Aircraft adaptive fault-tolerant control method under multiple uncertainties

Abstract

The invention discloses a self-adaptive fault-tolerant control method for an aircraft under multiple uncertainties, and relates to the technical field of flight control, and the method comprises the steps: building an aircraft comprehensive model under multiple uncertainties; equivalently decomposing the aircraft comprehensive model into three subsystems based on additive state decomposition, and obtaining a control-oriented equivalent model of the three subsystems after model transformation; designing a first observer and a second observer; designing controllers: a proportional-integral controller, a self-adaptive controller and a state feedback controller; and adding the three controllers to obtain a composite controller, and combining the composite controller and the observer to obtain a final controller, thereby realizing adaptive fault-tolerant tracking control of the aircraft. According to the method, an aircraft system is decomposed into three subsystems according to an additive state decomposition theory, corresponding controllers are designed respectively, and finally the three designed controllers are added to obtain a composite controller, so that the robust tracking control requirement of the aircraft under multiple constraints such as input saturation is met.

Description

Technical Field

[0001] This invention relates to the field of flight control technology, specifically an adaptive fault-tolerant control method for aircraft under multiple uncertainties. Background Technology

[0002] In the field of aircraft development, flight control technology is one of the key core technologies for ensuring safe flight and mission completion. Whether it is hypersonic flight, complex maneuvers, or long-endurance cruise, stable operation and performance are highly dependent on flight control technology. However, in actual flight scenarios, multiple constraints such as unknown disturbances, input saturation, and actuator failures are often coupled together, leading to a sharp increase in the complexity of control system design.

[0003] Currently, existing flight control methods still have significant shortcomings in handling the aforementioned coupling problems: some control strategies may be able to handle one type of problem—unknown disturbances, input saturation, or actuator failure—individually, but lack an effective synergistic approach to address the comprehensive challenges posed by the coupling problem; other schemes considering multiple constraints often rely on complex coupled control law designs or precise aircraft models, resulting in overly complex final control designs. Therefore, aircraft tracking control systems must possess high precision, strong robustness, and adaptive control capabilities under strong uncertainty, actuator failure, and input saturation constraints, while also requiring a simple controller design.

[0004] Based on this, we now present an adaptive fault-tolerant control method for aircraft under multiple uncertainties, which can eliminate the drawbacks of existing technical solutions. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive fault-tolerant control method for aircraft under multiple uncertainties, so as to solve the problems of the shortcomings of existing flight control methods in the background art.

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

[0007] An adaptive fault-tolerant control method for aircraft under multiple uncertainties includes the following steps: Step S1: Establish a comprehensive model of the aircraft under multiple uncertainties; Step S2: Based on additive state decomposition, the integrated model of the aircraft is equivalently decomposed into three subsystems, namely a deterministic linear system, an uncertain nonlinear system without saturation, and a deterministic nonlinear system with only saturation. After model transformation, an equivalent model of three subsystems oriented towards control is obtained. Step S3: Based on the equivalent model of the three subsystems for control, design the first observer and the second observer for observing the state and output of the three subsystems; Step S4: Based on the equivalent model of the three subsystems for control, design three controllers: the deterministic linear system corresponds to the proportional-integral controller, the uncertain nonlinear system without saturation corresponds to the adaptive controller, and the deterministic nonlinear system with only saturation corresponds to the state feedback controller. Step S5: Add the three controllers together to obtain a composite controller. Combine the composite controller and the observer to obtain the final controller, thereby realizing the adaptive fault-tolerant tracking control of the aircraft.

[0008] Preferably, the multiple uncertainties include actuator failure, input saturation, and unknown disturbances, and the expression of the integrated aircraft model is: ; in, For the aircraft system status, To control the input, For system output, For the system matrix, For the input matrix, For the output matrix, For and A related nonlinear function vector, Due to unknown interference, The fault coefficient matrix satisfies , The actuator failure coefficient and satisfying The system expects the output to be expressed as , Represents a saturation function. The initial value is set for the system state;

[0009] The saturation function The expressions include: ; in, It is a saturation function. For input Minimum saturation limit, For input The maximum saturation limit; The system control objective is: to achieve the following in any initial state Under these conditions, when the aircraft system experiences actuator failure, input saturation, or unknown disturbances, adaptive fault-tolerant tracking control of the aircraft system is achieved, i.e., when... hour, .

[0010] Preferably, step S2 specifically includes: Decompose the integrated aircraft model containing actuator failure items and separate the actuator failure items; The integrated model of the aircraft is decomposed into a deterministic linear system and an uncertain nonlinear system, wherein the uncertain nonlinear system is a system containing actuator saturation. The system containing actuator saturation is decomposed into an uncertain nonlinear system without saturation and a deterministic nonlinear system containing only saturation, thereby obtaining three subsystems, namely a deterministic linear system, an uncertain nonlinear system without saturation, and a deterministic nonlinear system containing only saturation; Based on the model transformation, we obtain the equivalent models of the three subsystems oriented towards control.

[0011] Preferably, the expression for the actuator fault item is: ; in, Indicates actuator fault items, Represents a saturation function. To control input abbreviation, Actuator failure coefficient The abbreviation, and satisfying ;

[0012] Incorporating actuator fault items, the integrated model of the aircraft is represented as follows: ; in, for abbreviation, For the aircraft system status abbreviation, Saturation function abbreviation, Unknown interference abbreviation, Vector of nonlinear functions The abbreviation of .

[0013] Preferably, the determined linear system is represented as: ; in, To represent a deterministic linear system, It is a state related to expectations Related functions, expected state Satisfying the relation , The system's expected output abbreviation, To determine a linear system state, To determine a linear system Input, To determine a linear system The output;

[0014] The uncertain nonlinear system is represented as: ; in, To represent an uncertain nonlinear system, For uncertain nonlinear systems The state and satisfy the relation , For uncertain nonlinear systems The input satisfies the relation , For uncertain nonlinear systems The output satisfies the relation. , For system output This is an abbreviation for , and the initial value of the system is 0;

[0015] According to additive state decomposition, the system With the system The following relationship is satisfied between them: ; ; ;

[0016] The uncertain nonlinear system that does not contain saturation is represented as: ; in, This represents an uncertain nonlinear system that does not contain saturation. For the system state, For the system Input, For the system The output of is initialized to 0 in the system's initial state.

[0017] The deterministic nonlinear system containing only saturation is expressed as: ; in, This represents a deterministic nonlinear system containing only saturation. For the system The state and satisfy the relation , For the system The input satisfies the relation , For the system The output satisfies the relation. The initial state of the system is 0;

[0018] According to additive state decomposition, the system ,system With the system The following relationship is satisfied between them: ; ; ; The system ,system With the system This is an equivalent model for three subsystems oriented towards control.

[0019] Preferably, in step S3, the first observer is used to acquire the system. With the system The state and output are expressed as follows: ; in, , and They are respectively states , and output The estimate;

[0020] The second observer is used to acquire the system. With the system The state and output are expressed as follows: ; in, , and They are respectively states , and output The estimate.

[0021] Preferably, in step S4, the proportional-integral controller constructs an augmented vector based on the state of the linear system and the integral of the output tracking error to achieve system output tracking. The expression of the proportional-integral controller is: ; When hour, ; in, Indicates a proportional-integral controller. and The control gain matrix to be designed, It is the error integral and satisfies the relation , The system outputs tracking error and satisfies , As the integration variable, in the integration operation In, it is used to represent from 0 to Any time within the time interval.

[0022] Preferably, in step S4, the adaptive controller uses a radial basis function neural network to estimate and compensate for actuator faults and unknown disturbances, and designs an adaptive law for neural network weights to achieve system stabilization. The specific expression includes: ; ; When hour, ; in, This indicates an adaptive controller. For the matrix to be designed, and These are all controller parameters. It is a virtual output variable and satisfies the relation. , Unknown interference The estimated value, Actuator fault items The estimated value, The learning rate and satisfy , It is a Gaussian function. and The relationship between them is satisfied , For ideal weights The estimate.

[0023] Preferably, the expression for the state feedback controller in step S4 is: ; When hour, ; in, Indicates a state feedback controller. This is the feedback matrix to be designed.

[0024] Preferably, the composite controller in step S5 is the superposition of the controllers corresponding to the three subsystems, expressed as: ; in, Indicates a composite controller, such that when hour, .

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention decomposes the aircraft system into three subsystems based on additive state decomposition theory, then designs corresponding controllers for each subsystem, and finally adds the three designed controllers to obtain the final composite controller. By integrating actuator failures and unknown disturbances as composite uncertainties, a radial basis function neural network adaptive compensator is designed to approximate and dynamically cancel their effects online. This satisfies the robust tracking control requirements of the aircraft under multiple constraints such as input saturation, achieving high control accuracy and strong robustness. This invention fully considers the coupling effects of system nonlinearity, actuator failures, input saturation, and unknown disturbances, making it easy to achieve good trajectory tracking results and showing good application prospects. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the steps of the control method of the present invention; Figure 2 This is a schematic diagram of step S2 of the present invention; Figure 3 This is a closed-loop block diagram of the adaptive fault-tolerant controller for aircraft based on additive decomposition according to the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0028] like Figures 1-3 As shown, an adaptive fault-tolerant control method for aircraft under multiple uncertainties includes the following steps: Step S1: Establish a comprehensive model of the aircraft under multiple uncertainties;

[0029] In this embodiment, multiple uncertainties include actuator failure, input saturation, and unknown disturbances. The expression for the aircraft integrated model is: ; in, For the aircraft system status, To control the input, For system output, For the system matrix, For the input matrix, For the output matrix, For and A related nonlinear function vector, Due to unknown interference, The fault coefficient matrix satisfies , The actuator failure coefficient and satisfying The system expects the output to be expressed as , Represents a saturation function. The initial value is set for the system state;

[0030] Saturation function The expressions include: ; in, It is a saturation function. For input Minimum saturation limit, For input The maximum saturation limit;

[0031] For the expression of the integrated aircraft model, the following assumptions are made: Assumption 1: (A, B) is controllable; Assumption 2: The system state is measurable; The system control objective is: to achieve the following in any initial state Under these conditions, when the aircraft system experiences actuator failure, input saturation, or unknown disturbances, adaptive fault-tolerant tracking control of the aircraft system is achieved, i.e., when... hour, ; Step S2: Based on additive state decomposition, the integrated model of the aircraft is equivalently decomposed into three subsystems. The three subsystems are a deterministic linear system, an uncertain nonlinear system without saturation, and a deterministic nonlinear system with only saturation. After model transformation, an equivalent model of the three subsystems oriented towards control is obtained.

[0032] Among them, such as Figure 2 and Figure 3 As shown, this step specifically includes: Decompose the integrated aircraft model containing actuator failure items and separate the actuator failure items; The integrated model of the aircraft is decomposed into a deterministic linear system and an uncertain nonlinear system, wherein the uncertain nonlinear system is a system containing actuator saturation. The system containing actuator saturation is decomposed into an uncertain nonlinear system without saturation and a deterministic nonlinear system containing only saturation, resulting in three subsystems: a deterministic linear system, an uncertain nonlinear system without saturation, and a deterministic nonlinear system containing only saturation. Based on the model transformation, we obtain the equivalent models of the three subsystems oriented towards control.

[0033] In this embodiment, for the sake of simplicity, the time variables in this invention are omitted. The aircraft integrated model mentioned above is an aircraft model that includes actuator faults. Considering that a radial basis function neural network is needed to jointly estimate the disturbance and actuator fault terms, the actuator fault terms are separated:

[0034] Specifically, the expression for the actuator fault item is: ; in, Indicates actuator fault items, Represents a saturation function. To control input abbreviation, Actuator failure coefficient The abbreviation, and satisfying ;

[0035] Incorporating actuator failure terms, the integrated aircraft model can be represented as: ; in, for abbreviation, For the aircraft system status abbreviation, Saturation function abbreviation, Unknown interference abbreviation, Vector of nonlinear functions abbreviation;

[0036] In this embodiment, to simplify controller design, a model transformation is performed on the aircraft model considering multiple constraints, decomposing the comprehensive aircraft model expression (the original aircraft system equations) into a deterministic linear system. and uncertain nonlinear systems Due to uncertain nonlinear systems The defined aircraft model is subject to saturated nonlinear constraints, which increases the complexity of controller design. Therefore, this invention addresses this saturated nonlinearity by decoupling it, thus improving the system with actuator saturation. To reduce the aforementioned design complexity, an additive state decomposition is performed again, further decomposing it into an uncertain nonlinear system without saturation. and deterministic nonlinear systems containing only saturation The specific steps are as follows:

[0037] A linear system is represented as: ; in, To represent a deterministic linear system, It is a state related to expectations Related functions, expected state Satisfying the relation , The system's expected output abbreviation, To determine a linear system state, To determine a linear system Input, To determine a linear system The output is determined by the linear system. The state, input, and output of an uncertain nonlinear system can be defined. Based on the state, input, and output, we can conclude: , , ;

[0038] An uncertain nonlinear system is represented as: ; in, To represent an uncertain nonlinear system, the system For the original aircraft system equations and system The difference, For uncertain nonlinear systems The state and satisfy the relation , For uncertain nonlinear systems The input satisfies the relation , For uncertain nonlinear systems The output satisfies the relation. , For system output This is an abbreviation for , and the initial value of the system is 0;

[0039] According to additive state decomposition, the system With the system The following relationship is satisfied between them: ; ; ;

[0040] An uncertain nonlinear system without saturation is represented as: ; in, This represents an uncertain nonlinear system that does not contain saturation. For the system state, For the system Input, For the system The output of the system is given by an initial state of 0, and the system passes through an uncertain nonlinear system without saturation. The state, input, and output of a deterministic nonlinear system containing only saturation can be defined. Based on the state, input, and output, we can conclude: , , ;

[0041] A deterministic nonlinear system containing only saturation is expressed as: ; in, This represents a deterministic nonlinear system containing only saturation. For uncertain nonlinear systems With the system The difference, For the system The state and satisfy the relation , For the system The input satisfies the relation , For the system The output satisfies the relation. The initial state of the system is 0;

[0042] According to additive state decomposition, the system ,system With the system The following relationship is satisfied between them: ; ; ; system ,system With the system An equivalent model for three subsystems oriented towards control; Step S3: Based on the equivalent model of the three subsystems for control, design the first observer and the second observer for observing the state and output of the three subsystems;

[0043] In this embodiment, in step S3, the first observer is used to acquire the system. With the system The state and output are expressed as follows: ; in, , and They are respectively states , and output The estimate;

[0044] The second observer is used to acquire system data. With the system The state and output are expressed as follows: ; in, , and They are respectively states , and output The estimate; Step S4: Based on the equivalent model of the three subsystems for control, design three controllers accordingly: determine the proportional-integral controller for the linear system, the adaptive controller for the uncertain nonlinear system without saturation, and the state feedback controller for the deterministic nonlinear system with only saturation.

[0045] In this embodiment, for a given linear system The controller is designed to achieve system output tracking. Therefore, this invention designs a proportional-integral (PI) controller, which can construct an augmented vector based on the state of a deterministic linear system and the integral of the output tracking error to achieve system output tracking. The expression of the PPI controller is as follows: ; When hour, ; in, Indicates a proportional-integral controller. and The control gain matrix to be designed, It is the error integral and satisfies the relation , The system outputs tracking error and satisfies , As the integration variable, in the integration operation In, it is used to represent from 0 to Any time within the time interval;

[0046] For uncertain nonlinear systems that do not contain saturation The controller is designed to achieve system stabilization. Therefore, this invention designs an adaptive controller. The adaptive controller uses a radial basis function neural network to estimate and compensate for actuator faults and unknown disturbances. An adaptive law for neural network weights is designed to achieve system stabilization. The specific operation is as follows: First, design a virtual output variable: , For the matrix to be designed, For the system The state; In practical engineering, due to unknown interference and actuator fault items Since both are unknown, a radial basis function neural network is used to estimate and compensate for the unknown disturbances and actuator faults, as shown below: , Unknown interference The estimated value, Actuator fault items The estimated value, For ideal weights The estimate, The function is Gaussian, and the radial basis function neural network is the core component used to estimate and compensate for actuator faults and unknown disturbances;

[0047] Then, an adaptive controller and an adaptive law for neural network weights are designed to handle system nonlinearity and uncertainty. The adaptive law is a parameter adjustment rule that complements the adaptive controller and is used to update the neural network weights online to compensate for uncertainty. The adaptive controller is expressed as follows: ; ; When hour, ; in, This indicates an adaptive controller. and These are all controller parameters. It is a virtual output variable and satisfies the relation. , The learning rate and satisfy ;

[0048] For deterministic nonlinear systems containing only saturation The controller is designed to quickly remove the control input from the saturation state and achieve system stabilization. Therefore, this invention designs a state feedback controller, the expression of which is: ; When hour, ; in, Indicates a state feedback controller. The feedback matrix to be designed; Step S5: Add the three controllers together to obtain a composite controller. Combine the composite controller with the observer to obtain the final controller, thereby realizing the adaptive fault-tolerant tracking control of the aircraft.

[0049] In this embodiment, since the three sub-problems have been solved above, the control problem of the original system equations is thus solved, resulting in the final designed composite controller for the original aircraft system (integrated aircraft model). The composite controller is the superposition of the controllers corresponding to the three subsystems, and its expression is: ; in, Indicates a composite controller, such that when hour, ; The system control objective is thus achieved as follows: in any initial state Under these conditions, when the aircraft system experiences actuator failure, input saturation, or unknown disturbances, adaptive fault-tolerant tracking control of the aircraft system is achieved, i.e., when... hour, ;

[0050] Specifically, taking the tracking control of a hypersonic vehicle as an example, we will design an adaptive fault-tolerant controller:

[0051] Step S1, the longitudinal dynamic model expression of the hypersonic vehicle is:

[0052] The model includes 5 state variables. and 2 control inputs , For flight speed, For height, For the angle of attack, For the track angle, The pitch angular velocity, To deflect the elevator, For throttle valve opening, For thrust, For lift, For the mass of the aircraft, It is the acceleration due to gravity. As resistance, For pitching moment, It is the moment of inertia;

[0053] This model can be represented as: ,in, This represents a synthesis function of the longitudinal dynamics model of a hypersonic vehicle, which is transformed into an expression style of the vehicle's synthesis model through model transformation: ; in, The state of the aircraft system satisfies the following relation. , , and To achieve equilibrium, To control the input and satisfy the relational expression , The system output must satisfy the relational expression. , The initial state satisfies the relation. , The initial values ​​are assigned to the system. Is and A related nonlinear term, The saturation function is represented by the system matrix. The input matrix is The output matrix is The fault coefficient matrix is , and All are actuator failure coefficients. Indicates lumped interference;

[0054] The expression for the actuator fault item is: Combined with actuator fault items The longitudinal dynamics model of a hypersonic vehicle can be expressed as: ;

[0055] Step S2: To simplify the controller design, the longitudinal dynamics model expression of the hypersonic vehicle (the original vehicle system equations) is decomposed into a deterministic linear system. Uncertain nonlinear systems without saturation and deterministic nonlinear systems containing only saturation The specific steps are as follows:

[0056] Determine linear system The expression is: ;

[0057] Uncertain nonlinear systems without saturation The expression is: ;

[0058] Deterministic nonlinear systems containing only saturation The expression is: ; in, The desired state and satisfying the relation , To determine a linear system The state and satisfy the relation , To determine a linear system The output satisfies the relation. , For the system The state and satisfy the relation , For the system The output satisfies the relation. , For the system The state and satisfy the relation , For the system The output satisfies the relation. , , and These are the control inputs for the three subsystems;

[0059] Step S3: Design the following two observers to observe the states of the three subsystems. The first observer is used to acquire system... With the system The state and output are expressed as follows: ;

[0060] The second observer is used to acquire system data. With the system The state and output are expressed as follows: ; in, and They are states and output The estimate, and They are states and output The estimate, and They are states and output The estimate; Step S4: Design three controllers: determine the proportional-integral controller for linear systems, the adaptive controller for uncertain nonlinear systems without saturation, and the state feedback controller for deterministic nonlinear systems with only saturation. For the system The system outputs tracking error. Considering the error integral, it is defined as: ; An augmenting system can be represented as: ; The proportional-integral controller expression is: ; in, , The gain matrix is ​​determined using a linear quadratic regulator method. For the system Design an adaptive controller. For the redefinition of the output matrix, according to the Lyapunov function, there exists a matrix... and Make: Output matrix It can be determined as follows: ;

[0061] The expression for the adaptive controller is: ; in, , ; The adaptive law is: ;

[0062] For the system Design a state feedback controller with the following expression: ; in, It can be determined through pole placement;

[0063] Step S5: The final controller is composed of the controllers and observers of each subsystem. .

[0064] In summary, this invention fully considers the coupling effects of system nonlinearity, actuator failure, input saturation, and unknown interference, making it easy to achieve good trajectory tracking results and showing good application prospects.

[0065] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An adaptive fault-tolerant control method for aircraft under multiple uncertainties, characterized in that, Specifically, the following steps are included: Step S1: Establish a comprehensive model of the aircraft under multiple uncertainties; Step S2: Based on additive state decomposition, the integrated model of the aircraft is equivalently decomposed into three subsystems, namely a deterministic linear system, an uncertain nonlinear system without saturation, and a deterministic nonlinear system with only saturation. After model transformation, an equivalent model of three subsystems oriented towards control is obtained. Step S3: Based on the equivalent model of the three subsystems for control, design the first observer and the second observer for observing the state and output of the three subsystems; Step S4: Based on the equivalent model of the three subsystems for control, design three controllers: the deterministic linear system corresponds to the proportional-integral controller, the uncertain nonlinear system without saturation corresponds to the adaptive controller, and the deterministic nonlinear system with only saturation corresponds to the state feedback controller. Step S5: Add the three controllers together to obtain a composite controller. Combine the composite controller and the observer to obtain the final controller, thereby realizing the adaptive fault-tolerant tracking control of the aircraft.

2. The adaptive fault-tolerant control method for aircraft under multiple uncertainties according to claim 1, characterized in that, The multiple uncertainties include actuator failure, input saturation, and unknown disturbances. The expression for the comprehensive aircraft model is: ； in, For the aircraft system status, To control the input, For system output, For the system matrix, For the input matrix, For the output matrix, For and A related nonlinear function vector, Due to unknown interference, The fault coefficient matrix satisfies , The actuator failure coefficient and satisfying The system expects the output to be expressed as , Represents a saturation function. The initial value is set for the system state; The saturation function The expressions include: ； in, It is a saturation function. For input Minimum saturation limit, For input The maximum saturation limit; The system control objective is: to achieve the following in any initial state Under these conditions, when the aircraft system experiences actuator failure, input saturation, or unknown disturbances, adaptive fault-tolerant tracking control of the aircraft system is achieved, i.e., when... hour, .

3. The adaptive fault-tolerant control method for aircraft under multiple uncertainties according to claim 1, characterized in that, Step S2 specifically includes: Decompose the integrated aircraft model containing actuator failure items and separate the actuator failure items; The integrated model of the aircraft is decomposed into a deterministic linear system and an uncertain nonlinear system, wherein the uncertain nonlinear system is a system containing actuator saturation. The system containing actuator saturation is decomposed into an uncertain nonlinear system without saturation and a deterministic nonlinear system containing only saturation, thereby obtaining three subsystems, namely a deterministic linear system, an uncertain nonlinear system without saturation, and a deterministic nonlinear system containing only saturation; Based on the model transformation, we obtain the equivalent models of the three subsystems oriented towards control.

4. The adaptive fault-tolerant control method for aircraft under multiple uncertainties according to claim 3, characterized in that, The expression for the actuator fault item is: ； in, Indicates actuator fault items, Represents a saturation function. To control input abbreviation, Actuator failure coefficient The abbreviation, and satisfying ; Incorporating actuator fault items, the integrated model of the aircraft is represented as follows: ； in, for abbreviation, For the aircraft system status abbreviation, Saturation function abbreviation, Unknown interference abbreviation, Vector of nonlinear functions The abbreviation of .

5. The adaptive fault-tolerant control method for an aircraft under multiple uncertainties according to claim 3, characterized in that, The defined linear system is represented as follows: ； in, To represent a deterministic linear system, It is a state related to expectations Related functions, expected state Satisfying the relation , The system's expected output abbreviation, To determine a linear system state, To determine a linear system Input, To determine a linear system The output; The uncertain nonlinear system is represented as: ； in, To represent an uncertain nonlinear system, For uncertain nonlinear systems The state and satisfy the relation , For uncertain nonlinear systems The input satisfies the relation , For uncertain nonlinear systems The output satisfies the relation. , For system output This is an abbreviation for , and the initial value of the system is 0; According to additive state decomposition, the system With the system The following relationship is satisfied between them: ； ； ； The uncertain nonlinear system that does not contain saturation is represented as: ； in, This represents an uncertain nonlinear system that does not contain saturation. For the system state, For the system Input, For the system The output of is initialized to 0 in the system's initial state. The deterministic nonlinear system containing only saturation is expressed as: ； in, This represents a deterministic nonlinear system containing only saturation. For the system The state and satisfy the relation , For the system The input satisfies the relation , For the system The output satisfies the relation. The initial state of the system is 0; According to additive state decomposition, the system ,system With the system The following relationship is satisfied between them: ； ； ； The system ,system With the system This is an equivalent model for three subsystems oriented towards control.

6. The adaptive fault-tolerant control method for an aircraft under multiple uncertainties according to claim 1, characterized in that, In step S3, the first observer is used to acquire the system. With the system The state and output are expressed as follows: ； in, , and They are respectively states , and output The estimate; The second observer is used to acquire the system. With the system The state and output are expressed as follows: ； in, , and They are respectively states , and output The estimate.

7. The adaptive fault-tolerant control method for aircraft under multiple uncertainties according to claim 1, characterized in that, In step S4, the proportional-integral controller constructs an augmented vector based on the state of the linear system and the integral of the output tracking error to achieve system output tracking. The expression for the proportional-integral controller is: ； When hour, ; in, Indicates a proportional-integral controller. and The control gain matrix to be designed, It is the error integral and satisfies the relation , The system outputs tracking error and satisfies , As the integration variable, in the integration operation In, it is used to represent from 0 to Any time within the time interval.

8. The adaptive fault-tolerant control method for aircraft under multiple uncertainties according to claim 1, characterized in that, In step S4, the adaptive controller uses a radial basis function neural network to estimate and compensate for actuator faults and unknown disturbances. An adaptive law for the neural network weights is designed to achieve system stabilization. The specific expression includes: ； ； When hour, ; in, This indicates an adaptive controller. For the matrix to be designed, and These are all controller parameters. It is a virtual output variable and satisfies the relation. , Unknown interference The estimated value, Actuator fault items The estimated value, The learning rate and satisfy , It is a Gaussian function. and The relationship between them is satisfied , For ideal weights The estimate.

9. The adaptive fault-tolerant control method for an aircraft under multiple uncertainties according to claim 1, characterized in that, The expression for the state feedback controller in step S4 is: ； When hour, ; in, Indicates a state feedback controller. This is the feedback matrix to be designed.

10. The adaptive fault-tolerant control method for an aircraft under multiple uncertainties according to claim 1, characterized in that, The composite controller in step S5 is the superposition of the controllers corresponding to the three subsystems, and its expression is: ； in, Indicates a composite controller, such that when hour, .

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