Hybrid-order multi-agent control method, device and equipment and readable storage medium

Abstract

A hybrid-order multi-agent control method, apparatus, device, and readable storage medium are disclosed. The hybrid-order multi-agent control method includes: for each iteration of each follower agent, calculating the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents; calculating the sliding mode error based on the following consistency error and the neighbor consistency error; calculating the control input using the controller's control law based on the sliding mode error, the Nussbaum gain function, and a composite control term; controlling the follower agent based on the control input to enable it to follow the leader agent in performing the same task; and updating the parameters of the controller's control law based on the sliding mode error. Through this application, after multiple iterative learning and optimizations, even in the face of component failures and unknown interference, the follower agent can effectively follow the leader agent.

Description

Technical Field

[0001] This application relates to the field of intelligent agent control technology, and in particular to a hybrid multi-agent control method, apparatus, device, and readable storage medium. Background Technology

[0002] Hybrid-order multi-agent cooperative control has significant application value in fields such as collaborative reconnaissance and marine surveys of heterogeneous unmanned systems including UAVs, unmanned surface vessels, unmanned underwater vehicles, and unmanned vehicles. Among these applications, the research and optimization of consistency control technology is crucial for improving the performance of complex distributed systems.

[0003] However, when faced with repetitive tasks such as reciprocating patrols and reconnaissance or fixed-route collaborative detection, existing hybrid multi-agent control systems struggle to enable follower agents to quickly converge and accurately follow the leader agent within a limited timeframe. Summary of the Invention

[0004] This application provides a hybrid-level multi-agent control method, apparatus, device, and readable storage medium, aiming to solve the technical problem that in existing hybrid-level multi-agent control systems, when facing repetitive tasks with limited time, such as reciprocating patrol and reconnaissance or fixed-route cooperative detection, follower agents struggle to achieve rapid convergence and accurate following of the leader agent within a limited time.

[0005] In a first aspect, embodiments of this application provide a hybrid-order multi-agent control method. The hybrid-order multi-agent system includes a leader and multiple followers. The leader is a second-order agent, and the followers include first-order agents and second-order agents. Each follower agent repeatedly performs the same task with the leader agent within a finite time period. Each execution of the same task constitutes one iteration. The hybrid-order multi-agent control method includes: For each iteration of each follower agent, calculate the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents. Based on the following consistency error and the neighbor consistency error, calculate the sliding mode error. Based on sliding mode error, Nussbaum gain function, and composite control terms, the controller's control law is used to calculate the control input. Based on the control input, the follower agent is controlled to follow the leader agent in performing the same task. The composite control terms include a feedback control term based on sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term. The parameters of the controller's control law are updated based on the sliding mode error.

[0006] Optionally, before calculating the follower consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, the following steps are included: The dynamic model of the second-order leader agent is established as follows: ; The dynamic model of the second-order follower agent is established as follows: ; The dynamic model of the first-order follower agent is established as follows: ; in, Let be the state vector of the leader agent. and These represent the position and velocity of the leader agent, respectively. Let k be an unknown nonlinear smooth function of the leader agent, where k represents the k-th iteration. Indicates a given repetition time. Let represent the position and state vector of the z-th follower agent in the k-th iteration. It is an unknown nonlinear smooth function of the follower agent. For time-varying gain, all Same symbols Actuator failure, actuator failure The expression is: ; in, Gain fault, For bounded bias faults, Provide the actual input control signal to the actuator; Unknown nonlinear smooth function of the follower agent The expression approximated using a fuzzy logic system is: ; in, For the fuzzy weight coefficient vector, and For compactness, To approximate the error, For fuzzy basis function vectors, The expression is: ; in, For fuzzy sets Fuzzy membership function.

[0007] Optionally, calculating the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, includes: The following consistency error between the follower agent and the leader agent is calculated using Formula 1, which is: ; The neighbor consistency error between the follower agent and other follower agents is calculated using Formula 2, which is: ; in, It is a set of second-order follower agents. For the set of all follower agents, These are elements of the communication topology adjacency matrix, representing the communication connection relationships between follower agents z and j. The adjacency matrix elements of the follower agent and the leader agent indicate whether the follower agent z can receive information from the leader.

[0008] Optionally, the calculation of sliding mode error based on follower consensus error and neighbor consensus error includes: Convert the neighbor consistency error to: ; in, , , , and Let these represent the transformation matrices of the second-order system and the first-order system, respectively. and The expression is: ; in, and The Laplace matrix corresponding to the network topology. and This represents the adjacency matrix between the states of the follower and leader agents. Formula 3 is used to analyze the following consistency error. Neighbor consistency error Perform zero-padding dimension expansion to obtain the expanded follower consistency error and neighbor consistency error, as shown in Formula 3: ; in, , , This is the corresponding block diagonal expansion matrix; The sliding mode error is calculated using the extended follower consistency error and neighbor consistency error, through Formula 4, which is: ; in, It is a constant.

[0009] Optionally, the control law of the controller is:

[0010] ; in, This is the control input for the z-th agent in the k-th iteration. The Nussbaum gain function, For the online learning variables of the Nussbaum gain function, For composite control items, For feedback control terms based on sliding mode error, For approximating unknown nonlinear unmodeled dynamics, (This refers to a fuzzy control term used to approximate the fuzzy control term.) For robust control terms used to compensate for controller execution failures and upper bounds of uncertainty, , , and The expression is: ; in, It is a constant. satisfy and , For online learning of gain control, and These are parameters for online learning.

[0011] Optionally, the parameters for updating the controller control law based on sliding mode error include: Based on sliding mode error, the weights of the fuzzy logic system are adjusted using Formula 5. Upper bound of uncertainty and feedback gain The updated formula five is as follows: ; in, Indicates to Weight estimation for fuzzy logic systems This represents an estimate of the upper bound of uncertainty. , For learning rate, For correction factor, To meet The convergent sequence.

[0012] Secondly, embodiments of this application provide a hybrid-level multi-agent control device, wherein the hybrid-level multi-agent includes a leader and multiple followers, the leader being a second-order agent, and the followers including first-order agents and second-order agents. Each follower agent repeatedly performs the same task with the leader agent within a finite time, and one execution of the same task constitutes one iteration. The hybrid-level multi-agent control device includes: The error calculation module is used to calculate the following consistency error between the follower agent and the leader agent and the neighbor consistency error between the follower agent and other follower agents for each iteration of each follower agent. Based on the following consistency error and the neighbor consistency error, the sliding mode error is calculated. The control calculation module is used to calculate the control input based on the sliding mode error, the Nussbaum gain function, and the composite control term using the controller's control law. Based on the control input, the module controls the follower agent to perform the same task as the leader agent. The composite control term includes a feedback control term based on the sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term. The parameter update module is used to update the parameters of the controller's control law based on the sliding mode error.

[0013] Optionally, the hybrid-level multi-agent control device further includes a model building module, used for: The dynamic model of the second-order leader agent is established as follows: ; The dynamic model of the second-order follower agent is established as follows: ; The dynamic model of the first-order follower agent is established as follows: ; in, Let be the state vector of the leader agent. and These represent the position and velocity of the leader agent, respectively. Let k be an unknown nonlinear smooth function of the leader agent, where k represents the k-th iteration. Indicates a given repetition time. Let represent the position and state vector of the z-th follower agent in the k-th iteration. It is an unknown nonlinear smooth function of the follower agent. For time-varying gain, all Same symbols Actuator failure, actuator failure The expression is: ; in, Gain fault, For bounded bias faults, Provide the actual input control signal to the actuator; Unknown nonlinear smooth function of the follower agent The expression approximated using a fuzzy logic system is: ; in, For the fuzzy weight coefficient vector, and For compactness, To approximate the error, For fuzzy basis function vectors, The expression is: ; in, For fuzzy sets Fuzzy membership function.

[0014] Thirdly, embodiments of this application provide a hybrid-level multi-agent control device, which includes a processor, a memory, and a hybrid-level multi-agent control program stored in the memory and executable by the processor. When the hybrid-level multi-agent control program is executed by the processor, it implements the steps of the hybrid-level multi-agent control method as described above.

[0015] Fourthly, embodiments of this application provide a readable storage medium storing a hybrid-level multi-agent control program, wherein when the hybrid-level multi-agent control program is executed by a processor, it implements the steps of the hybrid-level multi-agent control method as described above.

[0016] The beneficial effects of the technical solutions provided in this application include: In this embodiment, for each iteration of each follower agent, the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents are calculated. Based on the following consistency error and the neighbor consistency error, the sliding mode error is calculated. Based on the sliding mode error, the Nussbaum gain function, and the composite control term, the controller's control law is used to calculate the control input. Based on the control input, the follower agent is controlled to follow the leader agent in performing the same task. The composite control term includes a feedback control term based on the sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term. Based on the sliding mode error, the parameters of the controller's control law are updated. In the embodiments of this application, for each iteration of each follower agent, firstly, the sliding mode error is calculated based on the follower consistency error and the neighbor consistency error. The control law of each follower agent controller combines fuzzy logic system, Nussbaum gain technology and adaptive learning mechanism, comprehensively considering the feedback control term based on sliding mode error, the nonlinear approximation control term based on fuzzy logic system and the robust control term. Among them, the nonlinear approximation control term based on fuzzy logic system is used to solve the problem of unknown nonlinearity not being modeled in the dynamic model of leader and follower agents. The robust control term is used to solve the controller execution failure (including gain failure and deviation failure) that may occur in the follower agent. The combination of the three successfully solves the key challenges of dynamic coordination of mixed-order system, unknown nonlinear approximation and controller execution failure compensation, which can improve the accuracy of the follower agent control input. At the same time, the parameters of the controller control law are updated in each iteration. After repeated iterative learning and optimization, even in the face of component failure and unknown interference, the follower agent can quickly converge and achieve accurate following of the leader agent. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating an embodiment of the hybrid multi-agent control method of this application; Figure 2 This is a schematic diagram of the communication topology of an embodiment of the hybrid multi-agent control method of this application; Figure 3 This is a schematic diagram of the controller design architecture of an embodiment of the hybrid multi-agent control method of this application; Figure 4 This is a schematic diagram of the fifth iteration result of an embodiment of the hybrid multi-agent control method of this application; Figure 5This is a schematic diagram of the 20th iteration result of an embodiment of the hybrid multi-agent control method of this application; Figure 6 This is a schematic diagram of the 45th iteration result of an embodiment of the hybrid multi-agent control method of this application; Figure 7 This is a schematic diagram of the simulation results of the traditional fault-intolerant iterative learning control method for following errors. Figure 8 This is a functional module diagram of an embodiment of the hybrid multi-agent control device of this application; Figure 9 This is a schematic diagram of the hardware structure of the hybrid multi-agent control device involved in the embodiments of this application. Detailed Implementation

[0018] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0020] In a first aspect, embodiments of this application provide a hybrid multi-agent control method.

[0021] In one embodiment, the hybrid multi-agent system includes a leader and multiple followers. The leader is a second-order agent, and the followers include first-order and second-order agents. Each follower agent repeatedly performs the same task with the leader agent within a finite time period. One execution of the same task constitutes one iteration. Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the hybrid multi-agent control method of this application, as shown below. Figure 1 As shown, the hybrid multi-agent control method includes: Step S10: For each iteration of each follower agent, calculate the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents. Based on the following consistency error and the neighbor consistency error, calculate the sliding mode error.

[0022] In this embodiment, refer to Figure 2 , Figure 2 This is a schematic diagram of the communication topology of an embodiment of the hybrid multi-agent control method of this application, as shown below. Figure 2 As shown, the hybrid multi-agent control system consists of one leader (agent 0) and four followers (agents 1-4). Agents 1 and 2 are surface ships (second-order dynamics models), while agents 3 and 4 are unmanned aerial vehicles (UAVs) (first-order dynamics models), forming a hybrid multi-agent control system. Follower agents 1-4 repeatedly perform the same task with the leader agent 0 within a finite time. For the hybrid multi-agent control system, accurately calculating the consensus error is fundamental to its distributed cooperative control. The follower consensus error reflects the deviation of the follower agent from the macroscopic target (leader), while the neighbor consensus error reflects the degree of coordination between the follower agent and its microscopic local environment (other follower agents). Based on the follower and neighbor consensus errors, a sliding mode error is constructed. Utilizing the insensitivity of sliding mode control to parameter perturbations and external disturbances, the multi-agent cooperative problem is transformed into a sliding surface arrival problem. The introduction of sliding mode error enhances the system's robustness to unknown disturbances, laying a stable error foundation for subsequent fault-tolerant control.

[0023] Step S20: Based on sliding mode error, Nussbaum gain function, and composite control term, calculate control input using the controller's control law. Control the follower agent based on the control input so that it can follow the leader agent to perform the same task. The composite control term includes a feedback control term based on sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term.

[0024] In this embodiment, refer to Figure 3 , Figure 3This is a schematic diagram of the controller design architecture of an embodiment of the hybrid-order multi-agent control method of this application. The control law design of the follower agent controller is the core component. The feedback control term is used to ensure the basic stability of the system and drive the sliding mode error to approach zero. The fuzzy control term utilizes the universal approximation characteristics of fuzzy logic systems to learn online and cancel out unknown nonlinear dynamic components in the system (such as complex environmental factors such as aerodynamic drag and water resistance). The robust control term is used to handle the residual error after fuzzy approximation and external bounded disturbances. In particular, to address the problem of unknown control direction caused by possible gain faults (such as efficiency reduction) in the actuator, a Nussbaum gain function is introduced. The Nussbaum gain function has the characteristic of oscillating between positive and negative infinity, which can adaptively search for the correct control direction without prior knowledge of the specific sign or magnitude of the fault. This achieves a combination of "active fault tolerance" and "passive robustness". The fuzzy system solves the problem of "unknown model", the Nussbaum gain function solves the problem of "unknown control direction", and the composite control term ensures that even in extreme cases where the actuator fails severely and the system model is not fully known, the follower agent can still generate effective control input, which significantly improves the reliability of task execution of the hybrid multi-agent control system.

[0025] Step S30: Update the parameters of the controller's control law based on the sliding mode error.

[0026] In this embodiment, we continue to refer to... Figure 3 The parameter update of the controller's control law, namely the adaptive update law of the controller's parameters, is the key difference between Iterative Learning Control (ILC) and traditional adaptive control. In traditional control, parameters typically converge within a single run time. However, this step utilizes the characteristic that the system repeatedly executes the same task within a finite time interval. The sliding mode error information generated in the k-th iteration is stored and used to correct the controller parameters in the (k+1)-th iteration (such as the weights of the fuzzy logic system used to calculate the fuzzy control term, the upper bound of uncertainty in the robust control term, and the feedback gain of the feedback control term). By designing a specific adaptive update law, the parameters of the controller's control law continuously approach the optimal value as the number of iterations increases, thus giving the system the ability to "get better and better." As the number of iterations increases, the controller's compensation accuracy for unknown dynamics and faults becomes increasingly higher, and the following error monotonically decreases with the number of iterations and eventually converges to zero. This not only improves the execution accuracy of a single task but also achieves continuous performance optimization in long-term repetitive tasks, making it particularly suitable for scenarios such as formation patrol and repetitive operations.

[0027] In this embodiment, in a hybrid-order multi-agent control system, for each iteration of each follower agent, a sliding mode error is first constructed based on the following consistency error and the neighbor consistency error. Utilizing the insensitivity of sliding mode control to parameter perturbations and external disturbances, the multi-agent cooperation problem is transformed into a sliding surface arrival problem. The introduction of the sliding mode error enhances the system's robustness to unknown disturbances, laying a stable error foundation for subsequent fault-tolerant control. The control law design of the follower agent controller is the core component. The feedback control term ensures the system's basic stability, driving the sliding mode error towards zero; the fuzzy control term utilizes the universal approximation characteristic of fuzzy logic systems to learn online and cancel out unknown nonlinear dynamics in the system; and the robust control term handles the residual error after fuzzy approximation and external bounded disturbances. To address the problem of unknown control direction caused by potential actuator gain faults, a Nussbaum gain function is introduced. The Nussbaum gain function oscillates between positive and negative infinity, adaptively searching for the correct control direction without prior knowledge of the fault's specific sign or magnitude. This achieves a combination of "active fault tolerance" and "passive robustness." The fuzzy system addresses the "unknown model" problem, the Nussbaum gain function solves the "unknown control direction" problem, and the composite control term ensures that even in extreme cases where the actuator experiences severe failure and the system model is not fully known, the follower agent can still generate effective control inputs, significantly improving the reliability of the hybrid-order multi-agent control system's task execution. Utilizing the system's characteristic of repeatedly executing the same task within a finite time interval, the sliding mode error information generated in the k-th iteration is stored and used to correct the controller parameters in the (k+1)-th iteration. By designing a specific adaptive update law, the controller's control law parameters continuously approach their optimal values ​​with increasing iteration count, thus endowing the system with the ability to "learn and improve." As the number of iterations increases, the controller's compensation accuracy for unknown dynamics and faults becomes increasingly higher, and the following error monotonically decreases with the number of iterations and eventually converges to zero. This not only improves the execution accuracy of a single task but also achieves continuous performance optimization in long-term repetitive tasks, making it particularly suitable for scenarios such as formation patrols and repetitive operations.

[0028] Further, in one embodiment, before calculating the follower consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, the following steps are included: The dynamic model of the second-order leader agent is established as follows: ; The dynamic model of the second-order follower agent is established as follows: ; The dynamic model of the first-order follower agent is established as follows: ; in, Let be the state vector of the leader agent. and These represent the position and velocity of the leader agent, respectively. Let k be an unknown nonlinear smooth function of the leader agent, where k represents the k-th iteration. Indicates a given repetition time. Let represent the position and state vector of the z-th follower agent in the k-th iteration. It is an unknown nonlinear smooth function of the follower agent. For time-varying gain, all Same symbols Actuator failure, actuator failure The expression is: ; in, Gain fault, For bounded bias faults, Provide the actual input control signal to the actuator; Unknown nonlinear smooth function of the follower agent The expression approximated using a fuzzy logic system is: ; in, For the fuzzy weight coefficient vector, and For compactness, To approximate the error, For fuzzy basis function vectors, The expression is: ; in, For fuzzy sets Fuzzy membership function.

[0029] In this embodiment, establishing an accurate mathematical model is a prerequisite for controller design. By distinguishing between first-order and second-order dynamic equations, the physical characteristics of the hybrid system are realistically reflected. The actuator fault model includes both gain faults and bounded bias faults, covering various practical fault modes such as actuator jamming, failure, and deviation. Using fuzzy logic to approximate unknown nonlinear functions avoids the difficulty of establishing an accurate physical model and reduces modeling costs. The established second-order leader agent dynamic model, second-order follower agent dynamic model, and first-order follower agent dynamic model all possess high versatility and realism. The comprehensiveness of the fault model ensures the applicability of the control method in practical engineering, while the fuzzy approximation technique reduces the dependence on an accurate mathematical model of the system, enabling the method to be applied to complex nonlinear systems that are difficult to model precisely.

[0030] Further, in one embodiment, calculating the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, includes: The following consistency error between the follower agent and the leader agent is calculated using Formula 1, which is: ; The neighbor consistency error between the follower agent and other follower agents is calculated using Formula 2, which is: ; in, It is a set of second-order follower agents. For the set of all follower agents, These are elements of the communication topology adjacency matrix, representing the communication connection relationships between follower agents z and j. The adjacency matrix elements of the follower agent and the leader agent indicate whether the follower agent z can receive information from the leader.

[0031] In this embodiment, based on graph theory, follower consistency error and neighbor consistency error are defined. Follower consistency error ensures that individuals do not deviate from the global goal, while neighbor consistency error ensures close cooperation within the group, reflecting the characteristics of distributed control. Furthermore, continuing to refer to... Figure 2 This approach defines an associative communication topology within the error context, where each agent utilizes only local neighbor information rather than global information. This design effectively reduces communication burden and computational complexity, enhancing system scalability. As the number of agents increases, there is no need to redesign the global controller; only local communication connections need to be maintained, meeting the practical application requirements of large-scale multi-agent systems.

[0032] Furthermore, in one embodiment, calculating the sliding mode error based on the follower consistency error and the neighbor consistency error includes: Convert the neighbor consistency error to: ; in, , , , and Let these represent the transformation matrices of the second-order system and the first-order system, respectively. and The expression is: ; in, and The Laplace matrix corresponding to the network topology. and This represents the adjacency matrix between the states of the follower and leader agents. Formula 3 is used to analyze the following consistency error. Neighbor consistency error Perform zero-padding dimension expansion to obtain the expanded follower consistency error and neighbor consistency error, as shown in Formula 3: ; in, , , This is the corresponding block diagonal expansion matrix; The sliding mode error is calculated using the extended follower consistency error and neighbor consistency error, through Formula 4, which is: ; in, It is a constant.

[0033] In this embodiment, since the system contains both first-order (e.g., only position information) and second-order (e.g., position + velocity information) agents, directly calculating the error would lead to a dimensionality mismatch, making unified control impossible. Therefore, this step introduces a zero-filling matrix to expand the dimension of the first-order agent's error, making it mathematically equivalent to a second-order system, thus solving the problem of dimensional inconsistency caused by mixed orders. This dimensionality expansion technique breaks the limitation of traditional methods that can only handle systems of the same order, enabling heterogeneous devices such as UAVs (usually first- or second-order) and surface ships (usually second-order) to collaborate within a unified framework.

[0034] According to Formula 4, we can obtain... The global vector composed of the sliding mode errors of all followers is According to the differentiation rule, we get Combining dynamic relationships and ,get The expression is ,according to ,in It is a vector-valued nonlinear function. Time-varying gain matrix. , It is a structured matrix vector of external perturbations. Depend on and Calculation generated, retaining the previous result Dimensionality reduction is achieved by reducing the number of components. and Substitution The expression yields .

[0035] Furthermore, in one embodiment, the control law of the controller is:

[0036] ; in, This is the control input for the z-th agent in the k-th iteration. The Nussbaum gain function, For the online learning variables of the Nussbaum gain function, For composite control items, For feedback control terms based on sliding mode error, For approximating unknown nonlinear unmodeled dynamics, (This refers to a fuzzy control term used to approximate the fuzzy control term.) For robust control terms used to compensate for controller execution failures and upper bounds of uncertainty, , , and The expression is: ; in, It is a constant. satisfy and , For online learning of gain control, and These are parameters for online learning.

[0037] In this embodiment, the control law adopts a hierarchical structure. The Nussbaum gain function serves as the pre-gain, dynamically adjusting the amplitude and direction of the control signal. The composite control term consists of three parts: feedback, fuzzy term, and robust term. The feedback term provides basic damping, the fuzzy term cancels out the unknown nonlinearity of the known structure, and the robust term suppresses residual uncertainty. This composite structure achieves a progressive improvement in control accuracy. The feedback term ensures stability, the fuzzy term improves nominal performance, and the robust term provides a safety net. The introduction of the Nussbaum gain function allows the controller to find the correct control direction through iterative learning even when it is completely unaware of the actuator fault sign (i.e., it does not know whether the control action is positive or negative), greatly enhancing the system's fault tolerance.

[0038] Further, in one embodiment, step S30 includes: Based on sliding mode error, the weights of the fuzzy logic system are adjusted using Formula 5. Upper bound of uncertainty and feedback gain The updated formula five is as follows: ; in, Indicates to Weight estimation for fuzzy logic systems This represents an estimate of the upper bound of uncertainty. , For learning rate, For correction factor, To meet The convergent sequence.

[0039] In this embodiment, the adaptive update law employs the gradient descent concept, utilizing sliding mode error as the driving signal. When the error is large, the parameter update speed is fast, quickly compensating for faults and uncertainties; when the error is small, the update speed slows down to prevent parameter drift. The introduction of the convergence sequence ensures the boundedness of the parameters in the iteration domain, guaranteeing the iterative stability of the closed-loop system. Lyapunov stability analysis proves that under this update law, all signals are uniformly bounded in the iteration domain, and the following error converges uniformly to zero as the number of iterations approaches infinity. This means that the system is not only stable but also possesses asymptotically perfect following performance, meeting the requirements of high-precision cooperative control.

[0040] The constructed Lyapunov function includes sliding mode error, extended neighbor consensus error, and all parameter estimation errors, and can comprehensively reflect the dynamic characteristics and parameter estimation characteristics of the system. Its specific construction form is as follows:

[0041] Each variable is defined as follows:

[0042] The parameter matrix is: calculate The time derivative is obtained as follows: ; Applying Young's inequality, we get:

[0043] The normal form is defined as follows: ; Therefore, we can conclude that: ; Substituting the control rate into the above formula, we get: ; use We can obtain: ; The time derivative is:

[0044] in, ; Parameter matrix and The following constraints must be met:

[0045] Parameter adaptive term and The derivative is: ; By integrating and combining all components over the iterations, we can obtain... The parameter selection is as follows: ; in, The terms are positive constants. The first two terms on the right are negative definite terms, and the last three terms are the remainder terms that converge to zero with the number of iterations.

[0046] By analyzing the iterative difference using Barbara's theorem, it can be proven that: ; That is, as the number of iterations approaches infinity, the integrals of the sliding mode error and the extended neighbor consistency error converge to zero. Furthermore, through the matrix transformation relationship between the errors, it can be seen that the following consistency error converges to zero. ; This achieves complete and consistent following of the leader agent by all first- and second-order follower agents, proving the effectiveness of the control law designed in this invention.

[0047] Reference Figure 4 , Figure 4 This is a schematic diagram of the fifth iteration result of an embodiment of the hybrid multi-agent control method of this application, as shown below. Figure 4 As shown, the follower agent exhibits significant following error due to unknown nonlinearities, actuator malfunctions, and inconsistencies in mixed-order dimensions. (Refer to...) Figure 5 , Figure 5 This is a schematic diagram of the 20th iteration result of an embodiment of the hybrid multi-agent control method of this application, as shown below. Figure 5 As shown, the following error is significantly reduced, the fuzzy logic system effectively approximates the unknown nonlinearity, and the adaptive update law completes preliminary fault compensation. Figure 6 , Figure 6 This is a schematic diagram of the 45th iteration result of an embodiment of the hybrid multi-agent control method of this application, as shown below. Figure 6 As shown, the states of all follower agents completely overlap with the state of the leader agent, and the following error converges to zero, achieving precise and consistent following. (Refer to...) Figure 7 , Figure 7 This is a schematic diagram of the simulation results of the traditional fault-intolerant iterative learning control method following the error, such as... Figure 7 As shown, it can be seen that the error of the traditional iterative learning control method gradually diverges as the number of iterations increases. This is because the traditional controller lacks sufficient compensation mechanism, and the performance gap is particularly obvious under actuator failure conditions.

[0048] Secondly, embodiments of this application also provide a hybrid multi-agent control device.

[0049] In one embodiment, the hybrid multi-agent system includes a leader and multiple followers. The leader is a second-order agent, and the followers include first-order and second-order agents. Each follower agent repeatedly performs the same task with the leader agent within a finite time period. One execution of the same task constitutes one iteration. Figure 8 , Figure 8 This is a functional block diagram of an embodiment of the hybrid multi-agent control device of this application, as shown below. Figure 8 As shown, the hybrid multi-agent control device includes: Error calculation module 10 is used to calculate the following consistency error between the follower agent and the leader agent and the neighbor consistency error between the follower agent and other follower agents for each iteration of each follower agent, and calculate the sliding mode error based on the following consistency error and the neighbor consistency error. The control calculation module 20 is used to calculate the control input based on the sliding mode error, the Nussbaum gain function, and the composite control term using the controller's control law. Based on the control input, the module controls the follower agent to perform the same task as the leader agent. The composite control term includes a feedback control term based on the sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term. The parameter update module 30 is used to update the parameters of the controller's control law based on the sliding mode error.

[0050] Furthermore, in one embodiment, the hybrid-level multi-agent control device further includes a model building module, used for: The dynamic model of the second-order leader agent is established as follows: ; The dynamic model of the second-order follower agent is established as follows: ; The dynamic model of the first-order follower agent is established as follows: ; in, Let be the state vector of the leader agent. and These represent the position and velocity of the leader agent, respectively. Let k be an unknown nonlinear smooth function of the leader agent, where k represents the k-th iteration. Indicates a given repetition time. Let represent the position and state vector of the z-th follower agent in the k-th iteration. It is an unknown nonlinear smooth function of the follower agent. For time-varying gain, all Same symbols Actuator failure, actuator failure The expression is: ; in, Gain fault, For bounded bias faults, Provide the actual input control signal to the actuator; Unknown nonlinear smooth function of the follower agent The expression approximated using a fuzzy logic system is: ; in, For the fuzzy weight coefficient vector, and For compactness, To approximate the error, For fuzzy basis function vectors, The expression is: ; in, For fuzzy sets Fuzzy membership function.

[0051] Further, in one embodiment, the calculation of the follower consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, is used for: The following consistency error between the follower agent and the leader agent is calculated using Formula 1, which is: ; The neighbor consistency error between the follower agent and other follower agents is calculated using Formula 2, which is: ; in, It is a set of second-order follower agents. For the set of all follower agents, These are elements of the communication topology adjacency matrix, representing the communication connection relationships between follower agents z and j. The adjacency matrix elements of the follower agent and the leader agent indicate whether the follower agent z can receive information from the leader.

[0052] Furthermore, in one embodiment, the calculation of sliding mode error based on follower consistency error and neighbor consistency error is used for: Convert the neighbor consistency error to: ; in, , , , and Let these represent the transformation matrices of the second-order system and the first-order system, respectively. and The expression is: ; in, and The Laplace matrix corresponding to the network topology. and This represents the adjacency matrix between the states of the follower and leader agents. Formula 3 is used to analyze the following consistency error. Neighbor consistency error Perform zero-padding dimension expansion to obtain the expanded follower consistency error and neighbor consistency error, as shown in Formula 3: ; in, , , This is the corresponding block diagonal expansion matrix; The sliding mode error is calculated using the extended follower consistency error and neighbor consistency error, through Formula 4, which is: ; in, It is a constant.

[0053] Furthermore, in one embodiment, the control law of the controller is:

[0054] ; in, This is the control input for the z-th agent in the k-th iteration. The Nussbaum gain function, For the online learning variables of the Nussbaum gain function, For composite control items, For feedback control terms based on sliding mode error, For approximating unknown nonlinear unmodeled dynamics, (This refers to a fuzzy control term used to approximate the fuzzy control term.) For robust control terms used to compensate for controller execution failures and upper bounds of uncertainty, , , and The expression is: ; in, It is a constant. satisfy and , For online learning of gain control, and These are parameters for online learning.

[0055] Furthermore, in one embodiment, the parameter update module 30 is used for: Based on sliding mode error, the weights of the fuzzy logic system are adjusted using Formula 5. Upper bound of uncertainty and feedback gain The updated formula five is as follows: ; in, Indicates to Weight estimation for fuzzy logic systems This represents an estimate of the upper bound of uncertainty. , For learning rate, For correction factor, To meet The convergent sequence.

[0056] The functions of each module in the above-mentioned hybrid multi-agent control device correspond to the steps in the above-mentioned hybrid multi-agent control method embodiment, and their functions and implementation processes will not be described in detail here.

[0057] Thirdly, embodiments of this application provide a hybrid multi-agent control device.

[0058] Reference Figure 9 , Figure 9 This is a schematic diagram of the hardware structure of a hybrid-level multi-agent control device involved in an embodiment of this application. In this embodiment, the hybrid-level multi-agent control device may include a processor, a memory, a communication interface, and a communication bus.

[0059] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.

[0060] Communication interfaces include input / output (I / O) interfaces, physical interfaces, and logical interfaces used for interconnecting devices within the hybrid multi-agent control device, as well as interfaces used for interconnecting the hybrid multi-agent control device with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.

[0061] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0062] The processor can be a general-purpose processor, which can call the hybrid-level multi-agent control program stored in memory and execute the hybrid-level multi-agent control method provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the hybrid-level multi-agent control program is called can be referred to in the various embodiments of the hybrid-level multi-agent control method of this application, and will not be repeated here.

[0063] Those skilled in the art will understand that Figure 9 The hardware structure shown does not constitute a limitation of this application and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0064] Fourthly, embodiments of this application also provide a readable storage medium.

[0065] The present application has a readable storage medium storing a hybrid multi-agent control program, wherein when the hybrid multi-agent control program is executed by a processor, it implements the steps of the hybrid multi-agent control method as described above.

[0066] The method implemented when the hybrid multi-agent control program is executed can be referred to in various embodiments of the hybrid multi-agent control method of this application, and will not be repeated here.

[0067] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0068] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0069] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0070] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0071] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0072] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0073] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A hybrid-order multi-agent control method, characterized in that, The hybrid-order multi-agent system includes a leader and multiple followers. The leader is a second-order agent, and the followers include first-order and second-order agents. Each follower agent repeatedly performs the same task with the leader agent within a finite time. Each execution of the same task constitutes one iteration. The hybrid-order multi-agent control method includes: For each iteration of each follower agent, calculate the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents. Based on the following consistency error and the neighbor consistency error, calculate the sliding mode error. Based on sliding mode error, Nussbaum gain function, and composite control terms, the controller's control law is used to calculate the control input. Based on the control input, the follower agent is controlled to follow the leader agent in performing the same task. The composite control terms include a feedback control term based on sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term. The parameters of the controller's control law are updated based on the sliding mode error.

2. The hybrid-order multi-agent control method as described in claim 1, characterized in that, Before calculating the follower consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, the following is included: The dynamic model of the second-order leader agent is established as follows: ； The dynamic model of the second-order follower agent is established as follows: ； The dynamic model of the first-order follower agent is established as follows: ； in, Let be the state vector of the leader agent. and These represent the position and velocity of the leader agent, respectively. Let k be an unknown nonlinear smooth function of the leader agent, where k represents the k-th iteration. Indicates a given repetition time. Let represent the position and state vector of the z-th follower agent in the k-th iteration. It is an unknown nonlinear smooth function of the follower agent. For time-varying gain, all Same symbols Actuator failure, actuator failure The expression is: ； in, Gain fault, For bounded bias faults, Provide the actual input control signal to the actuator; Unknown nonlinear smooth function of the follower agent The expression approximated using a fuzzy logic system is: ； in, For the fuzzy weight coefficient vector, and For compactness, To approximate the error, For fuzzy basis function vectors, The expression is: ； in, For fuzzy sets Fuzzy membership function.

3. The hybrid-order multi-agent control method as described in claim 2, characterized in that, The calculation of the following consistency error between the follower agent and the leader agent, and the neighbor consistency error between the follower agent and other follower agents, includes: The following consistency error between the follower agent and the leader agent is calculated using Formula 1, which is: ； The neighbor consistency error between the follower agent and other follower agents is calculated using Formula 2, which is: ； in, It is a set of second-order follower agents. For the set of all follower agents, These are elements of the communication topology adjacency matrix, representing the communication connection relationships between follower agents z and j. The adjacency matrix elements of the follower agent and the leader agent indicate whether the follower agent z can receive information from the leader.

4. The hybrid-order multi-agent control method as described in claim 3, characterized in that, The calculation of sliding mode error based on follower consensus error and neighbor consensus error includes: Convert the neighbor consistency error to: ； in, , , , and Let these represent the transformation matrices of the second-order system and the first-order system, respectively. and The expression is: ； in, and The Laplace matrix corresponding to the network topology. and This represents the adjacency matrix between the states of the follower and leader agents. Formula 3 is used to analyze the following consistency error. Neighbor consistency error Perform zero-padding dimension expansion to obtain the expanded follower consistency error and neighbor consistency error, as shown in Formula 3: ； in, , , This is the corresponding block diagonal expansion matrix; The sliding mode error is calculated using the extended follower consistency error and neighbor consistency error, through Formula 4, which is: ； in, It is a constant.

5. The hybrid-order multi-agent control method as described in claim 4, characterized in that, The control law of the controller is: ； in, This is the control input for the z-th agent in the k-th iteration. The Nussbaum gain function, For the online learning variables of the Nussbaum gain function, For composite control items, For feedback control terms based on sliding mode error, For approximating unknown nonlinear unmodeled dynamics, (This refers to a fuzzy control term used to approximate the fuzzy control term.) For robust control terms used to compensate for controller execution failures and upper bounds of uncertainty, , , and The expression is: ； in, It is a constant. satisfy and , For online learning of gain control, and These are parameters for online learning.

6. The hybrid-order multi-agent control method as described in claim 5, characterized in that, The parameters for updating the controller control law based on sliding mode error include: Based on sliding mode error, the weights of the fuzzy logic system are adjusted using Formula 5. Upper bound of uncertainty and feedback gain The updated formula five is as follows: ； in, Indicates to Weight estimation for fuzzy logic systems This represents an estimate of the upper bound of uncertainty. , For learning rate, For correction factor, To meet The convergent sequence.

7. A hybrid-level multi-agent control device, characterized in that, The hybrid-order multi-agent system includes a leader and multiple followers. The leader is a second-order agent, and the followers include first-order and second-order agents. Each follower agent repeatedly performs the same task with the leader agent within a finite time. Each execution of the same task constitutes one iteration. The hybrid-order multi-agent control device includes: The error calculation module is used to calculate the following consistency error between the follower agent and the leader agent and the neighbor consistency error between the follower agent and other follower agents for each iteration of each follower agent. Based on the following consistency error and the neighbor consistency error, the sliding mode error is calculated. The control calculation module is used to calculate the control input based on the sliding mode error, the Nussbaum gain function, and the composite control term using the controller's control law. Based on the control input, the module controls the follower agent to perform the same task as the leader agent. The composite control term includes a feedback control term based on the sliding mode error, a fuzzy control term for approximating unknown nonlinear unmodeled dynamics, and a robust control term for compensating for controller execution failures and uncertainty upper bounds. The parameters of the controller's control law include the weights of the fuzzy logic system used to calculate the fuzzy control term, the uncertainty upper bound in the robust control term, and the feedback gain of the feedback control term. The parameter update module is used to update the parameters of the controller's control law based on the sliding mode error.

8. The hybrid-stage multi-agent control device as described in claim 7, characterized in that, The hybrid multi-agent control device further includes a model building module, used for: The dynamic model of the second-order leader agent is established as follows: ； The dynamic model of the second-order follower agent is established as follows: ； The dynamic model of the first-order follower agent is established as follows: ； in, Let be the state vector of the leader agent. and These represent the position and velocity of the leader agent, respectively. Let k be an unknown nonlinear smooth function of the leader agent, where k represents the k-th iteration. Indicates a given repetition time. Let represent the position and state vector of the z-th follower agent in the k-th iteration. It is an unknown nonlinear smooth function of the follower agent. For time-varying gain, all Same symbols Actuator failure, actuator failure The expression is: ； in, Gain fault, For bounded bias faults, Provide the actual input control signal to the actuator; Unknown nonlinear smooth function of the follower agent The expression approximated using a fuzzy logic system is: ； in, For the fuzzy weight coefficient vector, and For compactness, To approximate the error, For fuzzy basis function vectors, The expression is: ； in, For fuzzy sets Fuzzy membership function.

9. A hybrid-level multi-agent control device, characterized in that, The hybrid multi-agent control device includes a processor, a memory, and a hybrid multi-agent control program stored in the memory and executable by the processor, wherein when the hybrid multi-agent control program is executed by the processor, it implements the steps of the hybrid multi-agent control method as described in any one of claims 1 to 6.

10. A readable storage medium, characterized in that, The readable storage medium stores a hybrid-level multi-agent control program, wherein when the hybrid-level multi-agent control program is executed by a processor, it implements the steps of the hybrid-level multi-agent control method as described in any one of claims 1 to 6.

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