Cooperative control method and system for multiple single torsional pendulum systems

Abstract

The invention provides a multi-single torsional pendulum system cooperative control method and system, and the method comprises the steps: building a dynamic model of a multi-single torsional pendulum, and approaching an unknown nonlinear term in the dynamic model through a fuzzy logic system; a communication topological relation of multiple single torsional pendulums is considered, a consistency tracking error containing a dynamic boundary function is constructed, the singularity problem in an initial time tracking error is avoided, the boundary function is dynamically adjusted according to the initial distance of an agent, and therefore the adaptability of an execution mechanism is improved; according to the virtual controller and the actual controller triggered based on the switching dynamic event, the position of the following torsional pendulum can be controlled to be synchronous with the expected track of the leading torsional pendulum under the conditions that the communication range is limited and the communication topology is abnormal.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of multi-single pendulum system cooperative control, and particularly relates to a multi-single pendulum system cooperative control method and system. BACKGROUND

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

[0003] A single pendulum is a common mechanical system, usually consisting of a rigid swing arm and a fixed fulcrum, which has a wide range of applications in physics and control systems. A single pendulum system is composed of a swing arm, a fulcrum, a driving source, a sensor, and a computer controller. The motion of a single pendulum is usually described by angle and angular velocity, which can be used as a typical model for studying nonlinear control and stability analysis.

[0004] At present, when a single pendulum is applied in the engineering field, especially in a multi-single pendulum system or a control system involving multiple single pendulums, communication between two single pendulums becomes difficult when the geometric distance between them exceeds a predefined sensing range. This is because in practical applications, single pendulum systems often need to exchange information and transmit control instructions through wireless or wired networks, and the effectiveness of communication depends on the distance between them and the signal strength. When the distance between two single pendulums exceeds a certain range, due to signal attenuation, interference or bandwidth limitations, the quality of communication may decrease, resulting in data loss, increased delay or even inability to establish a connection, thereby affecting the stability and accuracy of the entire system.

[0005] In addition, the control scheme of a single pendulum usually adopts a time-triggered method to act on the controlled system through a digital controller, i.e. the system will sample at a fixed period and then update the control signal at the same period. Although the sampling method based on time as the period is simple, the control signal will still be updated at a fixed and relatively fast frequency even when the system has reached the desired control accuracy and no longer needs any operation on the control, greatly increasing the waste of system resources. In addition, when the various components of a single pendulum exchange information and control through a network, the network bandwidth will limit the amount of information transmitted, and if there is too much information, it will cause bandwidth congestion, resulting in the loss of some data and affecting control accuracy.

[0006] Due to the need for information exchange between single torsional pendulums, especially in a multi-single torsional pendulum system or a networked control environment, information leakage is inevitable. In these systems, state information, control signals, and sensor data need to be shared in real time between single torsional pendulums to ensure coordinated control and overall stability of the system. However, the existence of information leakage means that part of the data may be obtained or tampered with by unauthorized third parties during transmission, which poses a serious threat to the security and reliability of the system. If information leakage occurs, it may cause control commands to be misdelivered or distorted, thereby affecting the motion trajectory and accuracy of the single torsional pendulum. Therefore, when designing a single torsional pendulum system, the security of information transmission must be strengthened, and encryption measures must be taken to ensure data security during information exchange. SUMMARY

[0007] To overcome the shortcomings of the prior art, the present application provides a multi-single torsional pendulum system coordinated control method and system, which can control the position of the follower torsional pendulum to keep synchronized with the desired trajectory of the leader torsional pendulum under the conditions of limited communication range and limited communication bandwidth based on the virtual controller and the actual controller based on the switching dynamic event trigger.

[0008] To achieve the above-mentioned purpose, the present application adopts the following technical solutions: In a first aspect, the present application provides a multi-single torsional pendulum system coordinated control method, comprising: Under the condition of considering limited communication range and limited communication bandwidth, a dynamic model of the multi-single torsional pendulum is established, and a fuzzy logic system is used to approximate unknown nonlinear terms in the dynamic model; Considering the communication topology relationship of the multi-single torsional pendulum, a consistent tracking error containing a dynamic boundary function is constructed, and a virtual controller and the corresponding parameter adaptive rate are constructed based on the backstepping method and the fuzzy approximation term; Based on the estimated value of the virtual controller, the nonlinear terms in the estimated output of the virtual controller are compensated for, the consistent tracking error is suppressed, and the actual controller is constructed for the goal of synchronizing the state of the follower single torsional pendulum with the leader single torsional pendulum. The multi-single torsional pendulum system coordinated control is realized based on the actual controller; wherein the actual controller adopts a switching dynamic event trigger mechanism.

[0009] In a second aspect, the present application provides a multi-single torsional pendulum system coordinated control system, comprising: The model establishment module is configured to: under the condition of considering limited communication range and limited communication bandwidth, establish a dynamic model of the multi-single torsional pendulum, and use a fuzzy logic system to approximate unknown nonlinear terms in the dynamic model; The synchronization error processing module is configured to: considering the communication topology relationship of the multi-single torsional pendulum, construct a consistent tracking error containing a dynamic boundary function, and construct a virtual controller and the corresponding parameter adaptive rate based on the backstepping method and the fuzzy approximation term; The control module is configured to: compensate for nonlinear terms in virtual controller estimation output based on an estimated value of the virtual controller, suppress consistency tracking error, and synchronize a state of a follower single pendulum with a leader single pendulum as a target to construct an actual controller, and implement cooperative control of the multi-single pendulum system based on the actual controller; and the actual controller adopts a switching dynamic event triggering mechanism.

[0010] In a third aspect, the present application provides an electronic device, comprising a memory and a processor, and computer instructions stored in the memory and running on the processor, when the computer instructions are run by the processor, the method of the first aspect is completed.

[0011] In a fourth aspect, the present application provides a computer readable storage medium for storing computer instructions, when the computer instructions are executed by the processor, the method of the first aspect is completed.

[0012] The above one or more technical solutions have the following beneficial effects: In the present application, a dynamic model of multi-single pendulum is established, and a fuzzy logic system is used to approximate unknown nonlinear terms in the dynamic model; considering the communication topology relationship of multi-single pendulum, a consistency tracking error containing a dynamic boundary function is constructed, which not only avoids the singularity problem in the initial time tracking error, but also dynamically adjusts the boundary function according to the initial distance of the agent, thereby improving the adaptability of the actuator; according to the virtual controller and the actual controller based on the switching dynamic event triggering, the position of the follower pendulum can be controlled to keep synchronization with the expected trajectory of the leader pendulum under the condition of limited communication range and abnormal communication topology.

[0013] In the present application, the switching dynamic event triggering mechanism is designed, by introducing the hyperbolic tangent function and the inverse proportional function in the triggering threshold, the dynamic adjustment of the triggering threshold is ensured and the ideal communication threshold can be adaptively selected according to the tracking performance index, which not only improves the flexibility of the control system, but also reduces the communication burden.

[0014] In the present application, a second-order sliding mode integral filter is used to solve the "complexity explosion" problem caused by the traditional backstepping method; the mask function of the predefined time is designed to prevent information leakage during information exchange.

[0015] The advantages of the additional aspects of the present application will be partially given in the following description, partially will become obvious from the following description, or will be understood by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0016] The drawings accompanying the specification of the present application form a part thereof, serve to provide further understanding of the present application, and together with the description of the exemplary embodiments of the present application and their description serve to explain the present application, and do not constitute improper limitations on the present application.

[0017] Figure 1 Figure is a component of the torsional pendulum system; Figure 2 Figure is a flowchart of the method for cooperative control of the multi-single torsional pendulum system with maintained connectivity according to an embodiment of the present application; Figure 3 Figure is a directed communication topology diagram of the four single torsional pendulums according to an embodiment of the present application; Figure 4 Figure is an output and reference trajectory tracking diagram of the four single torsional pendulums according to an embodiment of the present application; Figure 5 Figure is a consistency tracking error curve diagram of the four single torsional pendulums according to an embodiment of the present application; Figure 6 Figure is a connection protection diagram of the four single torsional pendulums according to an embodiment of the present application; Figure 7 Figure is a trigger number diagram of the multi-single torsional pendulum under the switching dynamic event trigger mechanism according to an embodiment of the present application.

[0018] Figure 8 Figure is a control input curve diagram of the multi-single torsional pendulum according to an embodiment of the present application. DETAILED DESCRIPTION

[0019] It should be noted that the following detailed description is merely exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, 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 application belongs.

[0020] It is to be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application.

[0021] In the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0022] Embodiment One The present embodiment discloses a method for cooperative control of a multi-single torsional pendulum system, comprising: Under the condition of considering limited communication range and limited communication bandwidth, a dynamic model of the multi-single torsional pendulum is established, and a fuzzy logic system is used to approximate unknown nonlinear terms in the dynamic model; Considering the communication topology relationship of the multi-single torsional pendulum, a consistency tracking error containing a dynamic boundary function is constructed, and a virtual controller and corresponding parameter adaptive rate are constructed based on the backstepping method and fuzzy approximation terms; Based on the estimated value of the virtual controller, the nonlinear term in the virtual controller estimated output is compensated, the consistency tracking error is suppressed, the state of the following single pendulum is synchronized with the leader single pendulum, and the actual controller is constructed, and the multi-single pendulum system cooperative control is realized based on the actual controller; wherein the actual controller adopts a switching dynamic event trigger mechanism.

[0023] The embodiment establishes a dynamic model of the multi-single pendulum, and uses a fuzzy logic system to approximate the unknown nonlinear term in the dynamic model; considering the communication topology relationship of the multi-single pendulum, a consistency tracking error containing a dynamic boundary function is constructed, which not only avoids the singularity problem in the initial time tracking error, but also dynamically adjusts the boundary function according to the initial distance of the agent, thereby improving the adaptability of the actuator; according to the virtual controller and the actual controller based on the switching dynamic event trigger, the position of the following pendulum can be controlled to keep synchronized with the expected trajectory of the leader pendulum under the condition of limited communication range and abnormal communication topology.

[0024] The following will be combined Figures 1-8 The multi-single pendulum system cooperative control method proposed in the embodiment will be described in detail; Taking four multi-single pendulums as an example, according to the Euler-Lagrange equation and Newton's second law, the dynamic model of the multi-single pendulum is obtained, which is expressed as follows:

[0025]

[0026] In the dynamic model of the multi-single pendulum, and are the angular displacement and angular velocity of the first single pendulum, respectively. and represent the mass and length of the pendulum, respectively, represents the moment of inertia, represents the friction coefficient, represents the gravitational acceleration, is the external input control force.

[0027] Let and , the dynamic model can be converted into a state space equation, which is specifically as follows:

[0028]

[0029] wherein, represents the measurable system state, represents the measurable system output, are the the derivative of =1 / 3kg, =2 / 3m, =9.8 , and =0.2.

[0030] Approximating unknown nonlinear terms in multiple single torsion pendulum using fuzzy logic system: The actual single torsion pendulum has unknown uncertain nonlinear dynamics which are difficult to identify. In order to complete tracking control using less prior knowledge of single torsion pendulum, fuzzy logic system is used to identify unknown uncertain nonlinear terms in single torsion pendulum. When , the continuous function is defined on the compact set , there exists a fuzzy logic system such that:

[0031] where is the ideal weight vector, is the approximation error, is the fuzzy basis function vector. Based on fuzzy logic system, the state space equation of the system can be rewritten as:

[0032]

[0033]

[0034] where denotes the measurable system state, denotes the measurable system output, and are the derivatives of , denotes the weight vector, and the superscript T denotes the transpose, is the basis function vector, is the approximation error.

[0035] The directed communication topology relationship between multiple single torsion pendulums in cooperative tracking control is described using directed graph, specifically: The directed communication topology relationship between 4 multiple single torsion pendulums can be represented by a directed graph , where and denote the agent set, edge set and adjacency matrix respectively. The edge represents that the single torsion pendulum can receive the transmitted information from the single torsion pendulum . When , the weight of the adjacency matrix is defined as ; otherwise, The Laplacian matrix is defined as where Then, the Laplacian matrix is defined as There exists Then, the matrix is nonsingular.

[0036] Considering the multi-single pendulum communication topology, the multi-single pendulum consensus error is defined, and then based on the backstepping method, an adaptive fuzzy logic system control scheme is designed to reduce the tracking error, and finally the multi-single pendulum cooperation is realized.

[0037] The multi-single pendulum consensus error is defined as:

[0038]

[0039] where, is the multi-single pendulum consensus tracking error, N denotes the total number of neighbor sets of the i-th agent. i represents the output of the i-th single pendulum itself, represents the output of the "neighbor single pendulum" that has information interaction with the i-th single pendulum. The "neighbor" is defined by the "communication topology" of the system: if single pendulum i can receive information from single pendulum j, then j is the neighbor of i. If the following single pendulum

[0040] can receive information sent by adjacent single pendulums, then i , otherwise .

[0041] is the connectivity maintenance performance function, which is expressed as: where,

[0042] . and are positive numbers, is the designed convergence time. is the virtual control signal designed for subsequent design. In the backstepping method, the virtual control signal is designed to make the consensus error tend to be small in the neighborhood around 0. Under the framework of the backstepping method, the virtual control signal and a novel adaptive law are designed:

[0043] The virtual controller is designed as follows:

[0044] ​where , , is a positive design parameter, represents the communication weight between the ith single pendulum and the leader single pendulum, denotes the estimation of the ideal weight vector of the fuzzy logic system, is the basis function vector.

[0045] The derivative of the tracking error is given by

[0046] where

[0047] is the state information, is a predefined time. ,m is a design constant, and its derivative is continuous.

[0048] To avoid the problem of complexity explosion in calculating the derivative of the virtual control law , a second-order sliding mode integral filter is designed to estimate the virtual control law , which is given by

[0049]

[0050] where and denote the states of the second-order sliding mode integral filter, , , , , and are all design constants. Thus, we have , denotes the estimation error of the second-order sliding mode integral filter.

[0051] where the input of the second-order sliding mode integral filter is and the output is .

[0052] Therefore, the derivative of the tracking error is given by

[0053] The adaptive law is designed as follows:

[0054] where, are suitable positive parameters.

[0055] To reduce the controller update frequency and the wear of the controller between multiple single pendulums, an adaptive cooperative controller based on a switching dynamic event-triggered mechanism is designed in this embodiment: The actual controller and event-triggered condition are constructed as follows:

[0056]

[0057]

[0058] where,

[0059]

[0060] where, and are user-designed parameters. Their selection range satisfies and . is a constant. is a real number. is the control signal change error caused by the switching dynamic event trigger. denotes the controller update time. If the trigger condition is satisfied, the actual control signal will be updated.

[0061] Further, the intermediate control signal is designed as:

[0062] where the parameters need to satisfy and . At each trigger, the time is set, and the intermediate control signal is applied to the system. During the time interval , the control signal remains constant, i.e. .

[0063] The adaptive rate

[0064]

[0065] where, , are suitable positive parameters. is the basis function vector.

[0066] In addition, in order to prevent information leakage in the information exchange process, a pre-defined time mask function is designed as:

[0067] where:

[0068] is the state information, is the pre-defined time. ,m is the designed constant, and its derivative is continuous.

[0069] In order to analyze the designed virtual controller, the actual controller and the adaptive law can make the multi-single pendulum stable, the following Lyapunov candidate function is selected :

[0070] where, is the appropriate design parameter. , are the estimation errors of the first step and the second step parameters of the i-th single pendulum system, respectively.

[0071] Taking the derivative of the selected Lyapunov candidate function , the calculation can be obtained:

[0072]

[0073] where, , . Multiply both sides by , and integrate on the interval , to get:

[0074] According to the definition of , we have:

[0075] Then, we get:

[0076] Obviously, each variable in the system is semi-globally uniformly bounded. The leader remains bounded. is bounded. Because , where It is a constant, which ensures The boundedness of. Furthermore, It is continuous, which means The system exhibits boundedness. Therefore, it can be concluded that all signals in a single torsion pendulum system are uniformly and eventually bounded, and the tracking error eventually converges to an arbitrarily small neighborhood of zero, thus proving the stability of the system.

[0077] To demonstrate the feasibility, effectiveness, and correctness of this example, the following simulation experiments were conducted: In this simulation experiment, for a multi-single torsion pendulum system with limited communication range, an adaptive fuzzy logic system cooperative controller based on a switching dynamic event triggering mechanism was designed. This ensures that the operating state of each single torsion pendulum is consistent with that of the leader single torsion pendulum, meaning that every variable of the multiple single torsion pendulums tends to be consistent. Furthermore, while achieving consistency, this not only improves the accuracy of identifying unknown nonlinearities in the system but also significantly reduces the number of controller updates and mechanical wear in the single torsion pendulum system.

[0078] First, the actual physical parameters were selected as =1 / 3kg, =2 / 3m, =9.8 , and =0.2. The system's reference signal is: The initial system state is: , The virtual controller gain is: , Connectivity Preservation Performance Function Parameters , , , , The parameters for switching the dynamic event triggering mechanism are: , , , , , , , , , , The privacy protection mechanism parameters are: , The parameters of the fuzzy logic system are: , , , , , The parameters of the second-order sliding membrane integral filter are: .

[0079] The communication topology diagram of multiple single torsion oscillators is as follows: Figure 3 As shown, the adjacency matrix of the system is obtained. for:

[0080] The effectiveness of this simulation is further illustrated by referring to the accompanying diagram: exist Figure 6 In (a) and (b), the initial leader-follower distance and the distance between followers remain within the convergence boundary. As the system runs, the boundary gradually converges to 0.21. To demonstrate the versatility of the proposed method, the initial values ​​are reset to... Its corresponding Figure 6 (c) and (d). By comparison Figure 6 (a), (b) and Figure 6 As can be seen in (c) and (d), the convergence boundary of the connection-preserving method proposed in this embodiment can be dynamically adjusted according to the initial proxy distance, which improves the adaptability of the system; Figure 7 The interval time of the four followers is shown. It is clear that the modified switching dynamic event triggering mechanism can effectively reduce the number of triggers of multiple single oscillations. Figure 8 The input signal was displayed. The curves demonstrate the practicality of the proposed control scheme.

[0081] This example investigates the distributed adaptive tracking control problem for a nonlinear multi-single torsion pendulum system with limited communication range and bandwidth. To avoid the "complexity explosion" problem of the virtual controller, a second-order sliding integral filter is employed. Furthermore, unlike existing connectivity-maintainer methods, a novel nonlinear transformation method for synchronization error is constructed to avoid the singularity problem of initial time tracking error, and it can dynamically adjust the boundary function based on the initial distance of the agents. An improved switching dynamic event triggering mechanism is proposed to reduce the number of controller updates and controller wear. Simultaneously, a privacy protection mechanism with adjustable protection time is applied to improve system security. Finally, simulations verify the applicability of the proposed multi-single torsion pendulum cooperative control method.

[0082] Example 2 The purpose of this embodiment is to provide a collaborative control system for multiple single torsion gyroscope systems, including: The model building module is configured to: establish a dynamic model of multiple single torsional pendulums under the conditions of limited communication range and limited communication bandwidth, and approximate the unknown nonlinear terms in the dynamic model using a fuzzy logic system; The synchronization error processing module is configured to: consider the communication topology of multiple single torsional pendulums, construct a consistent tracking error with dynamic boundary functions, and construct a virtual controller and corresponding parameter adaptive rate based on the backstepping method and fuzzy approximation terms; The control module is configured to: construct an actual controller based on the estimated value of the virtual controller to compensate for the nonlinear term in the estimated output of the virtual controller, suppress the consistency tracking error, and synchronize the state of the following single torsion pendulum with that of the leader single torsion pendulum; and realize the coordinated control of the multiple single torsion pendulum system based on the actual controller; wherein the actual controller adopts a switching dynamic event triggering mechanism.

[0083] 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.

[0084] 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.

[0085] 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.

[0086] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the method described in Embodiment 1.

[0087] 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.

[0088] A computer program product includes a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0089] 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.

[0090] 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.

[0091] 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.

[0092] 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.

[0093] 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 coordinated control of multiple single torsion pendulum systems, characterized in that, include: Considering the limitations of communication range and bandwidth, a dynamic model of multiple single torsional pendulums is established, and the unknown nonlinear terms in the dynamic model are approximated using a fuzzy logic system. Considering the communication topology of multiple single torsional pendulums, a consistent tracking error with dynamic boundary functions is constructed, and a virtual controller and corresponding parameter adaptive rate are constructed based on the backstepping method and fuzzy approximation terms. Based on the estimation value of the virtual controller, an actual controller is constructed to compensate for the nonlinear term in the estimated output of the virtual controller, suppress the consistency tracking error, and synchronize the state of the following single torsion pendulum with that of the leader single torsion pendulum. Based on the actual controller, the coordinated control of the multiple single torsion pendulum system is realized; wherein, the actual controller adopts a switching dynamic event triggering mechanism.

2. The method for coordinated control of multiple single torsion pendulum systems as described in claim 1, characterized in that, Considering the limitations of communication range and bandwidth, a dynamic model of multiple single torsional pendulums is established. A fuzzy logic system is used to approximate the unknown nonlinear terms in this dynamic model, specifically: A dynamic model of multiple single torsional pendulums is established, taking into account the limitations of communication range and bandwidth. The dynamic model of multiple single torsion pendulums is transformed into a state-space equation. The fuzzy logic system is introduced into the state-space equation to compensate for unknown nonlinear terms, resulting in a state equation containing approximation terms. The design incorporates an adaptive law to update the weight vector in the state equation containing approximation terms in real time.

3. The method for coordinated control of multiple single torsion pendulum systems as described in claim 1, characterized in that, Considering the communication topology of multiple single torsional pendulums, a consistent tracking error with dynamic boundary functions is constructed. A virtual controller and corresponding parameter adaptive rate are then built based on the backstepping method and fuzzy approximation terms, specifically: A directed graph is used to describe the directed communication topology between multiple single torsional pendulums, and the consistency tracking error is defined based on the adjacency matrix and dynamic boundary function. With the goal of eliminating consistency tracking error, a virtual controller is designed by combining the approximation results of the fuzzy logic system for unknown nonlinear terms; Based on the stability analysis of the backstepping method, a parameter adaptive rate for the virtual controller is designed so that the weight estimate of the virtual controller tracks the ideal weight.

4. The method for coordinated control of multiple single torsion pendulum systems as described in claim 1, characterized in that, The actual controller is specifically: ； ； in, This is an intermediate control signal. , Indicates the controller update time; Parameters designed for the user; For multiple single torsional oscillation consistency errors; ; , ; This is the virtual control rate.

5. The method for coordinated control of multiple single torsion pendulum systems as described in claim 1 or 4, characterized in that, The event triggering conditions for the actual controller are as follows: ； ； in, ; It is a constant; It is an error caused by changes in control signals triggered by switching dynamic events; Indicates the controller update time. It is a real number. This is due to the consistency error of multiple single torsional oscillations.

6. The method for coordinated control of multiple single torsion pendulum systems as described in claim 1, characterized in that, It also includes designing a predefined time masking function to prevent information leakage during information exchange; the predefined time masking function is specifically as follows: ； ； in, It is status information. It is a predefined time; m is a design constant.

7. The method for coordinated control of multiple single torsion pendulum systems as described in claim 1, characterized in that, When differentiating the virtual control law in the virtual controller, a second-order sliding integral filter is used to estimate the virtual control law.

8. A multi-single torsion pendulum system collaborative control system, characterized in that, include: The model building module is configured to: establish a dynamic model of multiple single torsional pendulums under the conditions of limited communication range and limited communication bandwidth, and approximate the unknown nonlinear terms in the dynamic model using a fuzzy logic system; The synchronization error processing module is configured to: consider the communication topology of multiple single torsional pendulums, construct a consistent tracking error with dynamic boundary functions, and construct a virtual controller and corresponding parameter adaptive rate based on the backstepping method and fuzzy approximation terms; The control module is configured to: construct an actual controller based on the estimated value of the virtual controller to compensate for the nonlinear term in the estimated output of the virtual controller, suppress consistency tracking error, and synchronize the state of the following single torsion pendulum with that of the leader single torsion pendulum; and realize the coordinated control of the multiple single torsion pendulum system based on the actual controller; wherein the actual controller adopts a switching dynamic event triggering mechanism.

9. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Used to store computer instructions, which, when executed by a processor, perform the method described in any one of claims 1-7.

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