A Smart Learning Control Method for Fractional-Order Nonlinear Systems under Communication Constraints

Abstract

This invention relates to the field of system control and discloses an intelligent learning control method for fractional-order nonlinear systems under communication constraints. The method includes constructing a networked fractional-order nonlinear system with external disturbances and uncertainties; identifying unknown uncertain nonlinear functions in the system using a radial basis function neural network; constructing the system's compensation signal; and designing the system's virtual controller, actual neural network controller, and parameter adaptive law by combining the backstepping method and command filter scheme. The stability of the closed-loop system is proven, ensuring that the tracking error converges to a neighborhood near the origin, and guaranteeing that all signals in the closed-loop system are semi-globally consistent and eventually bounded. This innovative method has broad application prospects in the field of automatic control systems, and is particularly suitable for handling systems with complex nonlinearities and uncertainties.

Description

Technical Field

[0001] This invention relates to the field of system control, and more specifically to an intelligent learning control method for fractional-order nonlinear systems under communication constraints. Background Technology

[0002] As a frontier of mathematical and nonlinear science research, the control theory of fractional-order nonlinear systems has always been a hot topic and a challenging area for scholars. It has already been applied in fields such as power systems, chaotic systems, and flexible robotic arm systems. These practical systems often exhibit characteristics such as uncertainty and inherent nonlinearity, which are difficult to model precisely, posing significant difficulties and challenges to system analysis and synthesis. Intelligent control algorithms such as neural networks, fuzzy logic systems, and expert systems provide good solutions for analyzing the tracking control problem of uncertain fractional-order nonlinear systems.

[0003] When using network communication to transmit signals in fractional-order nonlinear systems, the controller design must consider how to reduce the signal transmission frequency between the actuator and the controller due to communication resource limitations. Existing event-triggered control strategies effectively address this issue. However, a crucial consideration in event-triggered control is avoiding Zeno's phenomenon, i.e., the triggering condition cannot be allowed to trigger indefinitely within a finite time. Studies show that event-triggered strategies do not exhibit Zeno's phenomenon in the absence of external disturbances. However, avoiding Zeno's phenomenon becomes a challenging task when arbitrarily small external disturbances exist in the system. Therefore, how to avoid Zeno's phenomenon in fractional-order nonlinear systems with external disturbances has attracted considerable attention. Existing literature suggests that treating the event triggering threshold as a dynamically changing threshold is more appropriate in controller design. This means that when the amplitude of the control signal is large, the triggering threshold is also relatively large, thus keeping the control signal constant for a long period. For system states close to equilibrium, a smaller triggering threshold can be used. Therefore, event-triggered relative threshold strategies for fractional-order nonlinear systems warrant further investigation.

[0004] In practical industrial applications, actuators can suddenly fail, leading to a significant deterioration in control system performance and even directly compromising its stability and safety, posing a major threat to the system's stability and reliability. Therefore, the study of fault-tolerant control schemes for fractional-order nonlinear systems has attracted considerable interest from researchers. However, when the system has partially unmeasurable states and unknown control gain, how to design a controller to cope with the effects of actuator failures and disturbances in fractional-order nonlinear systems is a problem that urgently needs to be solved. Summary of the Invention

[0005] The present invention aims to provide an intelligent learning control method for fractional nonlinear systems under communication constraints, so as to ensure the tracking performance of the fractional closed-loop system under external disturbances and actuator failures, and to make the tracking error converge to a neighborhood near the origin.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for intelligent learning control of a fractional-order nonlinear system under communication constraints includes:

[0008] S1. Construct a fractional-order nonlinear system with external disturbances, uncertainties, and actuator failures;

[0009] S2. Construct a state observer based on a radial basis function neural network;

[0010] S3. In steps 1 to n-1, the compensation signal is constructed by combining the Backstepping method, fractional Lyapunov stability theory, and fractional command filter. The virtual control signal and parameter adaptive law of the system are constructed by constructing Lyapunov functions related to the compensation tracking error signal and the neural network weight estimation error.

[0011] S4. In step n, an event triggering strategy with a relative threshold is introduced to construct an adaptive neural network event triggering fault-tolerant controller for actuator failures.

[0012] S5. Combining stability theory, verify the stability of the closed-loop fractional-order system, ensuring that the tracking error can converge to the neighborhood near the origin, that all signals in the closed-loop system are semi-globally consistent and eventually bounded, and that the time interval between event triggers has a lower limit.

[0013] The principle and advantages of this scheme are as follows: In practical applications, firstly, a radial basis function neural network is used to identify unknown smooth nonlinear functions. Then, a state observer based on a neural network is constructed to estimate the unknown state of the original system. Next, an adaptive neural event-triggered fault-tolerant controller is developed using the Backstepping method, a fractional-order instruction filter scheme, and Lyapunov stability theory. Under external disturbances and actuator failures, the proposed control strategy not only ensures the tracking performance of the fractional-order closed-loop system, bringing the tracking error to near the origin, but also guarantees that all signals in the system are semi-globally consistent and eventually bounded. Furthermore, the neural network-based observer can approximate the original system state well. This application addresses networked fractional-order nonlinear systems under communication constraints, effectively solving problems related to external disturbances, uncertainties, and actuator failures through adaptive parameter learning and intelligent compensation strategies. By introducing a fractional-order instruction filter, the "computational explosion" problem caused by repeatedly solving the fractional derivative of the virtual control input signal is successfully avoided. At the same time, the error of the filter is compensated, which effectively improves the tracking performance of the system. This application adopts a relative threshold event triggering strategy, which effectively reduces the signal transmission frequency between the controller domain actuators while ensuring tracking performance, thus saving communication resources.

[0014] Preferably, as an improvement, the model of the fractional-order nonlinear system is:

[0015]

[0016] in, It is the Caputo fractional derivative, where q represents the order of the fractional nonlinear system, and h... i Let g be a known constant, and g be an unknown and non-zero control gain. Represents an unknown smooth nonlinear function, x = [x1, x2, ..., xn]. n ] T D represents the state variable of the system. i (t) represents the external disturbance of the system, u F y(t) and y(t) represent the control input vector and output quantity of a fractional-order nonlinear system.

[0017] Technical benefits: This fractional-order nonlinear system model can be further applied to characterize power systems, chaotic systems, and flexible robotic arm systems with uncertainties.

[0018] Preferably, as an improvement, the actuator fault is represented as follows:

[0019] u F (t)=(1-d)v(t)+u0(t)

[0020] Where d represents the unknown partial failure rate satisfying 0≤d<1, v(t) is the event-triggered control signal, u0(t) is an unknown but bounded time-varying function representing the bias fault, and t≥t f , t f This indicates the time when the actuator failure occurred.

[0021] Technical benefits: Facilitates the simulation of actuator failures.

[0022] Preferably, as an improvement, the networked fractional-order nonlinear system constructed in S1 with external disturbances, uncertainties, and actuator failures satisfies:

[0023] Condition 1, reference signal y d , and It is smooth and bounded;

[0024] Condition 2: There exists a known constant. For any vector Make It holds true, where ||·|| represents the 2-norm of the system;

[0025] Condition 3, unknown external disturbance D i (t) is bounded, that is in It is an unknown constant.

[0026] Technical benefits: It can provide support for subsequent controller design and ensure the boundedness of all signals in the system.

[0027] Preferably, as an improvement, the state observer based on the radial basis function neural network is:

[0028]

[0029] in, It is a parameter The estimated value, It is an estimate of the parameter β; the observation error is defined. The observation error system is obtained as follows:

[0030]

[0031] Where K = [k1,…,k n ] T , Δf=[Δf1,…,Δf n ] T ,

[0032]

[0033] Technical effect: By analyzing the stability of the observer error system, it is possible to determine the estimation effect of the observer state on the original system state.

[0034] Preferably, as an improvement, S2 includes estimating the unknown nonlinear function and bias fault in the system using a radial basis function neural network, expressed as:

[0035]

[0036] in Let x and f represent respectively. i The estimated value of (x), For radial basis function neural networks, W i * This represents the optimal parameter vector of a radial basis function neural network, where T denotes the transpose sign. This represents the optimal estimation error of the neural network;

[0037] Under this radial basis function neural network, the original fractional-order nonlinear system is rewritten as:

[0038]

[0039] Where β=g(1-d),

[0040] Technical benefits: By using neural networks to estimate unknown nonlinear functions, uncertainties in the system can be effectively handled.

[0041] Preferably, as an improvement, S3 includes:

[0042] S31 defines the coordinate transformation related to tracking error;

[0043] S32 defines the compensation tracking error signal;

[0044] S33, Construct an adaptive neural network event-triggered fault-tolerant controller, including:

[0045] Based on the coordinate transformation, set the Lyapunov function in step 1 as follows:

[0046]

[0047] Where γ1,ρ1>0 both represent the design parameters. This indicates the parameter estimation error. yes The estimated value;

[0048] Find the α-th derivative of V1(t) to construct the virtual control signal α1 and the parameter adaptive law. Ξ1:

[0049]

[0050] Where τ1>0 and π1>0 are design parameters; substituting them into... have to:

[0051]

[0052] Based on the coordinate transformation, set the Lyapunov function in step i as follows:

[0053]

[0054] Where, γ i ,ρ i >0 indicates the design parameters. This indicates the parameter estimation error. Ξ1 is The estimated value;

[0055] For V i (t) Find the α-th derivative and construct the virtual control signal α. i Adaptive Law of Parameters for:

[0056]

[0057] Among them, l i >0,τ i >0,π i >0 is a design parameter; substitute it into... have to:

[0058]

[0059] Technical benefits: By designing Lyapunov functions and combining them with backstepping theory, it is possible to design virtual control signals for fractional-order nonlinear systems, providing a recursive solution for the final design of the actual controller.

[0060] Preferably, as an improvement, the coordinate transformation related to the definition and tracking error is as follows:

[0061] e1 = yy d ,

[0062] Where e1 represents the tracking error variable, y d The reference signal for tracking, Let x represent the state variable of the observer system. i,cThe output of a fractional-order command filter can be represented in the following form:

[0063]

[0064] Where δ,ξ>0,ψ i,1 =x i,c ,α i It is the virtual control signal for the input filter.

[0065] Technical benefits: The introduction of the instruction filter can avoid repeatedly solving for the derivative of the virtual control law in the backstepping method, thus avoiding the "computation explosion problem".

[0066] Preferably, as an improvement, the defined compensation tracking error signal is:

[0067]

[0068] in To compensate for the signal, for:

[0069]

[0070] Among them l i ,η i >0 is a known constant, Ξ i This is a parameter adaptive law.

[0071] Technical benefits: It can be used to compensate for errors caused by filter estimation, further ensuring the final tracking performance.

[0072] Preferably, as an improvement, the event triggering strategy is expressed as follows:

[0073]

[0074] Where φ(t) represents the control law, t k >0 represents the system policy update time, 0 < σ < 1. ζ>0, These are design parameters;

[0075] Set the Lyapunov function in step n as follows:

[0076]

[0077] Where, γ n ,γ β ,γ θ ,γ n All represent positive parameters of the design. This indicates the parameter estimation error. It is θ * The estimated value θ* =1 / β, β≠0;

[0078] For V n (t) Find the α-th order derivative and, using Young's inequality, the actual adaptive neural network event-triggered fault-tolerant controller and parameter adaptation law are:

[0079]

[0080] Where, τ n ,l β ,l θ It is a positive parameter of the design.

[0081] Technical effect: A relative threshold event triggering strategy can update the signals transmitted between the actuator and the controller, reduce signal transmission, and save communication resources. Attached Figure Description

[0082] Figure 1 A schematic diagram of the framework for an intelligent learning control method for a fractional-order nonlinear system under communication constraints;

[0083] Figure 2 A diagram of a networked fractional-order interconnected power system with external disturbances, uncertainties, and actuator failures;

[0084] Figure 3 For the state x1 and observer state of the fractional-order nonlinear system and reference signal y d A schematic diagram of the trajectory;

[0085] Figure 4 For the tracking error e1 and observation error of a fractional-order nonlinear system A schematic diagram of the trajectory;

[0086] Figure 5 For the state x2 and the observer state of the fractional-order nonlinear system and observation error A schematic diagram of the trajectory;

[0087] Figure 6 To compensate for the signal and adaptive parameters Trajectory diagram

[0088] Figure 7 For adaptive parameter Ξ1, A schematic diagram of the trajectory;

[0089] Figure 8 The control law is φ(t), the event-triggered control signal is v(t), and the actuator signal is u. F A schematic diagram of the trajectory of (t);

[0090] Figure 9 This is a schematic diagram of the number of events triggered, the measurement error m(t) of the trigger threshold, and its upper bound η1. Detailed Implementation

[0091] The following detailed description illustrates the specific implementation method:

[0092] The basic implementation examples are as follows: Figure 1 As shown:

[0093] A method for intelligent learning control of a fractional-order nonlinear system under communication constraints includes:

[0094] S1. Construct a networked fractional-order nonlinear system with external disturbances, uncertainties, and actuator failures. The fractional-order nonlinear system is as follows:

[0095]

[0096] in, It is the Caputo fractional derivative, where q represents the order of the fractional nonlinear system, and h... u Let g be a known constant, and g be an unknown and non-zero control gain. Represents an unknown smooth nonlinear function, x = [x1, x2, ..., xn]. n ] T D represents the state variable of the system. i (t) represents the external disturbance of the system, u F y(t) and y(t) represent the control input vector and output quantity of a fractional-order nonlinear system.

[0097] The actuator fault is represented as follows:

[0098] u F (t)=(1-d)v(t)+u0(t)

[0099] Where d represents the unknown partial failure rate satisfying 0≤d<1, v(t) is the event-triggered control signal, u0(t) is an unknown but bounded time-varying function representing the bias fault, and t≥t F , t F This indicates the time when the actuator failure occurred.

[0100] Construct a networked fractional-order nonlinear system with external disturbances, uncertainties, and actuator failures that satisfies:

[0101] Condition 1, reference signal y d , and It is smooth and bounded;

[0102] Condition 2: There exists a known constant. For any vector Make It holds true, where ||·|| represents the 2-norm of the system;

[0103] Condition 3, unknown external disturbance D i (t) is bounded, that is in It is an unknown constant.

[0104] S2. Construct a state observer based on a radial basis function neural network; specifically, the radial basis function neural network has a universal approximation property and can be used to estimate the unknown nonlinear function G(s) in a system. For a continuous function g(s) defined on Ξ, there exists a radial basis function neural network such that...

[0105]

[0106] in, Let ε represent the ideal weight vector, and let ε represent the estimation error of the neural network satisfying |ε| < ε. * , constant ε * >0. Then the original fractional-order nonlinear system can be further expressed as:

[0107]

[0108] Among them, state variables and For x and f i The estimated value of (x),

[0109] The unknown nonlinear function and bias fault in the system are estimated using a radial basis function neural network, which can be further expressed as follows:

[0110]

[0111] in Let x and f represent respectively. i The estimated value of (x), For radial basis function neural networks, W i * This represents the optimal parameter vector of a radial basis function neural network, where T denotes the transpose sign. This represents the optimal estimation error of the neural network.

[0112] Under this radial basis function neural network, the original fractional-order nonlinear system can be further rewritten as:

[0113]

[0114] Where β=g(1-d), This represents the estimation error of an unknown nonlinear function.

[0115] The above system can be written in vector form as follows:

[0116]

[0117] in:

[0118] K = [k1, ..., k n ] T , C = [1, 0, ..., 0] T , Δf=[Δf1,…,Δf n ] T D(t) = [D1(t), D2(t), ..., D n (t)] T ;

[0119]

[0120] The observer based on the radial basis function neural network is constructed as follows:

[0121]

[0122] Define the observation error variable of the system Based on the original fractional-order system and the neural network state observer, the corresponding error system is obtained as follows:

[0123]

[0124] in, This indicates the estimation error.

[0125] S3. In steps 1 to n-1, a novel compensation signal is constructed by combining the Backstepping method, fractional-order Lyapunov stability theory, and fractional-order command filter. By constructing a Lyapunov function related to the compensation tracking error signal and the neural network weight estimation error, the virtual control signal and parameter adaptive law of the system are constructed. Specifically, this includes:

[0126] Define and define coordinate transformations related to tracking error:

[0127] e1 = yy d ,

[0128] Where e1 represents the tracking error variable, y d The reference signal for tracking, Let x represent the state variable of the observer system.i,c The output of a fractional-order command filter can be represented in the following form:

[0129]

[0130] Where δ,ξ>0,ψ i,1 =x i,c ,α i It is the virtual control signal for the input filter.

[0131] Define the compensation tracking error signal as:

[0132]

[0133] in To compensate for the signal, for:

[0134]

[0135] Among them l i ,η i >0 is a known constant, Ξ i This is a parameter adaptive law.

[0136] The construction of an adaptive neural network event-triggered fault-tolerant controller specifically includes:

[0137] Based on the coordinate transformation, set the Lyapunov function in step 1 as follows:

[0138]

[0139] Where γ1,ρ1>0 both represent the design parameters. This indicates the parameter estimation error. Ξ1 is The estimated value.

[0140] Find the α-th derivative of V1(t), the virtual control signal α1, and the parameter adaptive law. Ξ1 is:

[0141]

[0142] Where τ1>0, π1>0 are both design parameters, and the virtual control signal α1 and the parameter adaptive law are used. Substitute Ξ1 have to:

[0143]

[0144] Based on the coordinate transformation, set the Lyapunov function in step i as follows:

[0145]

[0146] Where, γ i ,ρ i >0 indicates the design parameters. This indicates the parameter estimation error. Ξ1 is The estimated value;

[0147] For V i (t) Find the α-th derivative and construct the virtual control signal α. i And parameter adaptive law w i ,Ξ i for:

[0148]

[0149] Among them, l i >0,τ i >0,π i >0 is a design parameter, representing the virtual control signal α. i Adaptive Law of Parameters Substitution have to:

[0150]

[0151] Next, a relative threshold event triggering strategy is designed to update the signal transmitted between the actuator and the controller. This strategy allows for more flexible signal sampling time intervals. The event trigger signal v(t) will vary with the value of the measurement error m(t). This relative threshold triggering strategy can extend the interval, thereby reducing the triggering frequency and saving communication resources.

[0152] S4. In step n, a relative threshold event triggering strategy is introduced to construct an adaptive neural network event-triggered fault-tolerant controller for actuator failures. The event triggering strategy is expressed as:

[0153]

[0154] Where φ(t) represents the control law, t k >0 represents the system policy update time, 0 < σ < 1. ζ>0, These are the design parameters.

[0155] Set the Lyapunov function for step n as follows:

[0156]

[0157] Where, γ n ,γ β ,γ θ ,γ nAll represent positive parameters of the design. This indicates the parameter estimation error. It is θ * The estimated value θ * =1 / β, β≠0;

[0158] For V n (t) Find the α-th order derivative and, using Young's inequality, the actual adaptive neural network event-triggered fault-tolerant controller and parameter adaptation law are:

[0159]

[0160] Where, τ n ,l β ,l θ It is a positive parameter of the design.

[0161] S5. Combining stability theory, prove the stability of the closed-loop fractional-order system, ensuring that the tracking error can converge to the neighborhood near the origin, guaranteeing that all signals in the closed-loop system are semi-globally consistent and eventually bounded, and that the time interval between event triggers has a lower bound, thus avoiding Zeno behavior.

[0162] Based on the result of step n, the Lyapunov function is obtained. The fractional derivative is:

[0163]

[0164] in,

[0165] From the above formula, we get:

[0166]

[0167] in,

[0168]

[0169] According to the existing lemma, That is, the error signal is bounded and will converge to a compact set. Simultaneously, it is possible to obtain the closed-loop system Boundedness. Based on the relation. To obtain the tracking error e i The boundedness of the compensation signal needs to be proven. It is bounded. Construct the following Lypunov function:

[0170]

[0171] Its fractional derivative is obtained as follows:

[0172]

[0173] in,

[0174] For example:

[0175] Consider a networked fractional-order interconnected power system with external disturbances, uncertainties, and actuator failures, whose structure is as follows: Figure 2 As shown, its fractional-order model is:

[0176]

[0177] Where δ(t) and w(t) represent the relative operating angle and relative speed of the generator rotor, respectively; the system parameter P max ,P m ,H,D,P e Let ψ represent the generator's mechanical power, electromagnetic power, equivalent moment of inertia, equivalent damping coefficient, disturbance power amplitude, and disturbance power frequency, respectively. u(t) is the mechanical torque controlling the generator rotor speed. Select parameter value P. max / H=1,D / H=0.02,P m / H=0.2,P e / H=0.2593, ψ=1. Let x1=δ(t), x2=w(t), then the fractional model can be rewritten as:

[0178]

[0179] in:

[0180] q = 0.86, f1(x) = 0, h1 = g = 1,

[0181] D1(t)=0.2tanh(2t), D2(t)=-0.4sin(2πt).

[0182] In this simulation, a 5-node Gaussian function is selected, with the centers of the Gaussian nodes uniformly distributed over the interval [-1.5, 1.5] × [-1.5, 1.5], and a width of ι. i =2,i=1,...,5.

[0183] Other parameters are set to k1=50, k2=140, l1=70, l2=100, η1=0.13, ξ=0.8, δ=110, ρ1=0.5, π1=0.18, γ1=γ2=0.021, τ1=τ2=0.2,γ β =0.12,l β =0.15,γ θ=0.016,l θ =0.05, σ=0.3, ζ=0.6, c1 = c2 = 0.5. Partial initial conditions are: x1(0) = -0.02, x2(0) = 0.3. All other initial conditions are 0. The system's reference signal y d =sin(1.5t). The experimental simulation results are as follows: Figures 3-9 As shown.

[0184] Figure 3 The system state x1 and the observer state are displayed. and reference signal y d The trajectory. Figure 4 The system tracking error e1 and observation error are displayed. The trajectory. Figure 5 The system state x2 and the observer state are displayed. and observation error The trajectory. Compensation signal. and adaptive parameters The trajectory is as follows Figure 6 As shown. Adaptive parameter Ξ1, The trajectory is as follows Figure 7 As shown. Figure 8 The control law φ(t), the event-triggered control signal v(t), and the actuator signal u are shown. F The trajectory of (t). Figure 9 This diagram illustrates the number of event triggers, the trigger threshold measurement error m(t), and its upper bound η1. Simulation results show that the intelligent learning control method for fractional-order nonlinear systems under communication constraints proposed in this paper has good tracking performance, ensures the boundedness of all signals in the closed-loop system, and minimizes the transmission frequency of the control signal, thus saving communication resources.

[0185] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0186] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0187] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0188] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. An intelligent learning control method for a fractional-order nonlinear system under communication constraints, characterized in that, include: S1. Construct a fractional-order nonlinear system with external disturbances, uncertainties, and actuator failures; S2. Construct a state observer based on a radial basis function neural network; S3. In steps 1 to n-1, a compensation signal is constructed by combining the Backstepping method, fractional-order Lyapunov stability theory, and fractional-order command filter. A virtual control signal and parameter adaptive law for the system are constructed by building a Lyapunov function related to the compensation tracking error signal and the neural network weight estimation error. S3 includes: S31 defines the coordinate transformation related to tracking error; S32 defines the compensation tracking error signal; S33, Construct an adaptive neural network event-triggered fault-tolerant controller, including: Based on the coordinate transformation, set the Lyapunov function in step 1 as follows: Where γ1,ρ1>0 both represent the design parameters. This indicates the parameter estimation error. yes The estimated value; Find the α-th derivative of V1(t) to construct the virtual control signal α1 and the parameter adaptive law. Where τ1>0 and π1>0 are design parameters; substituting them into... have to: Based on the coordinate transformation, set the Lyapunov function in step i as follows: Where, γ i ,ρ i >0 indicates the design parameters. This indicates the parameter estimation error. yes The estimated value; For V i (t) Find the α-th derivative and construct the virtual control signal α. i Adaptive Law of Parameters for: Among them, l i >0,τ i >0,π i >0 is a design parameter; substitute it into... have to: S4. In step n, an event triggering strategy with a relative threshold is introduced to construct an adaptive neural network event triggering fault-tolerant controller for actuator failures. S5. Combining stability theory, verify the stability of the closed-loop fractional-order system, ensuring that the tracking error can converge to the neighborhood near the origin, that all signals in the closed-loop system are semi-globally consistent and eventually bounded, and that the time interval between event triggers has a lower limit.

2. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, The model of the fractional-order nonlinear system is as follows: in, It is the Caputo fractional derivative, where q represents the order of the fractional nonlinear system, and h... i f is a known constant, g is an unknown and non-zero control gain, and f is a constant. i (x):R n →R represents an unknown smooth nonlinear function, x=[x1,x2,...,x n ] T D represents the state variable of the system. i (t) represents the external disturbance of the system, u F y(t) and y(t) represent the control input vector and output quantity of a fractional-order nonlinear system.

3. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 2, characterized in that, The actuator fault is represented as follows: u F (t)=(1-d)v(t)+u0(t) Where d represents the unknown partial failure rate satisfying 0≤d<1, v(t) is the event-triggered control signal, u0(t) is an unknown but bounded time-varying function representing the bias fault, and t≥t F , t F This indicates the time when the actuator failure occurred.

4. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, The networked fractional-order nonlinear system constructed in S1 with external disturbances, uncertainties, and actuator failures satisfies the following: Condition 1, reference signal y d , and It is smooth and bounded; Condition 2: There exists a known constant. For any vector x, y ∈ R n Make It holds true, where ||·|| represents the 2-norm of the system; Condition 3, unknown external disturbance D i (t) is bounded, that is in It is an unknown constant.

5. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, The state observer based on the radial basis function neural network is: in, It is a parameter The estimated value, It is an estimate of the parameter β; the observation error is defined. The observation error system is obtained as follows: in, 6. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, S2 includes estimating unknown nonlinear functions and bias faults in the system using a radial basis function neural network, expressed as: in Let x and f represent respectively. i The estimated value of (x), For radial basis function neural networks, W i * This represents the optimal parameter vector of a radial basis function neural network, where T denotes the transpose sign. This represents the optimal estimation error of the neural network; Under this radial basis function neural network, the original fractional-order nonlinear system is rewritten as: Where β=g(1-d), 7. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, The coordinate transformation related to the definition and tracking error is as follows: Where e1 represents the tracking error variable, y d The reference signal for tracking, Let x represent the state variable of the observer system. i,c The output of a fractional-order command filter can be represented in the following form: Where δ,ξ>0,ψ i,1 =x i,c ,α i It is the virtual control signal for the input filter.

8. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, The defined compensation tracking error signal is: in To compensate for the signal, for: Among them l i ,η i >0 is a known constant. This is a parameter adaptive law.

9. The intelligent learning control method for a communication-constrained fractional-order nonlinear system according to claim 1, characterized in that, The event triggering strategy is expressed as follows: Where φ(t) represents the control law, t k >0 represents the system policy update time. These are design parameters; Set the Lyapunov function in step n as follows: Where, γ n ,γ β ,γ θ ,Υ n All represent positive parameters of the design. This indicates the parameter estimation error. yes The estimated value θ * =1 / β, β≠0; For V n (t) Find the α-th order derivative and, using Young's inequality, the actual adaptive neural network event-triggered fault-tolerant controller and parameter adaptation law are: in, It is a positive parameter of the design.

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