Cooperative control method and system of nonlinear multi-agent system

Abstract

According to the cooperative control method and system of the non-linear multi-agent system, under the condition that communication link faults are considered, a non-linear dynamic model of each single-connecting-rod mechanical arm is established, and unknown uncertain non-linear dynamic states in the single-connecting-rod mechanical arms are fuzzified through a fuzzy logic system; a mixed event triggering mechanism is introduced, so that state information of a leader is estimated, and the communication frequency is effectively reduced; and constructing a virtual controller and an actual controller by utilizing a backstepping method based on the estimated state information, so as to control the position of the following mechanical arm to be synchronous with the expected trajectory of the leading mechanical arm under the condition of being influenced by the communication link fault. According to the method, the state of the multi-single-connecting-rod mechanical arm system can be kept consistent and stable tracking control can be achieved under the condition that communication link faults and nonlinear uncertainty exist without global information.

Description

Technical Field

[0001] This invention belongs to the technical field of multi-manipulator system control, and particularly relates to a cooperative control method and system for nonlinear multi-agent systems. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] A robotic arm is a mechanical arm that operates under computer control. It has been widely used in various fields such as transportation and manufacturing. For example, in industrial manufacturing, some repetitive or hazardous tasks are performed by robotic arms, which can reduce labor costs, improve productivity and manufacturing safety, and offer greater flexibility compared to specialized machines. A robotic arm consists of links connected by joints to form a kinematic chain; these joints are typically rotary or linear (prismatic). However, a robot manipulator should not be viewed merely as a series of mechanical links; the robotic arm is a component of an overall robot system. A robotic arm system comprises the robotic arm itself, an external power supply, an end effector, and a computer controller, among other components.

[0004] Currently, robotic arm control schemes typically employ a time-triggered method, where a digital controller acts on the controlled system. This means the system samples the signal at a fixed period and then updates the control signal at the same period. While this time-period sampling method is simple, even when the system has reached the desired control accuracy and no further control is needed, the control signal continues to update at a fixed and relatively fast frequency, significantly wasting system resources. Furthermore, when different components of the robotic arm or the robotic arms themselves exchange information and control each other via a network, network bandwidth limits the amount of information that can be transmitted. Excessive data transmission can lead to bandwidth congestion, resulting in data loss and impacting control accuracy.

[0005] However, in practical industrial applications, when robotic arms interact with each other via a network, communication links may experience temporary or intermittent failures due to interference, equipment malfunctions, or channel instability, resulting in the failure to transmit some information. Communication link failures not only degrade the overall control performance of the system but may even lead to control instability, and in severe cases, system paralysis. Therefore, it is crucial to design robust and adaptive control strategies to address control problems under communication link failure conditions, ensuring that multi-robotic arm systems can still achieve collaborative control objectives even under unstable communication conditions. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a cooperative control method and system for nonlinear multi-agent systems. Without global information, it can ensure the consistency of the state of multiple single-link robotic arm systems and achieve stable tracking control under conditions of communication link failure and nonlinear uncertainty.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a cooperative control method for a nonlinear multi-agent system, comprising: Considering communication link failures, a nonlinear dynamic model of each single-link manipulator is established, and the unknown, uncertain, and nonlinear dynamics of the single-link manipulator are fuzzy using a fuzzy logic system. The leader's state information is estimated based on the local information of each following robotic arm itself and its neighboring nodes, and a hybrid event triggering mechanism is embedded in the estimation so that the state update is only performed when specific triggering conditions are met. Based on the estimated leader state information, an actual controller is constructed using the backstepping method. This actual controller is used to keep the position of the following robotic arm synchronized with the desired trajectory of the leader robotic arm in the event of a communication link failure.

[0008] In a second aspect, the present invention provides a cooperative control system for a nonlinear multi-agent system, comprising: The model building module is configured to: establish a nonlinear dynamic model for each single-link manipulator, considering communication link failures, and use a fuzzy logic system to fuzz the unknown, uncertain, and nonlinear dynamics of the single-link manipulator. The estimation module is configured to estimate the leader's state information based on the local information of each following robotic arm itself and its neighboring nodes, and to embed a hybrid event triggering mechanism in the estimation so that the state update is only performed when specific triggering conditions are met. The control module is configured to construct an actual controller based on the estimated leader state information using a backstepping method, and through the actual controller, control the position of the following robotic arm to keep it synchronized with the desired trajectory of the leader robotic arm in the event of a communication link failure.

[0009] Thirdly, the present invention provides an electronic device including a memory and a processor, and computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the method described in the first aspect.

[0010] Fourthly, the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in the first aspect.

[0011] Fifthly, the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the method described in the first aspect.

[0012] The above one or more technical solutions have the following beneficial effects: In this invention, considering communication link failures, a nonlinear dynamic model is established for each single-link robotic arm, and a fuzzy logic system is used to fuzzify the unknown, uncertain, and nonlinear dynamics of the single-link robotic arms. A hybrid event triggering mechanism is introduced to estimate the leader's state information, effectively reducing communication frequency. Based on the estimated state information, a virtual controller and a physical controller are constructed using a backstepping method to keep the position of the following robotic arm synchronized with the desired trajectory of the leader robotic arm under the influence of communication link failures. This invention's method, without requiring global information, can ensure the state consistency of a multi-link robotic arm system and achieve stable tracking control even under conditions of communication link failures and nonlinear uncertainties.

[0013] In this invention, the hybrid event triggering mechanism improves the system's resource utilization efficiency while reducing communication frequency by introducing a two-stage triggering rule. The constructed triggering function does not rely on the traditional exponential decay function, but is constructed based on a combination of error signal and adaptive gain, which simplifies the parameter design process and reduces implementation complexity.

[0014] In this invention, the distributed estimator avoids using high Vic Rönek product operations during construction. Instead, it constructs the estimation error dynamics through local observations of the leader's trajectory from each robotic arm, achieving adaptive correction of information inconsistency caused by communication link failures. Based on this, a hybrid event-triggered mechanism is used to update the observation information, and the error convergence condition is derived based on Lyapunov analysis theory. This ensures the consistency and boundedness of the system state even under discontinuous communication conditions, effectively improving the estimation and control performance of the system in complex network environments.

[0015] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0016] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0017] Figure 1 This is a diagram showing the components of a robotic arm system; Figure 2This is a control block diagram of the multi-single-link robotic arm collaborative control method provided in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of an actual single-link robotic arm provided in Embodiment 1 of the present invention; Figure 4 This is a topology diagram of the communication network consisting of five single-link robotic arms provided in Embodiment 1 of the present invention; Figure 5 This is a diagram showing the output and reference trajectory tracking of five single-link robotic arms provided in Embodiment 1 of the present invention; Figure 6 The estimation results of the desired trajectory of the leader robot arm by the five single-link robotic arms provided in Embodiment 1 of the present invention; Figure 7 The first derivative of the desired trajectory of the leader robot arm by the five single-link robotic arms provided in Embodiment 1 of the present invention is estimated. Figure 8 This is a synchronization error curve diagram of five single-link robotic arms provided in Embodiment 1 of the present invention under the influence of communication link failure; Figure 9 This is a control input curve diagram of the multi-link robotic arm provided in Embodiment 1 of the present invention; Figure 10 This is a graph showing the variation of the triggering time intervals of each robotic arm under the hybrid event triggering mechanism provided in Embodiment 1 of the present invention. Detailed Implementation

[0018] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0019] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0020] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0021] Example 1 This embodiment discloses a cooperative control method for a nonlinear multi-agent system, including: Considering communication link failures, a nonlinear dynamic model of each single-link manipulator is established, and the unknown, uncertain, and nonlinear dynamics of the single-link manipulator are fuzzy using a fuzzy logic system. The leader's state information is estimated based on the local information of each following robotic arm itself and its neighboring nodes, and a hybrid event triggering mechanism is embedded in the estimation so that the state update is only performed when specific triggering conditions are met. Based on the estimated leader state information, an actual controller is constructed using the backstepping method. This actual controller is used to keep the position of the following robotic arm synchronized with the desired trajectory of the leader robotic arm in the event of a communication link failure.

[0022] This embodiment utilizes a distributed estimator to address the adverse effects of communication link failures and employs a hybrid event-triggered mechanism to avoid continuous communication between adjacent single-link robotic arms, thus reducing the communication burden. It approximates unknown nonlinear terms in the dynamic model using a fuzzy logic system and finally obtains the corresponding controller through backstepping. This enables collaborative tracking of the leader's trajectory by all following robotic arms. This method, without requiring global information, ensures the consistency of the state of the multi-link robotic arm system and achieves stable tracking control even under conditions of communication link failures and nonlinear uncertainties.

[0023] like Figures 1-2 As shown, this embodiment provides a cooperative control method for a multi-manipulator system. This method can be applied to a nonlinear multi-agent system composed of multiple manipulators, and achieves distributed tracking control of a reference trajectory under conditions of communication instability and external disturbances. Specifically, it includes the following steps: This embodiment describes a multi-link robotic arm composed of rigid links coupled to a DC motor via gears, and its structure is as follows: Figure 3 As shown. Taking a multi-bar linkage robotic arm with five links as an example, based on the Euler-Lagrange equations and Newton's second law, the dynamic model of the multi-bar linkage robotic arm with external disturbances is obtained, as follows:

[0024] The system parameters are set to constants. , and . Indicates the first i The angular displacement of the first robotic arm, the... i The angular velocity of the robotic arm is . Functions represent non-modeled dynamic terms that exist in the system. The corresponding control input applied to the system.

[0025] make , , , .in, This is the actual control input. Therefore, the dynamic model can be transformed into state-space equations, in the following form:

[0026] in, The nonlinear component representing the known terms in the system is defined as follows:

[0027] The undirected communication topology among multiple single-link robotic arms in cooperative tracking control is described using an undirected graph. Specifically: The undirected communication topology between five multi-link robotic arms can be represented by an undirected graph. ; where the node set is defined as The edge set is defined as ,side This means a single-link robotic arm i Can receive from single-link robotic arm j The transmission of information, if the side exist, ; For the relevant adjacency weight matrix, if a single-link robotic arm i It can receive signals from a single-link robotic arm. Communication information, ,otherwise If the leader robotic arm can transmit information to the single-link robotic arm... i ,mean ,otherwise Diagonal matrix Each element is defined as follows: , representing a node i The sum of in-degrees.

[0028] definition It is a Laplacian matrix.

[0029] Fault Model , The description is as follows:

[0030] The ideal communication weight is set as follows: and ,and and This indicates the weight that is disrupted due to a communication link failure.

[0031] The Laplacian matrix under the considered communication link failure condition is defined as follows: ;in, This represents the in-degree matrix affected by link failure. To account for the adjacency matrix after communication failure, This is the adjacency weight matrix between leaders and followers.

[0032] Furthermore, define This matrix comprehensively reflects the structural characteristics of the communication topology under the influence of communication failures.

[0033] In this embodiment, a fuzzy logic system is used to approximate the unknown nonlinear terms in multiple robotic arms, specifically: In practice, single-link robotic arms have unknown, uncertain, and nonlinear dynamics that are difficult to identify. In order to complete tracking control with less prior knowledge of the single-link robotic arm, a fuzzy logic system is used to approximate the unknown, uncertain, and nonlinear dynamics in the single-link robotic arm.

[0034] In close proximity Above, given a continuous function There exist fuzzy logic systems for satisfy:

[0035] in, For the weight vector, The Gaussian function is usually chosen. It is a basis function vector.

[0036] Using the unknown, uncertain, and nonlinear dynamics of a fuzzy single-link robotic arm in a fuzzy logic system, the state-space equations are rewritten as follows:

[0037] in, Indicates the system status. The derivative representing the system state, , , Indicates system input, Indicates system output, It is an unknown smooth function.

[0038] To avoid the adverse effects of communication link failures, this embodiment constructs a distributed estimator to provide the expected trajectory of the leader robot arm for each following robot arm. The distributed estimator is designed as follows:

[0039] in, , , For the first An estimate, Indicates the leadership robotic arm The expected trajectory of the first derivative, express The estimation of adaptive gain. The selection must meet the following requirements ,in .

[0040] Consider the following triggering time series ,in , and indicate the first The next trigger moment.

[0041] The synchronization error of the distributed estimator in the event of a communication link failure is defined as follows:

[0042] Synchronization error as assumed to be affected by communication link failure It is measurable.

[0043] The following error variables are then defined:

[0044] To avoid continuous communication between adjacent robotic arms and reduce communication overhead, the following hybrid event triggering mechanism is established:

[0045] in:

[0046] in , When the event triggering condition is met, the designed error variable returns to 0.

[0047] make , Its dynamic expression can be obtained:

[0048] Among them, matrix Defined as:

[0049] And define:

[0050] Due to the matrix It is a positive definite matrix, and because the matrix... Since it is a Hurwitz matrix, therefore for any positive definite matrix There exists a symmetric positive definite matrix. , making Established.

[0051] To evaluate the effectiveness of the distributed hybrid event-triggered estimator, the following Lyapunov function is constructed:

[0052] Based on the above estimator dynamics, the derivative of the Lyapunov function can be obtained as follows:

[0053] Applying Young's inequality to the second term, we obtain the following relationship:

[0054]

[0055] in, For adjustable design constants, Representation matrix The maximum singular value.

[0056] Substituting the above inequality into the Lyapunov derivative, we get:

[0057] Note that in each trigger time interval The following relationship exists:

[0058] Right now:

[0059] in, , For the design parameters, It is a constant.

[0060] Substituting this into the Lyapunov derivative expression, we further obtain:

[0061] in, , .

[0062] When the design parameters meet When this is done, it can be ensured that the Lyapunov function is boundedly decreasing, thus proving the error variable... The boundedness of [the property]. Considering synchronization error. It includes both local state and leader estimation error, and Since it is a positive definite matrix, Bounded further means that each estimation error It is also uniformly bounded.

[0063] In summary, even under communication link failure conditions, the proposed distributed hybrid event-triggered estimator can still effectively approximate the expected trajectory of the leader robotic arm and its derivative, with the estimation error guaranteed to be bounded, thus verifying the robustness and effectiveness of the estimator structure.

[0064] The control law incorporates the output of a fuzzy logic system to approximate unknown nonlinear terms in the modeling process. Combined with the feedback structure of the estimated tracking error, it ensures that the states of each slave node eventually converge. To address the tracking control problem of a multi-link robotic arm under the influence of communication link failures, the following coordinate transformation is proposed:

[0065] in, The estimated tracking error, It is a virtual controller.

[0066] The Lyapunov function is constructed as follows:

[0067]

[0068]

[0069] in, yes The estimated value, whose estimation error is defined as .

[0070] Due to the function Since it is unknown, we use a fuzzy logic system for approximation:

[0071] in, For fuzzy basis function vectors, This is the approximation error.

[0072] To achieve effective tracking of the leader robotic arm by the follower robotic arm, guide the system state into the subsequent error feedback stage, and lay the structural foundation for the next step of backstepping design, a virtual controller is needed. Adaptive law and the actual controller The design is as follows:

[0073]

[0074]

[0075] in It controls the gain.

[0076] To address the nonlinearity and uncertainty of the system, an adaptive law is developed based on the approximation characteristics of fuzzy logic systems. The specific design is as follows:

[0077]

[0078]

[0079] in, For the corresponding fuzzy basis function vector.

[0080] Based on the system state-space equations, the virtual controller, the adaptive law, and the estimated error signal, Differentiation yields:

[0081]

[0082]

[0083] in, This represents the corresponding approximation error.

[0084] To eliminate Zeno behavior caused by event-triggered mechanisms in the estimator, a proof is provided below. First, based on the design of the estimator, its derivative is expressed in the following form:

[0085] Among them, matrix sum matrix They are defined as follows:

[0086] Define the estimation error of the leader's state as .make , , , .

[0087] Therefore, the following relationship can be obtained: , and .

[0088] Furthermore, the derivative form of the estimation error can be obtained:

[0089] Through event triggering The following relationship was obtained:

[0090] Based on this, the following triggering criteria can be derived:

[0091] in, .

[0092] analyze The relationship between them can be expressed in the following form, where their derivative can be written as follows:

[0093] Based on the relationship derived above, and by transforming it using the norm inequality, we obtain:

[0094] Further derivation yields:

[0095] in, , .

[0096] Will use This means that the above formula can be simplified to:

[0097] Based on the above relationship, we can conclude that:

[0098] Due to the specific nature of the design, the initial conditions can be obtained as follows: .function This constitutes a The constraint can be considered as its upper bound. This ensures that for any... They all .

[0099] In summary, the triggering mechanism of the estimator depends on the error signal ratio function. The evolutionary process. At each triggering moment. This ratio satisfies The next trigger will occur when it grows to a threshold. It happens at any time.

[0100] To analyze the lower bound of the event trigger interval, we can construct... upper bound function Used to estimate its growth rate, thereby obtaining its growth from the initial value to the threshold. Shortest required time .because Controlled The increase in the upper limit, for By integrating the results, the event trigger interval can be obtained:

[0101] in, It's obvious. , With appropriate transformation and arrangement, it can be verified. .

[0102] The triggering mechanism can also be proven in a similar way. Zeno behavior does not exist. Therefore, it can be proven that the hybrid event-triggered Zeno behavior proposed in this embodiment is excluded.

[0103] To analyze the stability of the multi-link robotic arm by analyzing the designed virtual controller, actual controller, and adaptive law, the following Lyapunov function is selected:

[0104] Further derivation yields the following relationship:

[0105] in, ,and .

[0106] From the above equation, we obtain the following relationship:

[0107] Then, by integrating both sides of the equation:

[0108] get:

[0109] Furthermore, the estimation error satisfies the following relationship:

[0110] in, .

[0111] Therefore, it can be concluded that all signals of the multi-link robotic arm system are uniformly bounded, and the final tracking error is also ultimately bounded, thus proving the stability of the system.

[0112] To demonstrate the feasibility, effectiveness, and correctness of this example, the following simulation experiments were conducted: In this simulation experiment, a distributed cooperative control method integrating a distributed estimator and a hybrid event-triggered mechanism was designed for a multi-link robotic arm system where communication links may fail and communication bandwidth is limited. The proposed method uses a fuzzy logic system to approximate unknown nonlinear terms and constructs controllers for each following robotic arm based on a backstepping method, enabling the system to effectively track the leader's trajectory even in the absence of global information. Simulation results show that while ensuring the operating state of each link robotic arm remains consistent with the leader link robotic arm, the hybrid event-triggered mechanism significantly reduces the information update frequency and communication burden, verifying the feasibility and stability of the proposed method in complex communication environments.

[0113] The weights of all communication links in the provided system are affected by fault disturbances, and the fault disturbance terms are set as follows: as well as .in Indicates the range of values ​​within A random function is used to simulate the uncertainties caused by communication channel failures. The initial state settings of the system are as follows: initial state of each following robotic arm. , , , , The estimator is initially set to... , In a fuzzy logic system, the initial estimate of the unknown parameter is set as follows: The designed parameters are taken as follows: , , , , , , , , , , , , , .

[0114] The communication topology diagram of a multi-link robotic arm is as follows: Figure 4 As shown, the adjacency matrix and Laplace matrix of the system are obtained as follows: ,

[0115] The effectiveness of this simulation is further illustrated by referring to the accompanying diagram: Simulation results are as follows Figures 5-10 , Figure 5The tracking performance of five single-link robotic arms on a reference trajectory was depicted under the condition of a communication link failure. As can be seen from the figures, all robotic arms achieved accurate tracking of the reference signal in a very short time, verifying the convergence capability of the proposed control scheme. Figure 6 and Figure 7 The proposed distributed estimator's estimation results for the leader robot's expected trajectory and its first derivative are presented. It can be observed that although the initial estimates of the slave robots differ, under the hybrid event triggering mechanism, all estimated trajectories rapidly converge to a consistent state within a short time, effectively achieving accurate tracking of the leader's trajectory and its rate of change. This result verifies the consistency performance and dynamic response capability of the designed estimator under communication link failure conditions. Figure 8 The figure shows the synchronization error curves among the five robotic arms under the condition of communication link failure. As can be seen from the figure, due to the impact of communication link failure, the communication topology is time-varying and unstable, so the system synchronization error has not fully converged and exhibits a large deviation. Figure 9 The graph shows the variation curve of the system control input. It can be seen from the graph that the control input always remains within a reasonable range, without any severe jitter or saturation problems, which further verifies the practicality and engineering feasibility of the controller design. Figure 10 The figure shows the trend of trigger time interval changes for each robotic arm under the designed hybrid event triggering mechanism. As can be seen from the figure, the event triggering designed in this embodiment effectively avoids frequent communication and reduces system resource overhead.

[0116] Based on the simulation results above, it can be fully verified that the distributed collaborative control strategy for multiple single-link robotic arms proposed in this embodiment can still achieve high-precision tracking, consistent synchronization, and bounded control input even under the complex impact of communication link failures. Moreover, the triggering mechanism is reasonably designed, effectively reducing the system load, and has strong practical application value.

[0117] This embodiment investigates a distributed adaptive cooperative control method for a nonlinear multi-bar linkage manipulator system with communication link failures, uncertain nonlinear dynamics, and limited communication resources. To address the problem of inaccurate information transmission caused by link failures, a distributed estimator structure is designed, incorporating a hybrid event-triggered mechanism to reduce communication frequency and avoid Zeno behavior. Simultaneously, for unknown nonlinear terms in the system, a fuzzy logic system is used for online approximation, coupled with a backstepping method to construct the controller layer by layer, achieving asymptotic convergence of tracking errors. The proposed method does not rely on global information and can guarantee system consistency and stability under communication uncertainties and disturbances. Finally, simulations of cooperative control of multiple single-bar linkage manipulators verify the effectiveness of the proposed method in terms of control performance, communication efficiency, and system robustness.

[0118] Example 2 The purpose of this embodiment is to provide a cooperative control system for a nonlinear multi-agent system, including: The model building module is configured to: establish a nonlinear dynamic model for each single-link manipulator, considering communication link failures, and use a fuzzy logic system to fuzz the unknown, uncertain, and nonlinear dynamics of the single-link manipulator. The estimation module is configured to estimate the leader's state information based on the local information of each following robotic arm itself and its neighboring nodes, and to embed a hybrid event triggering mechanism in the estimation so that the state update is only performed when specific triggering conditions are met. The control module is configured to construct an actual controller based on the estimated leader state information using a backstepping method, and through the actual controller, control the position of the following robotic arm to keep it synchronized with the desired trajectory of the leader robotic arm in the event of a communication link failure.

[0119] In further embodiments, the following is also provided: An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When executed by the processor, the computer instructions perform the method described in Embodiment 1. For brevity, further details are omitted here.

[0120] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0121] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0122] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in Embodiment 1.

[0123] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0124] A computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0125] The present invention also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in program modules, which execute in a device on a target real or virtual processor to perform the processes / methods described above. Typically, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of program modules can be combined or divided among program modules as needed. The machine-executable instructions for the program modules can execute within a local or distributed device. In a distributed device, the program modules can reside in both local and remote storage media.

[0126] The computer program code used to implement the methods of the present invention may be written in one or more programming languages. This computer program code may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the computer or other programmable data processing device, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a computer, partially on a computer, as a stand-alone software package, partially on a computer and partially on a remote computer, or entirely on a remote computer or server.

[0127] In the context of this invention, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, and the like. Examples of signals may include electrical, optical, radio, sound, or other forms of propagation signals, such as carrier waves, infrared signals, etc.

[0128] Those skilled in the art will recognize that the units and algorithm steps described in conjunction with the embodiments herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0129] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for cooperative control of a nonlinear multi-agent system, characterized in that, Comprise: In the case of communication link failure, a nonlinear dynamic model of each single-link robot arm is established, and the unknown and uncertain nonlinear dynamics in the single-link robot arm are fuzzified by using a fuzzy logic system, specifically: The communication topology relationship between the multiple single-link robot arms in the cooperative tracking control is described by using an undirected graph, and a Laplace matrix under the condition of communication link failure is established according to the in-degree matrix under the influence of link failure and the adjacency matrix after considering the communication failure; The unknown and uncertain nonlinear part in the Laplace matrix is approximated by using a fuzzy logic system, so as to effectively compensate for the nonlinear dynamic behavior.

2. The method of claim 1, wherein, The hybrid event-triggered mechanism is specifically: The leader state information is estimated based on the local information of each follower robot arm itself and the neighbor nodes of the follower robot arm, specifically: Further comprising an adaptive law designed to cope with the nonlinearity and uncertainty of the system based on the approximation characteristics of the fuzzy logic system, and the designed adaptive law is specifically:

3. The method of claim 1, wherein the nonlinear multi-agent system is a multi-agent system with a nonlinear dynamics. Comprise: ； wherein , , is an adaptive gain, is a synchronization error affected by a communication link failure, denotes the triggering time, , , denotes an error variable, .

4. The method of claim 1, wherein The model construction module is configured to: in the case of communication link failure, a nonlinear dynamic model of each single-link robot arm is established, and the unknown and uncertain nonlinear dynamics in the single-link robot arm are fuzzified by using a fuzzy logic system; wherein, , , For the first estimator, , denotes an estimate of ; the adaptive gain is chosen to satisfy wherein, .

5. The method of claim 1, wherein Based on the estimated leader state information, a virtual controller is constructed using backstepping method , and an actual controller , in particular: ； ； ； wherein, is a control gain; is an estimated tracking error; is an estimate of .

6. The method of claim 1, wherein The estimation module is configured to: estimate the leader state information based on the local information of each follower robot arm itself and the neighbor nodes of the follower robot arm, and embed a hybrid event-triggered mechanism in the estimation, so that the state update is only performed when a specific trigger condition is met; ； ； ； wherein, is the designed adaptive law; is the estimated tracking error.

7. A cooperative control system for a nonlinear multi-agent system, characterized by The control module is configured to: based on the estimated leader state information, an actual controller is constructed by using a backstepping method, and through the actual controller, the position of the follower robot arm is controlled to keep synchronization with the expected trajectory of the leader robot arm under the influence of communication link failure. Comprise a memory and a processor, and computer instructions stored on the memory and running on the processor, when the computer instructions are run by the processor, the method of any one of claims 1-6 is completed. For storing computer instructions, when the computer instructions are executed by the processor, the method of any one of claims 1-6 is completed. Comprise a computer program, when the computer program is executed by the processor, the method of any one of claims 1-6 is completed.

8. An electronic device, comprising: ​ 9. A computer-readable storage medium, characterized in that, ​ 10. A computer program product, characterised in that, ​

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