Fault-tolerant tracking control method, device and medium for nonlinear time-varying system

Abstract

The application provides a nonlinear time-varying system fault-tolerant tracking control method, device and medium. The method according to the application comprises the following steps: constructing a performance constraint function irrelevant to the initial state of the system, and defining a tracking error allowable range; generating an error variable based on the function to convert the tracking error and constructing a potential barrier function; updating the scalar estimation value of the system uncertainty parameter on line through a parameter adaptive update law containing a finite-time vanishing damping term; generating a continuous fault-tolerant control signal in combination with the error variable and the scalar estimation value; constructing a dynamic event-triggered control mechanism, judging the triggering condition based on the deviation of the continuous and discrete control signals and the dynamic threshold value; and outputting the discrete control signal to the controlled object when the condition is met. The application eliminates the dependence on the initial condition, reduces the calculation complexity, saves the communication resources, and realizes the fault-tolerant control on the actuator failure.

Description

Technical Field

[0001] This document relates to nonlinear time-varying systems, and more particularly to a fault-tolerant tracking control method, device, and medium for nonlinear time-varying systems. Background Technology

[0002] Nonlinear time-varying systems are widely used in industrial control, such as CNC machine tool cutting, boiler temperature control, and unmanned aerial vehicle (UAV) systems. Trajectory tracking control in such systems requires the system output to accurately track the desired trajectory, which has significant theoretical and practical value.

[0003] Existing tracking control methods are mainly divided into two categories: one is based on preset performance boundaries, which constrains the transient and steady-state behavior of tracking errors through performance functions; the other is event-triggered control methods, which reduce the communication frequency between the controller and the actuator by designing triggering mechanisms, thereby saving network resources.

[0004] However, existing technologies have the following shortcomings: First, traditional preset performance control methods usually rely on the initial conditions of the system, and when the initial tracking error is large, it may lead to a decrease in control performance or even system instability. Second, for unknown time-varying parameters, unknown control gains and external disturbances in the system, traditional methods need to estimate multiple parameter vectors separately, resulting in high computational complexity. Third, existing event triggering mechanisms mostly use fixed thresholds or relative thresholds, which cannot dynamically adjust the triggering frequency according to the system state, and resource utilization needs to be improved. Fourth, when the system experiences actuator failure, existing control methods cannot simultaneously guarantee tracking performance and stability. Summary of the Invention

[0005] This invention provides a fault-tolerant tracking control method, device, and medium for nonlinear time-varying systems, aiming to solve the above-mentioned problems.

[0006] According to an embodiment of the present invention, a fault-tolerant tracking control method for a nonlinear time-varying system is provided, characterized by comprising: S1. Construct a performance constraint function whose initial value is independent of the initial state of the system, to define the allowable range of variation of the system tracking error; S2. Based on the performance constraint function, perform error transformation on the tracking error of the current control cycle to generate the transformed error variable, and construct a barrier function based on the transformed error variable; S3. Based on the transformed error variable and barrier function, update the values ​​of the scalar estimation parameters online using the parameter adaptive update law; S4. Based on the current values ​​of the transformed error variable, the barrier function, and the scalar estimation parameter, a continuous fault-tolerant control signal is generated according to the preset control law calculation rules. S5. Construct a dynamic event triggering control mechanism, and determine whether the preset triggering conditions are met based on the deviation between the continuous fault-tolerant control signal and the discrete control signal actually applied to the controlled object. S6. When the triggering condition is met, the value of the current continuous fault-tolerant control signal is output as a discrete control signal and applied to the controlled object, and the next control cycle begins.

[0007] According to an embodiment of the present invention, an electronic device is provided, comprising: Processor; and, A memory is configured to store computer-executable instructions, which, when executed, cause the processor to perform the steps of the aforementioned fault-tolerant tracking control method for nonlinear time-varying systems.

[0008] According to an embodiment of the present invention, a storage medium is provided for storing computer-executable instructions, which, when executed, implement the steps of the above-described nonlinear time-varying system fault-tolerant tracking control method.

[0009] By employing embodiments of this invention, a performance constraint function is constructed to automatically bring any bounded initial tracking error within the allowable range, eliminating the need to adjust controller parameters for different initial conditions. By unifying all unknown time-varying parameters, unknown control gains, and external disturbances in the system as scalar unknown constants for online estimation, the multidimensional parameter estimation problem is transformed into a scalar estimation problem, reducing computational complexity. By introducing a finite-time vanishing damping term into the parameter adaptive update law, parameter estimation is driven to stop updating within a preset finite time, eliminating the problem of continuous parameter drift. A terminal fault-tolerant control signal is designed for actuator models with time-varying coefficient failures and additive faults, ensuring the system maintains tracking performance even in the event of actuator failure. The dynamic event-triggered control mechanism constructed in this application introduces a dynamic threshold variable, adjusting the trigger threshold in real time based on measurement errors, reducing the number of control signal updates while ensuring closed-loop stability, thus saving communication resources. This invention theoretically proves that the derivative of the terminal continuous fault-tolerant control signal is bounded and that there is a lower bound on the positive constant between adjacent trigger intervals, avoiding Zeno behavior of infinite triggers. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1This is a flowchart of a nonlinear time-varying system fault-tolerant tracking control method according to an embodiment of the present invention; Figure 2 Example 1 of the present invention and A schematic diagram of the trajectory; Figure 3 This is Example 1 of the present invention. and Trajectory diagram Figure 4 This is Example 1 of the present invention. and The estimated parameters; Figure 5 This is a schematic diagram illustrating the relationship between tracking error and performance limits in Example 1 of this invention; Figure 6 This is a schematic diagram of the time interval of the triggering event in Example 1 of the present invention; Figure 7 This is a schematic diagram of the system position tracking trajectory in Example 1 of the present invention; Figure 8 This is a schematic diagram of the trajectory of e(t) and the performance limit in Example 2 of the present invention; Figure 9 For the speed of Example 2 of the present invention and A schematic diagram of the trajectory; Figure 10 This is Example 2 of the present invention. and The trajectory; Figure 11 The trajectories of v(t) and u in Example 2 of this embodiment; Figure 12 This is a schematic diagram illustrating the event triggering time intervals of different ETMs in Example 2 of this embodiment of the invention; Figure 13 The trajectory of e(t) under different initial conditions in embodiments of the present invention. Detailed Implementation

[0012] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.

[0013] Method Implementation Examples According to an embodiment of the present invention, a fault-tolerant tracking control method for a nonlinear time-varying system is provided. Figure 1 This is a flowchart of a fault-tolerant tracking control method for a nonlinear time-varying system according to an embodiment of the present invention. Figure 1 As shown, the fault-tolerant tracking control method for nonlinear time-varying systems in this embodiment of the invention specifically includes: S1. Construct a performance constraint function whose initial value is independent of the initial state of the system, to define the allowable range of variation of the system tracking error; First, select a preset convergence time value that is independent of the system initial conditions and system parameters. and preset steady-state accuracy value ,in Used to set the upper limit of the time for the tracking error to converge to steady-state accuracy. Both are used to set the allowable error range for steady-state tracking, and can be flexibly set according to actual control requirements.

[0014] Then, construct the performance funnel function at the predetermined time: ; in, As the adjustment coefficient, this function satisfies the following properties: When t>0 And it increases monotonically; This performance constraint function reduces the tracking error. satisfy This forces the tracking error to converge within a preset time. The internal pressure is compressed to a preset steady-state accuracy. Within, due to (0)=0, any bounded initial tracking error can automatically fall into the allowable range defined by this function, without the need for additional adjustment of initial parameters, thus completely eliminating the dependence on the initial conditions of the system.

[0015] S2. Based on the performance constraint function, perform error transformation on the tracking error of the current control cycle to generate transformed error variables, and construct a barrier function based on the transformed error variables. S2 specifically includes: S21. Perform error variable transformation. Perform coordinate transformation on the tracking error to generate the first error variable: ; This transformation associates the tracking error with the performance constraint function, thereby achieving normalization of the error. The system state is transformed to generate the remaining error variables: , i = 2, 3, ..., n; in, Let i be the i-th state of the system. For the i-th The first-order virtual control signal will be gradually constructed using the backstepping design method.

[0016] S22, Construction of the Barrier Function Construct an asymmetric barrier function independent of initial conditions: ; in, >0 sets the width of the constraint boundary, satisfying... Used to strictly limit the first error variable after transformation. The range of values ​​should be determined to avoid errors exceeding the limits.

[0017] Differentiating the barrier function yields: ; in, , where is the derivative coefficient of the barrier function. This coefficient is always positive, ensuring that the dynamic change of the barrier function is in the same direction as the dynamic change of the first error variable, thus facilitating subsequent stability analysis.

[0018] S3. Based on the transformed error variable and barrier function, update the values ​​of the scalar estimation parameters online using the parameter adaptive update law. S3 specifically includes: S31. Definition of Uncertainty Parameters Define unknown constants This serves as a common upper bound for the uncertainty parameters of the i-th subsystem of the system, where the uncertainty parameters include unknown time-varying parameters, unknown control gain, and external disturbances. A unified scalar upper bound estimation method is adopted to transform the multidimensional parameter estimation problem into scalar estimation, significantly reducing computational complexity.

[0019] set up for The estimated value is defined as follows: The estimation error is: ; S32, Design of Finite-Time Vanishing Damping Term Introducing a finite-time vanishing damping term function The function satisfies continuity, boundedness, monotonically decreasing properties, and tends to 0 after a preset finite time, where T is the core convergence time. >0 represents the buffer time, specifically in the form of: ; in >0 is a positive constant. The introduction of this damping term can drive the parameter estimation to converge to near the true value in a finite time, breaking through the limitation of the traditional exponential convergence rate.

[0020] S33, Construction of Adaptive Update Law The adaptive update law for the parameters of the i-th subsystem is designed as follows: ; in, These are tuning parameters used to adjust the convergence rate of parameter estimation. Let be the error variable of the i-th subsystem after transformation, when i=1. , hour, , This is the uncertainty compensation term for the i-th subsystem, and its specific expression will be defined in detail in subsequent step S4.

[0021] S4. Based on the current values ​​of the transformed error variable, the potential barrier function, and the scalar estimation parameters, a continuous fault-tolerant control signal is generated according to the preset control law calculation rules to cope with actuator failures and ensure tracking performance. S4 specifically includes: S41. Definition of Uncertainty Compensation Term When i=1, the uncertainty compensation term is: ; Where X1 is the known core performance function vector of the first subsystem of the system, used to compensate for the uncertainty of the first error variable; At that time, the uncertainty compensation term is: ; in, Let be the comprehensive performance function matrix of the i-th subsystem, used to compensate for the uncertainty of the intermediate state; In the above expression, It is a positive integrable time-varying function that satisfies: This is used to further suppress system uncertainties and errors caused by external disturbances, and improve the robustness of parameter estimation.

[0022] S42, Virtual Control Signal Design Design the i-th order virtual control signal: ; in, , To control the gain, used to adjust the convergence speed of the system, which can be adjusted according to actual control requirements; S43. Actuator Fault Model and Terminal Control Signal Design For system terminals with actuator failures, an actuator failure model is adopted: ; in, For actuator fault time-varying coefficients, characterizing the degree of actuator fault, N(t) represents additive actuator fault, and both satisfy the conditions of unknown but bounded and piecewise continuous.

[0023] Design the terminal continuous fault-tolerant control signal: ; in, >0 represents the terminal control gain. This control signal can compensate for the effects of actuator failure and ensure that the system can still maintain stable tracking under fault conditions.

[0024] S5. Construct a dynamic event-triggered control mechanism. Based on the deviation between the continuous fault-tolerant control signal and the discrete control signal actually applied to the controlled object, determine whether the preset triggering conditions are met. By constructing a dynamic event-triggered control mechanism, communication and computing resource consumption can be reduced while ensuring control performance. S5 specifically includes: S51, Definition of Measurement Error Define measurement error ,in, The terminal continuous fault-tolerant control signal generated in step S4. It is a discrete control signal that actually acts on the controlled object; S52, Dynamic Threshold Variable Design Design dynamic threshold variables The dynamic equations are: ; in, , , These are positive definite design parameters used to dynamically adjust the changing trend of the trigger threshold, enabling the threshold to adaptively adjust in real time according to the system state. S53, Trigger Condition Settings Set the trigger condition as follows: ; For the k-th trigger time, When the measurement error meets this condition, a control signal update is triggered, and the current time is recorded as the new trigger time. S54, Definition of Comparison Trigger Mechanism To verify the superiority of the proposed Dynamic Event Triggering Mechanism (DETM), two types of comparative triggering mechanisms are defined: Fixed Threshold Event Triggering Mechanism (FETM): , The triggering condition is ,in, >0 is a fixed threshold. Relative Threshold Event Triggering Mechanism (RETM): , The triggering condition is ,in , This is a design constant.

[0025] Furthermore, the dynamic threshold variable satisfy This ensures that the trigger threshold is always positive and bounded. The time interval between two adjacent trigger times satisfies ,in, , >0; In the closed-loop system, all signals satisfy the globally uniform bounded property, and the tracking error e(t) asymptotically converges to zero.

[0026] S6. When the triggering condition is met, the value of the current continuous fault-tolerant control signal is output as a discrete control signal and applied to the controlled object, and the next control cycle begins.

[0027] When the triggering condition set in step S5 is met, the value of the continuous fault-tolerant control signal at the current moment is output as a discrete control signal and applied to the controlled object; between two triggering moments, the discrete control signal retains the value of the previous triggering moment, without the need for continuous updates, effectively reducing communication frequency and computational resource consumption.

[0028] After outputting the discrete control signal, the system enters the next control cycle and repeats steps S1 to S6 to achieve continuous fault-tolerant tracking control of the nonlinear time-varying system.

[0029] Based on Lyapunov stability theory, and following the recursive analysis logic from the first-order subsystem to the intermediate-order subsystem and finally to the terminal subsystem, a comprehensive stability verification of the control method proposed in this application is conducted. All analyses are based on the control law, parameter update law, and dynamic event triggering mechanism designed in this application. The core verification conclusions and derivation process are as follows: 1. Verification of globally consistent boundedness: To verify the boundedness of the system signals, Lyapunov functions were constructed sequentially according to the order of the subsystems. Starting with the first-order subsystem, intermediate-order subsystems were integrated in turn to obtain the global Lyapunov function of the terminal subsystem. After differentiating the global Lyapunov function, and combining the characteristics of the parameter adaptive update law, virtual control signals, and terminal fault-tolerant control signals designed in this application, the derivative results were integrally derived. It can be concluded that all signals in the closed-loop system satisfy global uniform boundedness, including error variables, parameter estimates, virtual control signals of all orders, terminal continuous fault-tolerant control signals, and discrete control signals. All signals have no risk of divergence, and the overall system state is stable.

[0030] 2. Verification of asymptotic convergence of tracking error: Based on the verification of global uniformity and boundedness, the derivative of the Lyapunov function is integralized over infinite time. Using Barbarat's lemma, the derivation leads to the conclusion that the system's first error variable gradually converges to zero. Combining the definitions of the relationship between the first error variable, tracking error, and performance constraint function, the tracking error is obtained as the ratio of the first error variable to the performance constraint function. Since the performance constraint function remains positive throughout the control process, it can be further verified that the system's tracking error asymptotically converges to zero, achieving accurate tracking of the desired reference signal by the system output. 3. Preset transient performance guarantee verification: Based on the core characteristics of the performance constraint function designed in this application, the absolute value of the tracking error is always less than the reciprocal of the performance constraint function, and the performance constraint function is zero at the control start-up time and strictly monotonically increases during the control process. Combining this characteristic, it can be deduced that within a preset convergence time, the tracking error can be forcibly compressed to a preset steady-state accuracy range. Simultaneously, because the performance constraint function is zero at the control start-up time, any bounded initial tracking error can automatically fall within the allowable range defined by the performance constraint function, without the need for additional adjustment of initial parameters, thus achieving globally preset performance control without initial condition dependence.

[0031] 4. Zeno behavior avoids validation: Zeno behavior, characterized by an infinite number of triggers, leads to the exhaustion of communication resources. This application verifies the absence of Zeno behavior through two layers of derivation: First, it verifies that the derivative of the terminal's continuous fault-tolerant control signal is bounded, with its rate of change always less than a certain positive constant. Second, based on the triggering conditions of the dynamic event triggering mechanism designed in this application, it can be deduced that the time interval between two adjacent triggers has a positive lower bound, meaning the trigger interval will not shrink indefinitely. Therefore, it is proven that the system will not exhibit Zeno behavior with an infinite number of triggers, and the dynamic event triggering control mechanism designed in this application is engineering feasible.

[0032] Furthermore, to verify the effectiveness, global applicability, and engineering practicality of the proposed fault-tolerant tracking control method for nonlinear time-varying systems, two simulation cases were designed: a nonlinear strict feedback system and an actual engineering mass-spring-damper system. The simulation results of different triggering mechanisms, different initial conditions, and existing control methods were compared, as detailed below: Case 1: Simulation Verification of Nonlinear Rigorous Feedback System A second-order nonlinear rigorous feedback system model is adopted, and the actuator fault model is configured as follows: =E(t)v(t)+N(t), with the reference signal set as =0.5sin(t), and simultaneously set all control parameters such as tuning parameters, control gain, performance funnel parameters, dynamic trigger parameters, and system initial conditions, combined with Figure 2-6 Complete the simulation result analysis: Figure 2 A comparative analysis of the system output tracking trajectory under two control algorithms is presented. Compared with the method proposed in the comparison algorithm, the control algorithm proposed in this embodiment enables the system output to converge to the reference trajectory quickly within a specified time, significantly reduces overshoot, and strictly limits the settling time within the predefined funnel function boundary.

[0033] like Figure 5 As shown in the tracking error curve, the method of this embodiment converges the tracking error to below the steady-state threshold of 0.1 within t < 1.5 seconds. Furthermore, even with actuator failure, the system maintains the specified control performance. In contrast, the comparative method does not incorporate error constraints, resulting in prolonged convergence time and slower convergence speed, while failing to address the issue of system stability or performance maintenance under actuator failure conditions.

[0034] according to Figure 3 The tracking comparison results between the system state variable x2 and the virtual control signal α1 show that the system state variable can accurately follow the virtual control signal, with a fast response speed and no obvious lag. according to Figure 4 The estimated values ​​of the system uncertainty parameters are known. , The evolution curves show that the parameter estimates converge to stable values ​​within a finite time, verifying the effectiveness of the finite-time disappearing damping term designed in this application. Figure 6 This paper demonstrates an event-triggered execution interval sequence based on dynamic signals. This triggering mechanism has a simple structure, is easy to implement in engineering, effectively reduces redundant signal transmission, and significantly lowers communication resource consumption.

[0035] Case 2: Simulation Verification of Actual Engineering Quality - Spring-Damper System A second-order mass-spring-damper system is adopted and converted into a strict feedback system. Unknown time-varying parameters, external disturbances, and actuator fault models are configured, and the reference signal is set as... =0.5sin(1.5t), and simultaneously set all control parameters, system initial conditions, and parameters for two types of comparative triggering mechanisms: fixed threshold event triggering mechanism and relative threshold event triggering mechanism, combined with Figure 6-12 Complete the simulation result analysis: like Figure 7 and Figure 8 As shown, the system's pose tracking trajectory and tracking error are illustrated. It can be seen that even when the initial error significantly exceeds the normal range, the controller proposed in this application can still enable the system output to converge rapidly to a steady state within a specified time (2 seconds), while exhibiting excellent dynamic response performance. During the steady-state phase, the error is consistently and strictly controlled within a preset range, fully demonstrating its high-precision characteristics. Experimental results show that even with actuator uncertainties and faults, the system can still maintain its predetermined performance control behavior and possess finite-time convergence characteristics. This not only verifies the effectiveness of the proposed control law in transient regulation but also proves its advanced nature in steady-state accuracy.

[0036] Figure 9 The system's velocity trajectory tracking performance is demonstrated, showing that under the control algorithm proposed in this embodiment, the system speed can closely follow the designed virtual control law.

[0037] Figure 10 This presents the results of adaptive estimation. By integrating the DvtF function into the adaptive law, this method achieves a better convergence speed compared to the traditional fixed-exponential convergence method.

[0038] Figure 11 The comparison between the output signal of the control algorithm and the actual signal is shown, where the actual signal is affected by both unknown bounded uncertainty and actuator failure.

[0039] Figure 12 The performance of the proposed DETM, FETM, and RETM in terms of trigger frequency and event interval was compared. As shown in the figure, the proposed triggering scheme designs a simple and easy-to-implement dynamic triggering behavior while significantly reducing the number of trigger events. Table 1 further quantifies and verifies the total number of triggers under the three mechanisms, confirming that the proposed method achieves the highest event sparsity without sacrificing system performance.

[0040] Table 1. Comparison of Trigger Times

[0041] To further demonstrate the global applicability of the proposed method, k1 was set to 20, while the remaining design parameters remained unchanged. Under various initial conditions (e.g., (-0.5, 0.0), (0.65, 0), and (1.0, 0)), the trajectory of the tracking error is as follows: Figure 13 As shown, all tracking errors asymptotically converge to zero without violating the preset performance constraints. These results confirm that the specified tracking performance can be achieved regardless of the initial conditions, thus verifying the global effectiveness of the proposed method.

[0042] The results of the two simulation cases above verify that the fault-tolerant tracking control method for nonlinear time-varying systems proposed in this application can achieve five major technical effects: 1. Global preset performance tracking without initial condition dependence; 2. Adaptive estimation of scalar parameters with low computational complexity; 3. Effective fault-tolerant control under actuator failure; 4. Communication resource saving triggered by dynamic events; 5. Engineering feasibility without Zeno behavior. It effectively solves the technical defects of existing control methods and the overall control performance is better than traditional control methods.

[0043] By employing the embodiments of the present invention, the following beneficial effects are achieved: By employing embodiments of this invention, a performance constraint function is constructed to automatically bring any bounded initial tracking error within the allowable range, eliminating the need to adjust controller parameters for different initial conditions. By unifying all unknown time-varying parameters, unknown control gains, and external disturbances in the system as scalar unknown constants for online estimation, the multidimensional parameter estimation problem is transformed into a scalar estimation problem, reducing computational complexity. By introducing a finite-time vanishing damping term into the parameter adaptive update law, parameter estimation is driven to stop updating within a preset finite time, eliminating the problem of continuous parameter drift. A terminal fault-tolerant control signal is designed for actuator models with time-varying coefficient failures and additive faults, ensuring the system maintains tracking performance even in the event of actuator failure. The dynamic event-triggered control mechanism constructed in this application introduces a dynamic threshold variable, adjusting the trigger threshold in real time based on measurement errors, reducing the number of control signal updates while ensuring closed-loop stability, thus saving communication resources. This invention theoretically proves that the derivative of the terminal continuous fault-tolerant control signal is bounded and that there is a lower bound on the positive constant between adjacent trigger intervals, avoiding Zeno behavior of infinite triggers.

[0044] Device Example 1 According to an embodiment of the present invention, an electronic device is provided, comprising: Processor; and, A memory is configured to store computer-executable instructions, which, when executed, cause the processor to perform the steps of the aforementioned fault-tolerant tracking control method for nonlinear time-varying systems.

[0045] Device Example 2 According to an embodiment of the present invention, a storage medium is provided for storing computer-executable instructions, which, when executed, implement the steps of the above-described nonlinear time-varying system fault-tolerant tracking control method.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fault-tolerant tracking control method for a nonlinear time-varying system, characterized in that... include: S1. Construct a performance constraint function whose initial value is independent of the initial state of the system, to define the allowable range of variation of the system tracking error; S2. Based on the performance constraint function, perform error transformation on the tracking error of the current control cycle to generate the transformed error variable, and construct a barrier function based on the transformed error variable; S3. Based on the transformed error variable and barrier function, update the values ​​of the scalar estimation parameters online using the parameter adaptive update law; S4. Based on the current values ​​of the transformed error variable, the barrier function, and the scalar estimation parameter, a continuous fault-tolerant control signal is generated according to the preset control law calculation rules. S5. Construct a dynamic event triggering control mechanism, and determine whether the preset triggering conditions are met based on the deviation between the continuous fault-tolerant control signal and the discrete control signal actually applied to the controlled object. S6. When the triggering condition is met, the value of the current continuous fault-tolerant control signal is output as a discrete control signal and applied to the controlled object, and the next control cycle begins.

2. The method according to claim 1, characterized in that, The steps for constructing the performance constraint function are as follows: Select a preset convergence time value that is independent of the system initial conditions and system parameters. and preset steady-state accuracy value ; Build to satisfy When t>0 And a monotonically increasing performance funnel function for predetermined time. ; ； in, ; Reduce tracking error satisfy and within the preset convergence time The internal pressure is forcibly compressed to a preset steady-state accuracy. Within.

3. The method according to claim 1, characterized in that, S2 specifically includes: Perform coordinate transformation on the tracking error to generate the first error variable: ； in, For system output, This is the desired reference signal; The system state is transformed to generate the remaining error variables: ,i=2,3,…,n; Let i be the i-th state of the system. For the i-th First-order virtual control signal; Construct an asymmetric barrier function independent of initial conditions: ； in, >0 sets the width of the constraint boundary, satisfying... ; Differentiating the barrier function yields: ； in .

4. The method according to claim 3, characterized in that, The design steps for the adaptive parameter update law in S3 are as follows: Define unknown constants Let this be the upper bound of the uncertainty parameter of the i-th subsystem of the system. for The estimated value has an estimation error of: ； Introducing a finite-time vanishing damping term function The finite-time disappearance damping term function satisfies continuity, boundedness, monotonically decreasing property, and tends to 0 after a preset finite time. The adaptive update law for the parameters of the i-th subsystem is designed as follows: ； in, For tuning parameters, Let be the error variable of the i-th subsystem after transformation, when i=1. , hour, , This is the uncertainty compensation term for the i-th subsystem.

5. The method according to claim 4, characterized in that, The The expression is: ； X1 is the known core performance function vector of the first subsystem of the system; hour, ; Let be the comprehensive performance function matrix of the i-th subsystem. It is a positive integrable time-varying function that satisfies: 。 6. The method according to claim 3, characterized in that, The preset control law calculation rules in S4 include virtual control signal design and terminal continuous fault-tolerant control signal design, specifically: Design the i-th order virtual control signal: ； in, , To control the gain; For system terminals with actuator failures, the actuator failure model is as follows: ； in, Let N(t) be the time-varying coefficient for actuator faults, and N(t) be the additive actuator fault. Design the terminal continuous fault-tolerant control signal: 。 7. The method according to claim 1, characterized in that, The steps for constructing the dynamic event triggering control mechanism in S5 are as follows: Define measurement error: ; in, This is a continuous fault-tolerant control signal for the terminal. Discrete control signals; Design dynamic threshold variables The dynamic equations are: ； in, , , These are positive definite design parameters; Set the trigger condition as follows: ； For the k-th trigger time, .

8. The method according to claim 7, characterized in that, The dynamic time-triggered control mechanism satisfies the following stability constraints: The dynamic threshold variable satisfy This ensures that the trigger threshold is always positive and bounded. The time interval between two adjacent trigger times satisfies ,in, , >0; In the closed-loop system, all signals satisfy the globally uniform bounded property, and the tracking error e(t) asymptotically converges to zero.

9. An electronic device, comprising: processor; as well as, A memory configured to store computer-executable instructions, which, when executed, cause the processor to perform the steps of the fault-tolerant tracking control method for a nonlinear time-varying system according to any one of claims 1-8.

10. A storage medium for storing computer-executable instructions, which, when executed, implement the steps of the fault-tolerant tracking control method for a nonlinear time-varying system according to any one of claims 1-8.

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