive control method, which integrates adaptive mechanism and interference suppression strategy. In its design process, the adaptive control law is introduced as an effective means to deal with external interference. By adaptively updating according to the local state error, the controller organically combines the adaptive adjustment mechanism, which not only ensures the realization of the inclusive control target, but also significantly improves the robustness and control accuracy of the system. With the help of Lyapunov method, rigorous analysis is carried out, which strongly proves that the designed control scheme can promote all follower states to converge asymptotically to the leader's dynamic convex hull, thereby ensuring the global stability of the closed-loop system. In addition, the adaptive adjustment capability of the controller further optimizes the dynamic performance and convergence speed of the system. Finally, the effectiveness of the proposed control method is verified by numerical simulation experiments. Under the severe test of various interference conditions, the experimental results clearly show that all follower states can quickly enter the convex hull formed by the leader state and maintain synchronous motion, which fully verifies the reliability and superiority of the control strategy.

[0151] Example 4

[0152] like Fig. 9 As shown, this embodiment proposes a second-order linear multi-agent system adaptive inclusion control system, which is applied to the second-order linear multi-agent system adaptive inclusion control method as described in the above embodiment, including: a construction module 100, an acquisition module 200, a generation module 300, an update module 400, a judgment module 500 and an adjustment module 600.

[0153] Among them, the construction module 100 is used to construct a second-order linear multi-agent system model including followers and leaders; the acquisition module 200 is used to obtain the status of followers and leaders; the generation module 300 is used to generate a control signal using a controller; the update module 400 is used to introduce external interference, update the second-order linear multi-agent system model according to the control signal and the external interference, and obtain the updated status of followers and leaders; the judgment module 500 is used to judge whether the simulation time is greater than or equal to the deadline, if so, it ends, otherwise it calls the execution adjustment module; the adjustment module 600 is used to adjust the controller to generate a new control input signal according to the updated status of the followers and leaders, using the preset adaptive law, and call the execution update module.

[0154] It should be noted that the above explanation of the embodiment of the second-order linear multi-agent system adaptive inclusion control method is also applicable to the second-order linear multi-agent system adaptive inclusion control system of this embodiment, and will not be repeated here.

[0155] Example 5

[0156] Fig.10The electronic device 700 provided in this embodiment is a schematic diagram of the structure of the electronic device 700. The electronic device 700 includes: a memory 701, a processor 702, and a computer program stored in the memory 701 and executable on the processor 702.

[0157] When the processor 702 executes the program, the second-order linear multi-agent system adaptive inclusion control method provided in the above embodiment is implemented.

[0158] Furthermore, the electronic device 700 also includes: a communication interface 703 for communication between the memory 701 and the processor 702 .

[0159] The memory 701 may include a high-speed RAM (Random Access Memory) memory, and may also include a non-volatile memory, such as at least one disk memory.

[0160] If the memory 701, the processor 702 and the communication interface 703 are implemented independently, the communication interface 703, the memory 701 and the processor 702 can be connected to each other through a bus and communicate with each other. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component) bus or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 3 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0161] Optionally, in a specific implementation, if the memory 701, the processor 702 and the communication interface 703 are integrated on a chip, the memory 701, the processor 702 and the communication interface 703 can communicate with each other through an internal interface.

[0162] The processor 702 may be a CPU (Central Processing Unit), or an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement the embodiments of the present invention.

[0163] Example 6

[0164] An embodiment of the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned second-order linear multi-agent system adaptive inclusion control method.

[0165] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms are not necessarily directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0166] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "N" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0167] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present invention belong.

[0168] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above embodiment, the N steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array, a field programmable gate array, etc.

[0169] A person skilled in the art may understand that all or part of the steps in the above-mentioned embodiment method may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0170] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the embodiments here. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A second-order linear multi-agent system adaptive inclusion control method, characterized in that: include: S1: Construct a second-order linear multi-agent system model including followers and leaders; S2: Get the status of followers and leaders; S3: Generate a control signal using a controller; S4: introducing external interference, updating the second-order linear multi-agent system model according to the control signal and the external interference, and obtaining the updated states of the follower and the leader; S5: Determine whether the simulation time is greater than or equal to the deadline, if so, end, if not, execute S6; S6: According to the updated states of the follower and the leader, the controller is adjusted to generate a new control input signal using the preset adaptive law, and the process jumps to S4.

2. The method for adaptive control of a second-order linear multi-agent system according to claim 1, characterized in that: The second-order linear multi-agent system model includes a dynamic model of followers and a dynamic model of leaders; The expression of the follower's dynamic model is as follows: In the formula, x i (t) represents the position of the ith agent, v i (t) represents the speed of the ith agent, u i (t) represents the control input signal of the ith agent, and F = {M+1,…,N} is the set of followers; The expression of the follower's dynamic model is as follows: In the formula, x i (t) represents the position of the kth agent, v i (t) represents the speed of the kth agent, and L = {1,…,M} is the leader set.

3. The adaptive inclusion control method for a second-order linear multi-agent system according to claim 2, characterized in that: The method also includes designing the second-order linear multi-agent system model as a graph And the figure The Laplacian matrix decomposition is: The node set V consists of N agents, the edge set E represents the information interaction connection between agents, and G FL ∈R (N -M)×M is the matrix related to the information flow from M leaders to NM followers, G F ∈R (N-M)×(N-M) is the matrix related to the information flow of NM followers.

4. The method for adaptive control of a second-order linear multi-agent system according to claim 3, characterized in that: The expression of the preset adaptive law is as follows: Where c(t) is the adaptive gain; is an exponential term, a1 is a preset parameter, t is a time constant; ρ is a preset parameter; e(t) is an error term, including the velocity error e of the i-th follower at time t v (t) and the position error e of the ith follower at time t x (t).

5. The method for adaptive inclusion control of a second-order linear multi-agent system according to claim 4, characterized in that: The position error e x (t) is defined as: In the formula, i is the number of the follower, N is the total number of agents, M is the number of leaders, NM is the number of followers, and a ij represents the connection relationship between the ith follower and the jth follower, a il represents the connection relationship between the i-th follower and the j-th leader, x i (t) represents the position of the ith follower at time t, x j (t) represents the position of the jth follower at time t, x l (t) represents the position of the lth leader at time t; The speed error e v (t) is defined as: In the formula, v i (t) represents the speed of the ith follower at time t, v j (t) represents the speed of the jth follower at time t, v l (t) represents the speed of the lth leader at time t.

6. The method for adaptive inclusion control of a second-order linear multi-agent system according to claim 5, characterized in that: Using the preset adaptive law, adjust the controller to generate a new control input signal u i (t), whose expression is as follows: Among them, α1,α 2, β1 and β2 are preset real number parameters, and 0<α1<1, sgn(·) represents the sign function.

7. The method for adaptive control of a second-order linear multi-agent system according to claim 1, characterized in that: When updating the second-order linear multi-agent system model, the method also includes using a Lyapunov function to monitor the stability of the second-order linear multi-agent system model in real time.

8. A second-order linear multi-agent system adaptive inclusion control system, characterized in that: include: Building blocks for constructing second-order linear multi-agent system models consisting of followers and leaders; The acquisition module is used to obtain the status of followers and leaders; A generating module, used for generating a control signal using a controller; An updating module, used for introducing external interference, updating the second-order linear multi-agent system model according to the control signal and the external interference, and obtaining the updated states of the follower and the leader; A judgment module is used to judge whether the simulation time is greater than or equal to the deadline. If so, the simulation ends. If not, the execution adjustment module is called; The adjustment module is used to adjust the controller to generate a new control input signal according to the updated states of the follower and the leader using a preset adaptive law, and call the execution update module.

9. An electronic device, characterized in that: The control device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, it implements the operations performed by the adaptive control method for the second-order linear multi-agent system as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a program, and the program is used by the processor to execute the operations performed by the adaptive inclusive control method for a second-order linear multi-agent system as described in any one of claims 1 to 7.

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