Multi-single pendulum system cooperative control method and system

Abstract

The application provides a multi-single pendulum system cooperative control method and system, a dynamic model of the multi-single pendulum is established, unknown nonlinear terms in the dynamic model are approximated by using a fuzzy logic system; a uniform tracking error containing a dynamic boundary function is constructed by considering a communication topological relationship of the multi-single pendulum, not only the singularity problem in the initial time tracking error is avoided, but also the boundary function is dynamically adjusted according to the initial distance of the agent, so that the adaptability of the actuator is improved; according to a virtual controller and an actual controller based on a switching dynamic event trigger, the position of the following pendulum and the expected trajectory of the leading pendulum can be kept synchronous under the condition that the communication range is limited and the communication topological relationship 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 torsos, especially in a multi-single torso 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 torsos 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 torsos. Therefore, when designing a single torso 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 torso system cooperative control method and system, which can control the position of the follower torsos to keep synchronized with the desired trajectory of the leader torso 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:

[0009] In a first aspect, the present application provides a multi-single torso system cooperative control method, comprising:

[0010] Under the condition of considering limited communication range and limited communication bandwidth, a dynamic model of the multi-single torso is established, and a fuzzy logic system is used to approximate unknown nonlinear terms in the dynamic model;

[0011] Considering the communication topology relationship of the multi-single torso, a consistent 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 term;

[0012] 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 state of the follower single torso is synchronized with the leader single torso as the goal to construct an actual controller, and the multi-single torso system cooperative control is realized based on the actual controller; wherein the actual controller adopts a switching dynamic event trigger mechanism.

[0013] In a second aspect, the present application provides a multi-single torso system cooperative control system, comprising:

[0014] 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 torso, and use a fuzzy logic system to approximate unknown nonlinear terms in the dynamic model;

[0015] The synchronization error processing module is configured to: consider the communication topological relationship of the multiple single pendulums, construct a consistency tracking error containing a dynamic boundary function, and construct a virtual controller and a corresponding parameter adaptive rate based on a backstepping method and a fuzzy approximation term;

[0016] The control module is configured to: based on the estimated value of the virtual controller, compensate for the nonlinear term in the estimated output of the virtual controller, suppress the consistency tracking error, construct an actual controller for the purpose of synchronizing the state of the follower single pendulum with the leader single pendulum, and realize cooperative control of the multiple single pendulum system based on the actual controller.

[0017] 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.

[0018] In a fourth aspect, the present application provides a computer readable storage medium for storing computer instructions, when the computer instructions are executed by a processor, the method of the first aspect is completed.

[0019] The above one or more technical solutions have the following beneficial effects:

[0020] In the present application, a dynamic model of the multiple single pendulums is established, and a fuzzy logic system is used to approximate the unknown nonlinear term in the dynamic model; considering the communication topological relationship of the multiple single pendulums, 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 follower pendulum can be controlled to keep synchronized with the desired trajectory of the leader pendulum under the condition of limited communication range and abnormal communication topology.

[0021] In the present application, the switching dynamic event trigger mechanism is designed, by introducing the hyperbolic tangent function and the inverse proportional function in the trigger threshold, the dynamic adjustment of the trigger 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.

[0022] 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 pre-defined time mask function is designed to prevent information leakage during information exchange.

[0023] The advantages of the additional aspects of the present application will be partially given in the following description, partially will become apparent from the following description, or will be understood by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0024] The accompanying drawings, which form a part of this specification, are included to provide a further understanding of the application, and are incorporated by reference in their entirety.

[0025] Figure 1 Figure is a part of the torsional pendulum system;

[0026] Figure 2 Figure is a flow chart of the method for controlling the multi-single torsional pendulum system with the communication maintaining provided in Embodiment One of the present application;

[0027] Figure 3 Figure is a directed communication topology of the four single torsional pendulums provided in Embodiment One of the present application;

[0028] Figure 4 Figure is an output and reference trajectory tracking graph of the four single torsional pendulums provided in Embodiment One of the present application;

[0029] Figure 5 Figure is a consistency tracking error graph of the four single torsional pendulums provided in Embodiment One of the present application;

[0030] Figure 6 Figure is a connection protection graph of the four single torsional pendulums provided in Embodiment One of the present application;

[0031] Figure 7 Figure is a trigger number graph of the multi-single torsional pendulum under the switching dynamic event trigger mechanism provided in Embodiment One of the present application.

[0032] Figure 8 Figure is a control input graph of the multi-single torsional pendulum provided in Embodiment One of the present application. DETAILED DESCRIPTION

[0033] 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.

[0034] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the example embodiments in accordance with the present application.

[0035] In the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0036] Embodiment One

[0037] The present embodiment discloses a method for controlling a multi-single torsional pendulum system, comprising:

[0038] Under the condition of limited communication range and limited communication bandwidth, a dynamic model of the multi-single pendulum is established, and a fuzzy logic system is used to approximate unknown nonlinear terms in the dynamic model;

[0039] Considering the communication topology of the multi-single pendulum, a consensus 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;

[0040] Based on the estimated value of the virtual controller, the nonlinear terms in the estimated output of the virtual controller are compensated, the consensus tracking error is suppressed, and the actual controller is constructed to synchronize the state of the follower single pendulum with the leader single pendulum. 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.

[0041] The embodiment establishes a dynamic model of the multi-single pendulum, uses a fuzzy logic system to approximate unknown nonlinear terms in the dynamic model, considers the communication topology of the multi-single pendulum, and constructs a consensus tracking error containing a dynamic boundary function. Not only the singularity problem in the initial time tracking error is avoided, but also the boundary function is dynamically adjusted 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 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.

[0042] 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;

[0043] 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:

[0044]

[0045]

[0046] 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.

[0047] Let and The dynamic model can be converted into a state space equation, which is given as follows:

[0048]

[0049]

[0050] where denotes the measurable system states, denotes the measurable system outputs, are the derivatives of , respectively. The actual physical parameters are chosen as = 1 / 3 kg, = 2 / 3 m, = 9.8 , and = 0.2.

[0051] Approximation of unknown nonlinear terms in multiple single pendulum using fuzzy logic system: The actual single pendulum has unknown and uncertain nonlinear dynamics which are difficult to identify. In order to complete the tracking control using less prior knowledge of the single pendulum, a fuzzy logic system is used to identify the unknown and uncertain nonlinear terms in the single pendulum. When is a continuous function defined on a compact set , there exists a fuzzy logic system such that:

[0052]

[0053] where is the ideal weight vector, is the approximation error, is the fuzzy basis function vector.

[0054] Based on the fuzzy logic system, the state space equation of the system can be rewritten as:

[0055]

[0056]

[0057]

[0058] where denotes the measurable system states, denotes the measurable system outputs, and are the derivatives of , respectively, denotes the weight vector, and the superscript T denotes the transpose, is the basis function vector, is the approximation error. ​

[0059] The directed communication topology among multiple single pendulums is described by a directed graph, which is denoted as G = (V, E, A), where V, E and A represent the set of agents, the set of edges and the adjacency matrix, respectively.

[0060] The directed communication topology among four single pendulums can be represented by a directed graph , where and represent the set of agents, the set of edges and the adjacency matrix, respectively. The edge represents that single pendulum can receive the transmitted information from single pendulum . When , the weight of the adjacency matrix is defined as ; otherwise, . The degree matrix is defined as , where . Then, the Laplacian matrix is defined as . It has . Then, the matrix is nonsingular.

[0061] Considering the communication topology among multiple single pendulums, the consensus error of multiple single pendulums is defined, and then an adaptive fuzzy logic system control scheme is designed based on the backstepping method to reduce the tracking error, and finally the coordination of multiple single pendulums is realized.

[0062] The consensus error of multiple single pendulums is defined as:

[0063]

[0064]

[0065] where is the consensus tracking error of multiple single pendulums, N denotes the total number of the neighbor set 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 the information of single pendulum j, then j is the neighbor of i. If the following single pendulum

[0066] can receive the information sent by the adjacent single pendulum, then i , otherwise .

[0067] is the connectivity preserving performance function, which is expressed as:

[0068] ​

[0069] where . and are positive numbers, is the designed convergence time. is the virtual control signal for the subsequent design. In the backstepping method, the virtual control signal is designed to make the consensus error tend to a small neighborhood around 0.

[0070] Under the framework of the backstepping method, the virtual control signal and a novel adaptive law are designed as follows:

[0071] Designing the virtual controller as follows:

[0072]

[0073] where , , is a suitable positive 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.

[0074] The derivative of the tracking error is expressed as:

[0075]

[0076] where

[0077]

[0078] is the state information, is a predefined time. ,m is a designed constant, and its derivative are continuous.

[0079] 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 rate , and its specific expression is as follows:

[0080]

[0081]

[0082] where and denote the states of the second-order sliding mode integral filter, , , , , and are design constants. Thus, we have , denotes the estimation error generated by the second-order sliding mode integral filter.

[0083] where the input of the second-order sliding mode integral filter is and the output is .

[0084] Thus, the derivative of the tracking error is given by:

[0085]

[0086] The adaptive law is designed as follows:

[0087]

[0088] where is a suitable positive parameter.

[0089] In order to reduce the controller update frequency and the wear and tear of the controller among multiple single pendulums, an adaptive cooperative controller based on a switching dynamic event-triggered mechanism is designed in this embodiment:

[0090] The actual controller and the event-triggered condition are constructed as follows:

[0091]

[0092]

[0093]

[0094] where

[0095]

[0096]

[0097] 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, the actual control signal will be updated if the triggering condition is satisfied.

[0098] Furthermore, the intermediate control signal is designed as

[0099]

[0100] where the parameters need to satisfy and . At each triggering time, the time is set as and the intermediate control signal is applied to the system. During the time interval , the control signal remains constant, i.e. .

[0101] The adaptive law

[0102]

[0103] where , are appropriate positive parameters. is the basis function vector.

[0104] In addition, in order to prevent information leakage during information exchange, a pre-defined time mask function is designed as

[0105]

[0106] where

[0107] is the state information, is the pre-defined time. ,m is a designed constant, and its derivative are continuous.

[0108] In order to analyze the designed virtual controller, actual controller and adaptive law can stabilize multiple single pendulums, the following Lyapunov candidate function is selected:

[0109]

[0110] where is an appropriate design parameter. , are the estimation errors of the first step and the second step parameters of the i-th single pendulum system, respectively.

[0111] For the selected Lyapunov candidate function Taking the derivative, we get

[0112]

[0113]

[0114] where , . Multiply both sides by and integrate over the interval to get

[0115]

[0116] According to the definition of , we have

[0117]

[0118] Then, we get

[0119]

[0120] Obviously, every variable in the system is semi-globally uniformly bounded. The leader remains bounded. is bounded. Because where is a constant, this ensures the boundedness of . In addition, is continuous, which means the boundedness of . Therefore, it can be known that all signals of the multi-single pendulum system are uniformly ultimately bounded, and the final tracking error can converge to an arbitrarily small neighborhood of zero, and the stability of the system is proved.

[0121] To prove the feasibility, effectiveness and correctness of the present example, the following simulation experiment is carried out in the example:

[0122] In this simulation experiment, for the multi-single pendulum system with limited communication range, a self-adaptive fuzzy logic system cooperative controller based on switching dynamic event trigger mechanism is designed to realize that the running state of each single pendulum can be consistent with the leader single pendulum, that is, each variable of the multi-single pendulum tends to be consistent. In addition, while achieving consistency, not only the identification accuracy of unknown nonlinearities in the system is improved, but also the update frequency of the single pendulum system controller and mechanical wear are greatly reduced.

[0123] First, the actual physical parameters are selected as = 1 / 3 kg, = 2 / 3 m, = 9.8 , and =0.2. The reference signal of the system is: . The initial value of the system state is: , ; the virtual controller gain is: , ; the connectivity maintenance performance function parameter , , , , ; the switching dynamic event triggering mechanism parameter is: , , , , , , , , , , ; the privacy protection mechanism parameter is: , ; the fuzzy logic system parameter is: , , , , , ; the second-order sliding mode integral filter parameter is .

[0124] The communication topology graph of the multi-single pendulum is shown in Figure 3 , and the adjacency matrix of the system is:

[0125]

[0126] The effectiveness of the simulation of the present example is further illustrated in combination with the accompanying drawings:

[0127] In Figure 6 (a) and (b), the initial leader-follower distance and the distance between followers are kept within the convergence boundary. As the system runs, the boundary gradually converges to 0.21. In order to demonstrate the versatility of the proposed method, the initial value is reset to . The corresponding Figure 6 (c) and (d) in Figure 6 . By comparing Figure 6 (a), (b) and Figure 7 (c), (d), it can be seen that the convergence boundary of the connection maintenance method proposed in the present embodiment can be dynamically adjusted according to the initial agent distance, which improves the adaptability of the system;The interval time of four followers is shown, and it is obvious that the modified switching dynamic event-triggered mechanism can effectively reduce the triggering times of multi-single pendulum; Figure 8 The curve of the input signal is shown, which proves the practicability of the proposed control scheme.

[0128] The present example is directed to a nonlinear multi-single pendulum system with limited communication range and limited communication bandwidth, and studies the problem of distributed adaptive tracking control. In order to avoid the "complexity explosion" problem of the virtual controller, a second-order sliding mode integral filter is used. In addition, unlike existing connectivity maintainers, by constructing a new synchronization error nonlinear transformation method, the singularity problem of the initial time tracking error is avoided, and it can also dynamically adjust the boundary function according to the initial distance of the agent. An improved switching dynamic event-triggered mechanism is proposed to reduce the update times of the controller and the wear and tear of the controller. At the same time, a privacy protection mechanism with adjustable protection time is also applied to improve the security of the system. Finally, the applicability of the proposed multi-single pendulum cooperative control method is verified through simulation.

[0129] Embodiment two

[0130] The purpose of the present embodiment is to provide a multi-single pendulum system cooperative control system, comprising:

[0131] 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 pendulum, and use a fuzzy logic system to approximate unknown nonlinear terms in the dynamic model;

[0132] The synchronization error processing module is configured to: consider the communication topology relationship of the multi-single pendulum, construct a consistent tracking error containing a dynamic boundary function, and construct a virtual controller and corresponding parameter adaptive rate based on the backstepping method and fuzzy approximation term;

[0133] The control module is configured to: based on the estimated value of the virtual controller, to compensate for the nonlinear terms in the estimated output of the virtual controller, suppress the consistent tracking error, and construct an actual controller for the goal of synchronizing the state of the follower single pendulum with the leader single pendulum, and realize cooperative control of the multi-single pendulum system based on the actual controller; wherein the actual controller adopts a switching dynamic event-triggered mechanism.

[0134] In more embodiments, there is also provided:

[0135] An electronic device comprising 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 described in embodiment one is completed. For brevity, it will not be repeated here.

[0136] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), and the processor can also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), ready programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor or the like.

[0137] The memory can include read-only memory and random access memory, and provide instructions and data to the processor, and a portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0138] A computer readable storage medium for storing computer instructions, the computer instructions being executed by a processor to complete the method described in embodiment one.

[0139] The method in embodiment one can be directly embodied as a hardware processor to complete, or be completed by a combination of hardware and software modules in the processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, and other mature storage media in the art. The storage medium is located in the memory, and the processor reads the information in the memory to complete the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0140] A computer program product, comprising a computer program, the computer program being executed by a processor to implement the method described in embodiment one.

[0141] The present application 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 are executed in devices on real or virtual processors of the target to perform processes / methods as described above. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform particular tasks or implement particular abstract data types. In various embodiments, the functions of the program modules can be combined or divided as desired. Machine executable instructions for program modules can be executed within a local or distributed device. In a distributed device, program modules can be located in local and remote storage media.

[0142] Computer program code for carrying out operations of the present application can be written in any combination of one or more programming languages. The computer program code can execute entirely on a computer, a special purpose computer, or other programmable apparatus to produce the functions / acts specified in the flow diagrams and / or block diagrams. The program code can execute entirely on a computer, a special purpose computer, or other programmable apparatus, as a stand-alone software package, partly on the computer and partly on a remote computer, or entirely on the remote computer or server.

[0143] In the context of the present application, the computer program code or related data can be carried by any suitable carrier to enable the 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 can include electrical, optical, radio, sound or other forms of propagated signals, such as carrier waves, infrared signals, and the like.

[0144] Those skilled in the art can realize that the units and algorithm steps of the examples described in conjunction with the present embodiments can be realized in electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized 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 realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0145] The above describes the specific embodiments of the present application in conjunction with the accompanying drawings, but is not a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without inventive labor are still within the scope of protection of the present application.

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; when differentiating the virtual control law in the virtual controller, a second-order sliding integral filter is used to estimate the virtual control rate; Based on the estimation value of the virtual controller, an actual controller is constructed with the goal of compensating for the nonlinear term in the estimated output of the virtual controller, suppressing the consistency tracking error, and synchronizing the state of the following single torsion pendulum with that of the leader single torsion pendulum. The actual controller is used to realize the coordinated control of the multiple single torsion pendulum system. The actual controller adopts a switching dynamic event triggering mechanism. 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; 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.

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. A multi-single torsion pendulum system collaborative control system, characterized in that, The method for coordinated control of a multi-single torsion gyroscope system according to any one of claims 1-4 includes: 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.

6. 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 1-4.

7. 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 1-4.

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