A nonlinear multi-agent system dynamic event-triggered fault-tolerant control method

Abstract

The application discloses a nonlinear multi-agent system dynamic event-triggered fault-tolerant control method. For the system with actuator faults, external disturbances and limited communication, a cooperative control framework including error conversion, backstepping recursion, dynamic event triggering, neural network, adaptive law and fault-tolerant controller is constructed. The method constrains the tracking error by error conversion and a preset performance function; the neural network is used to approximate unknown nonlinear dynamics; the parameter adaptive law is designed based on backstepping recursion and adaptive law; and a dynamic event triggering mechanism is introduced to adaptively reduce the update frequency of the control signal. The designed adaptive fault-tolerant controller can drive all followers to keep consistent with the leader within a fixed time, and ensures that all signals of the closed-loop system are bounded, and has the advantages of independent convergence time and initial state, saving of communication resources, strong fault-tolerant performance and the like.

Description

Technical Field

[0001] This invention relates to the field of cooperative control technology for multi-agent systems, and in particular to a fixed-time fault-tolerant control method that combines specified performance constraints and dynamic event triggering mechanisms for multi-agent systems with actuator failures, unknown nonlinear dynamics, and limited communication resources. It is applicable to cooperative control systems requiring high reliability and low communication overhead, such as UAV swarms, distributed robots, and intelligent transportation systems. Background Technology

[0002] With the increasing application of multi-agent systems in complex engineering projects, the stability and cooperative performance of these systems in the face of actuator failures, external interference, and communication resource limitations have become critical issues. While traditional finite-time control methods can achieve fast convergence, their convergence time depends on the initial state of the system. In practice, it is difficult to obtain accurate initial information, limiting the practicality of these methods. Existing technologies face the following challenges in addressing such problems:

[0003] First, while traditional finite-time control can achieve fast convergence, its upper bound on the convergence time depends on the initial state of the system. In practical engineering, the initial state of the system is often difficult to obtain or measure accurately, which makes it impossible to determine the theoretical convergence time in advance, thus limiting the predictability and practicality of the control strategy in real systems.

[0004] Second, specified performance control ensures the transient and steady-state performance of the system by pre-setting error boundaries. However, existing methods mostly use static performance functions, which make it difficult to achieve optimal coordination between convergence speed and performance constraints within a fixed-time convergence framework. When actuator failure occurs, static constraint functions may fail to adapt to dynamic changes in the system, leading to the violation of performance boundaries or controller instability.

[0005] Third, existing research on fault-tolerant control mainly focuses on ideal communication conditions or static event triggering mechanisms, which makes it difficult to effectively balance system performance and communication overhead in resource-constrained environments. Although dynamic event triggering mechanisms can adaptively adjust the triggering threshold, their stability analysis and triggering condition design lack systematic methods under complex operating conditions that simultaneously consider actuator failures, unknown nonlinearities, and specified performance constraints. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a fixed-time fault-tolerant control method based on dynamic event triggering and specified performance constraints, applicable to nonlinear multi-agent systems with actuator failures. This method uses a backstepping recursive method as its design framework, combines radial basis function neural networks to approximate unknown nonlinear dynamics, introduces a dynamic event triggering mechanism to reduce communication frequency, and constrains the transient and steady-state behavior of tracking errors through performance functions. Ultimately, it achieves consistent outputs from all followers and the leader within a fixed time period, and ensures that all closed-loop signals are bounded.

[0007] This invention discloses a dynamic event-triggered fault-tolerant control method for a nonlinear multi-agent system, wherein the nonlinear multi-agent system comprises N agents, where N is a positive integer, and the method includes the following steps:

[0008] A nonlinear multi-agent system model incorporating actuator failures and external disturbances is constructed, and a cooperative tracking error is built based on the communication topology and reference signal.

[0009] The cooperative tracking error is transformed based on a preset performance function to obtain an unconstrained error.

[0010] Based on the aforementioned unconstrained error, a backstepping recursive method is used to recursively design the virtual control law and intermediate control signals, and a fixed-time convergence term is introduced in each design step.

[0011] A radial basis function neural network is used to approximate the unknown nonlinear dynamics in the backstep recursion process and generate corresponding adaptive parameter estimates.

[0012] The design incorporates event-triggered conditions and adaptive laws with dynamic internal variables to adaptively determine the update time of control signals.

[0013] Based on the unconstrained error and the basis function information of the radial basis function neural network, an adaptive law is designed to update the adaptive parameter estimates online.

[0014] By integrating the intermediate control signal, the event triggering mechanism, and the adaptive parameter estimate, a final control signal is constructed to drive the multi-agent system and form a closed loop.

[0015] Furthermore, the actuator fault model is as follows: ,in For actual control input, For controller output, For unknown failure coefficients, For bounded additive fault signals, .

[0016] Furthermore, the performance function It is an exponential decay function ,in , , and It is a constant; error transformation is achieved through... Implementation, in which This refers to the collaborative tracking error.

[0017] Furthermore, the fixed-time convergence term includes + Two forms, of which For the first The agent in the th... Unconstrained error in step-by-step and backstep recursion > 0 represents the design parameter. These are parameters related to a fixed convergence time.

[0018] Furthermore, the radial basis function neural network approximation is as follows: ,in For the ideal weight vector, For the basis function vector, Define the bounded approximation error; define the adaptive parameters. Its ideal value satisfies The adaptive parameter estimate is .

[0019] Furthermore, the adaptive law is designed as follows: the adaptive parameter estimate... The update law includes an update term that is proportional to the square of the corresponding unconstrained error and the square of the norm of the radial basis function neural network basis function vector, as well as a negative feedback correction term to ensure that the estimate is bounded.

[0020] Furthermore, the event triggering condition is: ,in As a dynamic auxiliary variable, Designing continuous signals With trigger execution signal The difference, ∈ These are design parameters.

[0021] Furthermore, the dynamic auxiliary variable The adaptive law design is ,in These are positive design parameters.

[0022] Furthermore, the final control signal It is given by the following formula: ,in This refers to the intermediate control signal. This is a variable in the event triggering mechanism, and and .

[0023] Furthermore, the intermediate control signal It is constructed by introducing the Nussbaum gain function to address the problem of unknown system control direction due to actuator failure.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] First, this invention combines fixed-time control with specified performance constraints. The designed controller enables the system tracking error to converge within a predetermined performance boundary, and the upper bound of the convergence time is determined solely by the controller parameters, without requiring initial system state information. This effectively solves the problem of limited practicality of traditional finite-time control when the initial state is difficult to obtain accurately in actual engineering.

[0026] Second, this invention proposes an event triggering mechanism based on dynamic threshold adjustment for complex operating conditions involving actuator failures and communication resource limitations. This mechanism can adaptively adjust the triggering conditions according to system errors, significantly reducing unnecessary continuous communication frequency and computational load between agents while ensuring stability, thereby improving resource utilization efficiency.

[0027] Third, this invention systematically addresses the combined effects of unknown nonlinear dynamics, external disturbances, and actuator failures in the system through a neural network approximation and backstepping recursive method framework. The designed adaptive fault-tolerant control scheme ensures that all signals in the closed-loop system are bounded and achieves high-precision consistent tracking within a fixed time. Compared with existing technologies, this invention exhibits significant advantages in several aspects and has high practical application value. Attached Figure Description

[0028] This invention has a total of appendices Figure 8 Zhang, of which:

[0029] Figure 1 This is a schematic diagram of the design method for fixed-time fault-tolerant control of multi-agent systems.

[0030] Figure 2 This is a schematic diagram of the communication topology of a multi-agent system.

[0031] Figure 3 It is a trajectory diagram comparing the outputs of followers and leaders in a multi-agent system.

[0032] Figure 4 It is a tracking error trajectory diagram of a multi-agent system.

[0033] Figure 5 It is the control input signal of a multi-agent system. Trajectory diagram.

[0034] Figure 6 It is a controller The interval between triggering events.

[0035] Figure 7 It is a controller The interval between triggering events.

[0036] Figure 8 It is a controller The interval between triggering events. Detailed Implementation

[0037] The invention will be further described below with reference to the accompanying drawings. The invention designs a fixed-time fault-tolerant controller based on an agent-agent communication topology, the design structure of which is as follows: Figure 1 As shown.

[0038] The technical solution of this invention is implemented through the following collaborative control framework, which mainly includes the following modules: a nonlinear, non-strict feedback multi-agent system model, an error transformation module, a backstepping recursion technology module, a dynamic event triggering mechanism module, a neural network module, an adaptive law module, and an adaptive fault-tolerant controller module. The input of the error transformation module is connected to the output of the nonlinear, non-strict feedback multi-agent system, and its output is connected to the input of the backstepping recursion module; the input of the backstepping recursion module is connected to the output of the error transformation module, and its output is connected to the input of the dynamic event triggering mechanism module. The input of the dynamic event triggering mechanism module is connected to the output of the backstepping recursion technology module, and the output is connected to the input of the adaptive fault-tolerant controller; the input of the neural network module is connected to the output of the nonlinear non-strict feedback multi-agent system, and the output is connected to the input of the adaptive law module; the input of the adaptive law module is connected to the outputs of the nonlinear non-strict feedback multi-agent system, the neural network module, and the backstepping recursion technology module, and the output is connected to the input of the adaptive fault-tolerant controller; the output of the adaptive fault-tolerant controller is connected to the inputs of the nonlinear non-strict feedback multi-agent system and the adaptive law module.

[0039] A. Nonlinear, non-rigid feedback multi-agent system model

[0040] Construct a nonlinear multi-agent system model incorporating actuator failures and external disturbances. Consider a system with N agents, where the dynamics of the i-th agent are described as follows:

[0041] (1)

[0042] in, This represents the m-th state component of the i-th agent. express The derivative, For state vectors, To control the input, To control the output. For unknown constants, and For an unknown smooth nonlinear function, It is a bounded external disturbance in the system and satisfies , express There is an upper bound. The actuator's bias gain fault is defined as... ,in The rate of loss of control is unknown. It is a bounded signal and satisfies , Represents an unknown constant.

[0043] B. Error Conversion Module

[0044] The error transformation module converts the system's actual tracking error into an unconstrained transformed error that satisfies specified transient and steady-state performance constraints by introducing a preset performance function. This design enables the subsequent controller to drive the tracking error to converge to the preset boundary within a fixed time, laying an important foundation for backstepping recursion and controller design.

[0045] First, the coordinate transformation is defined as:

[0046]

[0047] (2)

[0048] in, . This represents the tracking error of the system. Indicates virtual control signal, This represents the output signal of the neighboring agent j of the i-th agent. This represents the reference signal, which is the target output that all agents need to track together.

[0049] in, . This represents the tracking error of the system. Indicates virtual control signal, This represents the output signal of the neighboring agent j of the i-th agent. This represents the reference signal, which is the target output that all agents need to track together.

[0050] To ensure that the tracking error converges to the predetermined region, a performance function and the following error transformation are introduced:

[0051] (3)

[0052] in, This represents a preset performance function that satisfies... ,in , and It is a constant. This indicates the tracking error.

[0053] This results in the following coordinate transformation:

[0054] (4)

[0055] in, express The derivative, Indicates unconstrained error. Indicates virtual control signal The derivative;

[0056] C. Backstepping recursion technique module

[0057] The backstepping recursion module utilizes error information from the error transformation module to construct a Lyapunov function for backstepping recursion design, laying the groundwork for subsequent adaptive fault-tolerant controller and adaptive law modules.

[0058] Step 1: Calculate the derivative of the tracking error as follows:

[0059] (5)

[0060] in, , Denotes the set of neighbors of agent i. This represents the elements of the adjacency matrix in the communication topology, used to quantify the connection strength between agents. This represents the connection weight between agent i and the leader. Let the second state variable of neighboring agent j be represented. This represents external interference to the neighboring intelligent agent j.

[0061] Design Lyapunov functions as follows:

[0062] (6)

[0063] in, Indicates design parameters, , The estimation error of the adaptive parameters, For adaptive parameters, It is an adaptive parameter The estimated value.

[0064] Differentiating equation (6), we get The expression, substituting formula (5) into The expression for is:

[0065] (7)

[0066] Step 2: Calculate the derivative of the tracking error as follows:

[0067] (8)

[0068] Design Lyapunov functions as follows:

[0069] (9)

[0070] in, , The estimation error of the adaptive parameters, For adaptive parameters, It is an adaptive parameter The estimated value.

[0071] right Differentiation yields:

[0072] (10)

[0073] in , , For unknown constants, , , , , , Indicates a positive design parameter.

[0074] No. step The derivative of the tracking error is calculated as follows:

[0075] (11)

[0076] Design No. Lyapunov function of step as follows:

[0077] (12)

[0078] in, , The estimation error of the adaptive parameters, For adaptive parameters, It is an adaptive parameter The estimated value.

[0079] right Differentiation yields:

[0080] (13)

[0081] in, , , It is an unknown constant.

[0082] No. Step: Calculation :

[0083] (14)

[0084] in , , The failure coefficient is unknown.

[0085] Design the Lyapunov function in step n. for:

[0086] (15)

[0087] in , The estimation error of the adaptive parameters, For adaptive parameters, It is an adaptive parameter The estimated value.

[0088] For Lyapunov functions Differentiation yields:

[0089] (16)

[0090] in , , For unknown constants, Represents an unknown constant.

[0091] D. Dynamic event triggering mechanism module

[0092] The dynamic event triggering mechanism module introduces a dynamic threshold containing auxiliary variables to adaptively adjust the update conditions of the control signals, effectively reducing unnecessary continuous communication between agents. This mechanism significantly reduces communication and computational resource consumption while ensuring system stability, and rigorous theoretical analysis prevents the occurrence of Zeno's behavior.

[0093] When the event triggering conditions are met, the signals related to trigger control will be updated in the following manner:

[0094] (17)

[0095] Construct the following event triggering conditions:

[0096] (18)

[0097] in Indicates a transition control signal. Represents measurement error. The range of values ​​is , It is the input update time, a dynamic auxiliary variable. The following design can be made:

[0098] (19)

[0099] in These are positive design parameters. Indicates a positive design parameter.

[0100] When the triggering condition is met, the control signal for event triggering is activated. It will be executed, and within the range Inside, It is a constant.

[0101] Based on the triggering condition, we can obtain:

[0102] (20)

[0103] in and It is a time-varying variable.

[0104] E. Neural Network Module

[0105] The neural network module utilizes state information and other information from the multi-agent system, and uses an adaptive parameter and radial basis function neural network to approximate the unknown nonlinear dynamics, which is then fed into the adaptive law module for subsequent work.

[0106] Due to nonlinear dynamics Completely unknown, processed using a neural network module and the following assumptions are made:

[0107] (twenty one)

[0108] (twenty two)

[0109] (twenty three)

[0110] in , , , To approximate the error and satisfy ( (where the unknown constant is) ( (The ideal weights for a radial basis function neural network). are basis functions .

[0111] F. Adaptive Law Module

[0112] The adaptive law module takes as input the state information of the multi-agent system and the output of the backstepping recursion technique module. The output signals are respectively , Its function is to reflect the dynamic changes of adaptive parameters in the controller, and it inputs the dynamic changes of parameters into the adaptive fault-tolerant controller module.

[0113] For multi-agent systems, the following adaptive law is designed:

[0114] (twenty four)

[0115] (25)

[0116] in , , , , , , , These are positive design parameters. , .

[0117] G. Adaptive Fault-Tolerant Controller Module

[0118] The input to the adaptive fault-tolerant controller module is the output of the backstepping recursion technology module. Output of the adaptive law module , State information of multi-agent systems.

[0119] Design the following adaptive fault-tolerant controller:

[0120] (26)

[0121] Design control signals The conversion formula is:

[0122] (27)

[0123] in , It is a positive number; ; Choosing the Nussbaum function .

[0124] In the control of nonlinear, non-strict feedback multi-agent systems, the state information of the system is input into a radial basis function neural network module (the basis function is typically initialized with a uniform distribution center and a width based on the center spacing, then fine-tuned based on simulation results); the state information is also input into an error conversion module; and the output of the error conversion module... , The system's state information, the outputs of the backstepping recursion module and the neural network module are input into the adaptive law module; the output of the backstepping recursion module is input into the dynamic event triggering mechanism module; the output of the adaptive law module is... , The output of the dynamic event triggering mechanism module is input to the adaptive fault-tolerant controller module; the output of the adaptive fault-tolerant controller module is... The input is fed into the adaptive law module and the nonlinear, non-strict feedback multi-agent system. The design goal of this invention is to design a distributed adaptive fault-tolerant controller that ensures that the output trajectories of all followers and leaders remain consistent within a fixed time period, and that all signals within the closed-loop system remain bounded.

[0125] The communication topology selected for simulation is as follows: Figure 2 As shown. Simulation results are as follows. Figure 3-8 As shown, under the dynamic event-triggered fixed-time fault-tolerant control strategy, all signals in the closed-loop multi-agent system remain bounded and have good transient and steady-state performance. Figure 3 The output trajectories of the leader and followers are shown under a fault-tolerant control strategy. The figure demonstrates that all followers can stably track the leader's output within a fixed timeframe, validating the effectiveness and stability of the proposed control strategy. Figure 4Tracking error curves for a multi-agent system are presented. The results show that even after an actuator failure, the system tracking error can still quickly converge to the preset performance boundary and fluctuate within a very small range. Figure 5 The changes in the control input signal are depicted. It can be seen that the input signal generated by the controller in response to actuator failure and external interference is smooth and bounded, without severe chattering or saturation, which conforms to the physical constraints and engineering feasibility of the actual actuator. Figure 6-8 The distribution of time intervals for event triggering under different controllers is shown. As can be seen from the figure, under the action of the dynamic event triggering mechanism, the update frequency of the control signal is significantly reduced, and the time interval between adjacent triggering events is greater than a certain normal number. This indicates that the system effectively avoids Zeno behavior and significantly saves communication and computing resources while ensuring control performance.

[0126] This invention is not limited to this embodiment. Any equivalent concept or modification within the technical scope disclosed in this invention shall be included within the protection scope of this invention.

Claims

1. A dynamic event-triggered fault-tolerant control method for a nonlinear multi-agent system, characterized in that, The system comprises N agents, where N is a positive integer, and the method includes the following steps: A nonlinear multi-agent system model incorporating actuator failures and external disturbances is constructed, and a cooperative tracking error is built based on the communication topology and reference signal. The cooperative tracking error is transformed based on a preset performance function to obtain an unconstrained error. Based on the aforementioned unconstrained error, a backstepping recursive method is used to recursively design the virtual control law and intermediate control signals, and a fixed-time convergence term is introduced in each design step. A radial basis function neural network is used to approximate the unknown nonlinear dynamics in the backstep recursion process and generate corresponding adaptive parameter estimates. The design incorporates event-triggered conditions and adaptive laws with dynamic internal variables to adaptively determine the update time of control signals. Based on the unconstrained error and the basis function information of the radial basis function neural network, an adaptive law is designed to update the adaptive parameter estimates online. By integrating the intermediate control signal, the event triggering mechanism, and the adaptive parameter estimate, a final control signal is constructed to drive the multi-agent system and form a closed loop.

2. The method according to claim 1, characterized in that, The actuator fault model is as follows: ,in For actual control input, For controller output, For unknown failure coefficients, For bounded additive fault signals, .

3. The method according to claim 1, characterized in that, The performance function It is an exponential decay function ,in , , and It is a constant; error transformation is achieved through... Implementation, in which This refers to the collaborative tracking error.

4. The method according to claim 1, characterized in that, The fixed-time convergence term includes + Two forms, of which For the first The agent in the th... Unconstrained error in step-by-step and backstep recursion > 0 represents the design parameter. These are parameters related to a fixed convergence time.

5. The method according to claim 1, characterized in that, The form of the radial basis function neural network approximation is as follows: ,in For the ideal weight vector, For the basis function vector, Define the bounded approximation error; define the adaptive parameters. Its ideal value satisfies The adaptive parameter estimate is .

6. The method according to claim 5, characterized in that, The adaptive law is designed as follows: the adaptive parameter estimate... The update law includes an update term that is proportional to the square of the corresponding unconstrained error and the square of the norm of the radial basis function neural network basis function vector, as well as a negative feedback correction term to ensure that the estimate is bounded.

7. The method according to claim 1, characterized in that, The event triggering condition is: ,in As a dynamic auxiliary variable, Designing continuous signals With trigger execution signal The difference, ∈ These are design parameters.

8. The method according to claim 7, characterized in that, The dynamic auxiliary variable The adaptive law design is ,in These are positive design parameters.

9. The method according to claim 7 or 8, characterized in that, The final control signal It is given by the following formula: ,in This refers to the intermediate control signal. This is a variable in the event triggering mechanism, and and .

10. The method according to claim 9, characterized in that, The intermediate control signal It is constructed by introducing the Nussbaum gain function to address the problem of unknown system control direction due to actuator failure.

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