A data-driven learning control method for hypersonic vehicles

Abstract

The present invention belongs to the technical field of hypersonic aircraft control, and relates to a data-driven learning control method for hypersonic aircraft. The purpose of the present invention is to provide a data-driven learning control method to realize stable tracking control of non-minimum phase hypersonic aircraft. The method includes constructing a longitudinal dynamics model of a non-minimum phase hypersonic aircraft; realizing zero dynamic reconstruction of the system by redefining the output; based on the deep Koopman operator theory, using a pre-collected data set to train the weights of a radial basis neural network, and accurately modeling the output redefinition dynamic equation. Design a data-driven output redefinition optimization learning controller to achieve stable tracking of reference instructions. The method is a data-driven learning control method and system for hypersonic aircraft, and has broad application prospects.

Description

Technical Field

[0001] The present invention belongs to the technical field of hypersonic aircraft control and relates to a data-driven learning control method for a hypersonic aircraft. Background Art

[0002] Since most hypersonic vehicles use a tail-controlled layout, traditional modeling cannot ignore the effect of the elevator on lift, and the dynamic model exhibits non-minimum phase characteristics. Non-minimum phase characteristics are a potential risk that affects the safe flight of hypersonic vehicles. If the controller is not designed properly, it will lead to zero dynamic divergence and destroy the stability of the system. For non-minimum phase systems, not only output tracking but also zero dynamic stabilization should be considered. Especially in the early stages of hypersonic vehicle maneuvering climb, in order to ensure flight safety and stable control, it is crucial to overcome the unstable zero dynamics in the model.

[0003] The patent "Neural network control method for hypersonic aircraft based on online data learning" (patent, Northwestern Polytechnical University, CN 107479382 B, 20191022) proposes a neural network control method for hypersonic aircraft based on online data learning, which can solve the technical problem of poor stability of existing hypersonic aircraft control methods. However, the steps of this method are relatively cumbersome in the design process, and the neural network control system needs to complete complex calculations in a very short time to ensure the real-time performance of the control commands, which is not conducive to engineering implementation and affects the operational safety and control accuracy of the aircraft. In addition, this method ignores the influence of the non-minimum phase characteristics of hypersonic aircraft, which poses potential risks to the safe flight of hypersonic aircraft.

[0004] The patent "Neural network composite learning control method for hypersonic aircraft based on high-gain observer" (patent, Northwestern Polytechnical University, CN 107632518 B, 20191018) proposes a neural network composite learning control method for hypersonic aircraft based on a high-gain observer to solve the technical problem of poor practicality of existing hypersonic aircraft control methods. However, while the high-gain observer improves the observation performance of the system, it also increases the system's sensitivity to noise, further affecting the accuracy and stability of the control system. In addition, the neural network composite learning control method may face challenges in processing speed and real-time performance, making it difficult for the system to respond in a very short time to adapt to the rapidly changing flight environment.

[0005] The patent "A global stabilization control method and system for hypersonic aircraft" (patent, Beijing Institute of Technology, CN114296352 A, 2022100) proposes a global stabilization control method for hypersonic aircraft to solve the global stabilization control problem of non-minimum phase hypersonic aircraft. However, the design process of this method is cumbersome, and the designed control scheme requires a high degree of modeling accuracy, which is not conducive to engineering implementation.

[0006] The paper "Adaptive robust fault-tolerant control of non-minimum phase hypersonic aircraft [J]. Journal of Northwestern Polytechnical University, 2021, 39: 1-9.) proposed an adaptive robust fault-tolerant control method based on output redefinition, which comprehensively considered the problems of rudder jamming and failure and system parameter uncertainty. Although the method in the paper can handle certain faults and interferences, its adaptability and robustness to complex or extreme fault conditions may be insufficient. In addition, the adaptive control strategy based on output redefinition requires a lot of calculations, and the computational complexity and resource consumption in real-time applications may limit its application.

[0007] The importance of considering non-minimum phase problems has been ignored in the prior art, which places higher demands on the control system design. Especially when faced with extreme flight conditions or emergencies, this may cause the control system to behave unstable in actual operation. In addition, existing control methods are usually based on specific assumptions about the aircraft model, which may lead to inflexible and poorly adaptable control strategies in practical applications, and may not be effective when dealing with unforeseen aircraft behaviors or environmental changes. In the current trend of technological development, data-driven and intelligent learning technologies (such as machine learning and artificial intelligence) play an important role in improving the performance and adaptability of the system. The prior art has failed to utilize these advanced technologies to optimize the control strategy, especially when faced with complex and highly dynamic flight environments, and lacks effective learning and adaptation mechanisms. Summary of the invention

[0008] The purpose of the present invention is to provide a data-driven learning control method to achieve stable tracking control of a non-minimum phase hypersonic aircraft.

[0009] The technical solution of the present invention is as follows:

[0010] A data-driven learning control method for a hypersonic vehicle includes: constructing a longitudinal dynamics model of a non-minimum phase hypersonic vehicle; realizing zero dynamic reconstruction of the system by redefining the output; based on the deep Koopman operator theory, using a pre-collected data set to train the weights of a radial basis neural network to accurately model the output redefinition dynamic equation; designing a data-driven output redefinition optimization learning controller to achieve stable tracking of reference instructions. The details are as follows:

[0011] (1) Constructing a longitudinal dynamics model of a non-minimum phase hypersonic vehicle

[0012]

[0013] Where V is the speed of the hypersonic vehicle, h is the flight altitude, γ is the track angle, θ is the pitch angle, Q is the pitch rate, α is the angle of attack, and θ=γ+α is satisfied. T, L, and D are thrust, pull, and drag, respectively. M is the pitch moment, m is the mass of the vehicle, g is the acceleration of gravity, and I yy is the moment of inertia. V d γ d Q They represent the external disturbances of the velocity subsystem, track angle subsystem, and pitch rate subsystem, respectively, and η i represents the elastic mode, ζ i represents the damping factor, ω i represents the natural oscillation frequency, N i represents generalized force, i=1,2 means considering the second-order mode.

[0014] (2) Systematic zero-dynamic reconstruction of output redefinition

[0015] For the velocity subsystem, V = f V -g V Φ+d V Where: f V and g V represents the transformed kinetic model coefficient, d V represents the external disturbance of the speed subsystem, and Φ represents the control input of the speed subsystem, namely, the fuel equivalence ratio.

[0016] For the height subsystem, in order to deal with the impact of non-minimum phase characteristics on system stability, it is necessary to construct a stable zero dynamic by redefining the output. According to the equal convergence principle, the redefined output H is selected and expressed as:

[0017] H=h+λ * θ(2)

[0018] Where: * H is the combination coefficient to be designed. * =h * +λ * θ * represents the reference command of the equilibrium point, where h * is the height reference command of the balance point, θ * It is the attitude reference instruction of the balance point.

[0019] make Combined with the velocity V at the equilibrium point* , the dynamic pressure at the equilibrium point can be obtained Pitch angle θ * 、Fuel equivalence ratio Φ * , and the elevator command δ e * .

[0020] (3) Accurate modeling based on deep Koopman operator theory

[0021] In order to achieve the learning of the combination coefficient λ within a reasonable operating range * , combined with the deep Koopman operator theory, the deep neural network is trained using the pre-collected data set to accurately model the output redefine dynamic equation. Specifically: for the current time k, define the state x corresponding to the state x at time k k , the control input u at time k corresponds to the input u k , and the next state x k+1 , R n represents an n-dimensional vector consisting of real numbers. Using the discrete time expression x k+1 =f(x k ,u k ), where The state quantity from the current state quantity and control quantity to the state quantity at the next moment can be expressed as a mapping R 3 ×R 4 |→R 3 , and the mapping is unknown. Therefore, the state of the lift space is described as Construct the Koopman operator structure, define the Koopman function as K, and use Implement a finite-dimensional approximation of K, where x * ∈R 7 The state of being promoted. Definition As a set of observations composed of l-dimensional data for actual flight calculation, l is the number of observations, represents the state value of the equilibrium point at time k, Represents the observation information of the i-th dimension data.

[0022] To evaluate the dynamic expression x k+1 =f(x k ,u k ), the Koopman approximation of , defines the following model:

[0023]

[0024] Where: For x k The estimated value of A∈R l×l , B∈Rl×4 , C∈R l×4 is the system matrix of the model in formula (3), which can be calculated by solving the following optimization problem

[0025]

[0026] Where: x k + Represents x k in u k Evolution of the dataset Contains M sequence snapshots, which are used in the optimization process. Through the original data learning and solving equation (4), we get the A, B, C matrices, while satisfying x k+1 =f(x k ,u k ) and y k =x k +1.

[0027] The observed quantity should contain as much nonlinear dynamic information as possible required for the output redefinition system. N groups of initial states randomly generated within the permissible flight range are selected for the construction of the training database. For each initial state, a combination coefficient λ of S samples is generated within a custom range that meets the requirements. * Considering that each set of initial states only stores one combination coefficient λ * , the proportional-integral-derivative (PID) controller with the same simulation environment and simulation parameters is used to test the robustness and tracking performance. Finally, the corresponding combination coefficient λ that takes into account both robustness and performance is obtained * , forming the lifting state vector corresponding to time k and observables in x c Represents its state reference quantity. On this basis, the deep neural network is trained using the pre-collected data set to obtain the dynamic equation x k+1 =f(x k ,u k ). For the loss function design of deep neural network training, based on the data pairs obtained in the above process, a weighted K-step prediction error is used. It is expressed as:

[0028]

[0029] Among them, r∈[0,1] represents the decay factor, Indicates that x is obtained through the deep Koopman operator k+1 The k-th step forward prediction error.

[0030] The system output is redefined with the help of the deep Koopman operator so that all V* 、h * The root of the zero dynamics is located in the left half plane of the coordinate system, and H is the minimum phase output, which can be used for the control design of step (4).

[0031] The reconstructed external dynamic structure is as follows:

[0032]

[0033] Where: d H (t,x) and d ψ (t, x, u) represent mismatched disturbance and matched disturbance respectively; ψ=Vsinγ+λ * Q,f ψ and g ψ represents the nominal known terms related to the model parameters.

[0034] (4) Optimizing learning control design based on data-driven output redefinition

[0035] Define the reference signal of the speed subsystem and reconstruction system as V d and H d , the corresponding tracking error is e V =VV d and e H =HH d The design fuel equivalence ratio command, virtual controller and elevator control command are:

[0036]

[0037] Where: k V >0,k H >0,k ψ >0 is a positive parameter to be designed. f and its micro-amount By virtual controller ψ d It is obtained by introducing a first-order filter and defining e ψ =ψ-ψ f is the tracking error of the redefinition attitude subsystem. and is the observed value of the disturbance term, which is expressed as the following data-driven neural perturbation observer:

[0038]

[0039] Where: z V 、z H 、z ψ They represent the observation errors of the velocity subsystem, the redefinition altitude subsystem, and the redefinition attitude subsystem, respectively, and η V =e V –zV , η H =e H –z H , η ψ =e ψ –z ψ .μ V >0,μ H >0,μ ψ >0 is a positive parameter to be designed. When x=V,H,ψ, use The disturbance term is estimated, where represents the estimated neural network weight vector, S x Denotes the corresponding basis function. Define the identification data storage stack and the overall data storage stack as and Among them l x Indicates the maximum number of rows, J x Indicates the maximum number of columns. Select and As the current storage stack, where 0≤j x ≤J x .

[0040] The following two-step online learning enhancement mechanism is designed to update the state changes of the data stack.

[0041]

[0042] Where: S1 and S2 are two online learning enhancement steps. In order to express the characteristics of data-driven, we select point As a data-driven update data point, the point The corresponding latest data storage stack and the latest overall data storage stack are defined as and in For point The corresponding tracking error, observation error, neural network weight vector and corresponding basis function. x (j x )=minSVD(D x (:,j x )) represents the minimum singular value. ρ x is a small positive constant to be designed. Indicates using the latest system data The target column to update.

[0043] Furthermore, the prediction error is constructed as

[0044]

[0045] Where: k x and represents the positive parameter to be designed, Indicates the jxth column reference instruction. and From the jxth column data stack D x (:,j x )get.

[0046] Beneficial effects of the present invention:

[0047] The present invention not only overcomes the limitations of traditional control strategies by introducing a data-driven learning control method, but also enables more precise and dynamic control of hypersonic vehicles. This technology uses real-time data analysis and machine learning algorithms to dynamically adjust the output redefine system reconstruction parameters, thereby effectively dealing with non-minimum phase problems and enhancing the control system's ability to adapt to uncertainties and changing conditions.

[0048] The present invention effectively copes with non-minimum phase problems through a data-driven learning control strategy, thereby improving the stability and reliability of the control system. The introduction of intelligent control technology enhances the adaptability and flexibility of the system, and can cope with uncertainty problems more flexibly. In addition, the present invention utilizes advanced data analysis and machine learning techniques to dynamically adjust control parameters, which not only overcomes the limitations of traditional control strategies, but also enhances the system's adaptability to complex and highly dynamic environments. This method improves the overall performance and response speed of the aircraft control system. Although the intelligent control strategy based on output redefinition requires more calculations, the present application reduces the computational complexity and resource consumption in real-time applications by optimizing algorithms and calculation processes, making this advanced control strategy more feasible and efficient in actual flight missions. In general, the data-driven learning control method and system of the present application show higher accuracy and adaptability when dealing with aircraft control problems, especially in the face of complex and uncertain factors in aircraft design and control, providing a more efficient and practical solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a technical block diagram of the data-driven learning control method for hypersonic vehicles;

[0050] Figure 2 It is a hypersonic aircraft speed tracking simulation curve diagram;

[0051] Figure 3 is a time graph of the velocity tracking error of a hypersonic vehicle;

[0052] Figure 4 It is a hypersonic aircraft altitude tracking simulation curve diagram;

[0053] Figure 5It is a time graph of the altitude tracking error of a hypersonic vehicle;

[0054] Figure 6 is a hypersonic vehicle track angle time curve;

[0055] Figure 7 It is a graph of the angle of attack time of a hypersonic vehicle;

[0056] Figure 8 is a hypersonic vehicle pitch rate time graph;

[0057] Fig. 9 is the time curve of elastic mode of hypersonic vehicle;

[0058] Fig.10 It is a hypersonic vehicle fuel equivalence ratio time curve;

[0059] Fig.11 It is a time curve diagram of the elevator command of a hypersonic vehicle. DETAILED DESCRIPTION

[0060] The following further illustrates the implementation of the present invention in conjunction with the accompanying drawings and technical solutions.

[0061] like Figure 1 As shown, a data-driven learning control method for a hypersonic aircraft of the present invention comprises:

[0062] (1) constructing a longitudinal dynamics model of a non-minimum phase hypersonic vehicle; based on the multi-time scale principle, the longitudinal dynamics model is divided into a velocity subsystem and an altitude subsystem; the velocity subsystem uses the velocity as an output signal and the fuel equivalence ratio as an input signal, and the altitude subsystem uses the altitude as an output signal and the elevator deflection angle as an input signal;

[0063] (2) Achieve zero dynamic reconstruction of the system by redefining the output;

[0064] (3) Based on the deep Koopman operator theory, the weights of the radial basis neural network are trained using a pre-collected dataset to accurately model the output redefinition dynamic equations;

[0065] (4) Design a data-driven output redefinition optimization learning controller to achieve stable tracking of reference instructions.

[0066] Specifically, the embodiments of the present invention are described as follows:

[0067] (1) A longitudinal dynamic model of a non-minimum phase hypersonic vehicle is constructed, and the main variables are defined as follows: V is the velocity of the hypersonic vehicle, h is the flight altitude, γ is the track angle, θ is the pitch angle, Q is the pitch rate, α is the angle of attack, and θ = γ + α is satisfied. T, L, and D are thrust, drag, and drag, respectively. M is the pitch moment, m is the mass of the vehicle, g is the gravitational acceleration, and I yy is the moment of inertia. V d γ d Q They represent the external disturbances of the velocity subsystem, track angle subsystem, and pitch rate subsystem, respectively, and η i represents the elastic mode, ζ i represents the damping factor, ω i represents the natural oscillation frequency, N i represents the generalized force, i=1,2 means considering the second-order mode. Combining the knowledge of dynamics and kinematics, the non-minimum phase hypersonic vehicle model is expressed as follows:

[0068]

[0069] Based on the multi-time scale principle, the longitudinal dynamics model is divided into a speed subsystem and an altitude subsystem; the speed subsystem takes the speed as the output signal and the fuel equivalence ratio as the input signal, and the altitude subsystem takes the altitude as the output signal and the elevator deflection angle as the input signal.

[0070] (2) The output redefinition is used to perform zero dynamic reconstruction of the system to achieve the transformation from a non-minimum phase system to a minimum phase system, thus avoiding the risk of system instability caused by the non-minimum phase characteristics. For the speed subsystem, it is expressed as Where: f V and g V Represent the transformed kinetic model coefficients, d V represents the external disturbance of the speed subsystem, and Φ represents the control input of the speed subsystem, that is, the fuel equivalence ratio. For the altitude subsystem, in order to deal with the influence of non-minimum phase characteristics on system stability, it is necessary to construct a stable zero dynamic by output redefinition. According to the equal convergence principle, the redefined output H is selected and expressed as:

[0071] H=h+λ * θ(13)

[0072] Where: * H is the combination coefficient to be designed. * =h * +λ * θ * represents the reference command of the equilibrium point, where h * is the height reference command of the balance point, θ* is the reference command of the attitude of the balance point. It should be pointed out that the combination coefficient λ * The selection will greatly affect the performance of the control system.

[0073] In finding λ * Before that, we need to obtain the state information and control information of the aircraft at the balance point. Combined with the velocity V at the equilibrium point * , the dynamic pressure at the equilibrium point can be obtained Pitch angle θ * 、Fuel equivalence ratio Φ * , and the elevator command δ e * .

[0074] (3) Accurate modeling based on deep Koopman operator theory to achieve the combination coefficient λ * Different from the existing solution technology, the present invention uses Koopman operator theory and deep neural network to solve the combination coefficient λ within a reasonable operating range. * Combined with the deep Koopman operator theory, the deep neural network is trained using the pre-collected data set to accurately model the output redefine dynamic equation. Specifically: for the current time k, define the state x corresponding to the state x at time k k , the control input u at time k corresponds to the input u k , and the next state x k+1 , R n represents an n-dimensional vector consisting of real numbers. Using the discrete time expression x k+1 =f(x k ,u k ), where The state quantity from the current state quantity and control quantity to the state quantity at the next moment can be expressed as a mapping R 3 ×R 4 |→R 3 , and the mapping is unknown. Therefore, the state of the lift space is described as Construct the Koopman operator structure, define the Koopman function as K, and use Implements a finite-dimensional approximation of K. Definition As a set of observations composed of l-dimensional data for actual flight calculation, the number of observations l in this implementation scheme is 7. represents the state value of the equilibrium point at time k, Represents the observation information of the i-th dimension data.

[0075] To evaluate the dynamic expression x k+1 =f(xk ,u k ), the Koopman approximation of , defines the following model:

[0076]

[0077] Where: For x k The estimated value of A∈R l×l , B∈R l×4 , C∈R l×4 is the system matrix of the model in formula (3), which can be calculated by solving the following optimization problem

[0078]

[0079] Where: Represents x k in u k Evolution of the dataset There are M sequence snapshots for the optimization process. In this embodiment, M=50 is selected. By collecting raw data from the system for learning and solving equation (4), the A, B, and C matrices are obtained, and x k+1 =f(x k ,u k ) and y k =x k +1.

[0080] 100,000 sets of initial states randomly generated within the permissible flight range are selected for the construction of the training database to ensure that the observed quantities should contain as much nonlinear dynamic information as possible required for the output redefinition system. For each initial state, a combination coefficient λ of 50 samples is generated within a custom range that meets the requirements. * Considering that each set of initial states only stores one combination coefficient λ * , the proportional-integral-derivative (PID) controller with the same simulation environment and simulation parameters is used to test the robustness and tracking performance. Finally, the corresponding combination coefficient λ that takes into account both robustness and performance is obtained * , forming the lifting state vector corresponding to time k and observables in x c On this basis, a deep neural network (DNN) is trained using a pre-collected data set to obtain the dynamic equation x k+1 =f(x k ,u k). In order to generate reliable, representative data that meets the control index requirements and can cover the complex flight conditions of hypersonic vehicles, a DNN model with high accuracy and high generalization is trained. To this end, 10,000 flight missions were designed to generate sample data sets, and each flight mission included 6,000 discrete sampling points with equal time intervals. By repeating the combined coefficient allocation and tracking control test process, 60,000,000 data samples for offline training of deep neural networks can be collected. This data set mainly contains the lifted state vector, observables, and state reference quantities. For the design of the loss function for deep neural network training, a weighted 15-step prediction error is used based on the data pairs obtained in the above process. It is expressed as:

[0081]

[0082] The decay factor is selected as r = 0.5. Indicates that x is obtained through the deep Koopman operator k+1 The k-th step forward prediction error.

[0083] The system output is redefined with the help of the deep Koopman operator so that all V * 、h * The root of the zero dynamics is located in the left half plane of the coordinate system, and H is the minimum phase output, which can be used for the control design of step (4).

[0084] The reconstructed external dynamic structure is as follows:

[0085]

[0086] Where: ψ=Vsinγ+λ * Q,f ψ and g ψ represents the nominal known terms related to the model parameters, d H (t,x) and d ψ (t,x,u) represent mismatched perturbations and matched perturbations respectively.

[0087] (4) Optimizing learning control design based on data-driven output redefinition

[0088] Define the reference signal of the speed subsystem and reconstruction system as V d and H d , the corresponding tracking error is e V =VV d and e H =HH d The design fuel equivalence ratio command, virtual controller and elevator control command are:

[0089]

[0090] Where: k V =5, k H =20, k ψ =0.7 is the positive parameter to be designed. is determined by the virtual controller ψ d It is obtained by introducing a first-order filter. and is the observed value of the disturbance term, which is expressed as the following data-driven neural perturbation observer:

[0091]

[0092] Where: z V 、z H 、z ψ They represent the observation errors of the velocity subsystem, the redefinition altitude subsystem, and the redefinition attitude subsystem, respectively, and η V =e V –z V , η H =e H –z H , η ψ =e ψ –z ψ .μ V >0,μ H >0,μ ψ >0 is a positive parameter to be designed. When x=V,H,ψ, use The disturbance term is estimated, where represents the estimated neural network weight vector, S x Denotes the corresponding basis function. Define the identification data storage stack and the overall data storage stack as and The maximum number of rows is l x Select 20, the maximum number of columns J x Select 50. Select and As the current storage stack, where 0≤j x ≤J x .

[0093] The following two-step online learning enhancement mechanism is designed to update the state changes of the data stack.

[0094]

[0095] Where: S1 and S2 are two online learning enhancement steps, The latest stack is defined as and Ψx (j x )=minSVD(D x (:,j x )) represents the minimum singular value. ρ x is a small positive constant to be designed, and is selected as 0.1 in this embodiment. Indicates using the latest system data The target column to update.

[0096] Where: S1 and S2 are two online learning enhancement steps. In order to express the characteristics of data-driven, we select point As a data-driven update data point, the point The corresponding latest data storage stack and the latest overall data storage stack are defined as and in For point The corresponding tracking error, observation error, neural network weight vector and corresponding basis function. x (j x )=minSVD(D x (:,j x )) represents the minimum singular value. ρ x is a small positive constant to be designed, and is selected as 0.1 in this embodiment. Indicates using the latest system data The target column to update.

[0097] Furthermore, the prediction error is constructed as

[0098]

[0099] Where: k x and represents the positive parameter to be designed, and k is selected x =5 and Indicates the jxth column reference instruction. and From the jxth column data stack D x (:,j x )get.

[0100] In order to verify the feasibility of the proposed data-driven learning control method for hypersonic aircraft, the following verification simulation was carried out. In the simulation scenario, the reference command consists of two basic maneuvering processes: in the first 300s, the speed and altitude reference commands are changed from the initial state to the expected value 1; in the next 300s, the speed and altitude reference commands are changed from the expected value 1 to the expected value 2. The initial state of the aircraft and the expected values ​​at different stages in the simulation test are given in Table 1. The reference signal is transmitted to the control system through a second-order command filter. The damping ratio of the second-order command filter used is 0.8 and the natural frequency is 0.03rad / s.

[0101] Table 1 Initial value and expected value of flight status

[0102]

[0103] The relevant simulation results are as follows Figures 2 to 11 shown. Figure 2 — Figure 5 It shows that the data-driven learning control method for hypersonic aircraft designed by the present invention can achieve rapid tracking of speed and altitude reference instructions and exhibits a small tracking error. Figures 6 to 9 The curves of track angle, angle of attack, pitch angle rate and elastic mode changing with time are shown. The attitude angle of the hypersonic vehicle shows a stable effect and smaller vibration. Figure 10 to Figure 11 The time variation curve of the control command in the verification simulation is given, showing a smooth response control input. In summary, under the data-driven learning control method proposed in the present invention, the hypersonic aircraft can achieve a satisfactory tracking effect.

Claims

1. A data-driven learning control method for a hypersonic vehicle, characterized in that: include: Construct a longitudinal dynamics model of a non-minimum phase hypersonic vehicle; achieve zero dynamic reconstruction of the system by redefining the output; based on the deep Koopman operator theory, use the pre-collected data set to train the weights of the radial basis neural network to accurately model the output redefinition dynamic equations; design a data-driven output redefinition optimization learning controller to achieve stable tracking of reference instructions; the details are as follows: (1) Constructing a longitudinal dynamics model of a non-minimum phase hypersonic vehicle Where V is the speed of the hypersonic vehicle, h is the flight altitude, γ is the track angle, θ is the pitch angle, Q is the pitch rate, α is the angle of attack, and θ=γ+α is satisfied. T, L, and D are thrust, pull, and drag, respectively. M is the pitch moment, m is the mass of the vehicle, g is the acceleration of gravity, and I yy is the moment of inertia; d V d γ d Q They represent the external disturbances of the velocity subsystem, track angle subsystem, and pitch rate subsystem, respectively, and η i represents the elastic mode, ζ i represents the damping factor, ω i represents the natural oscillation frequency, N i represents generalized force, i=1,2 means considering the second-order mode; (2) Systematic zero-dynamic reconstruction of output redefinition For the velocity subsystem, V = f V -g V Φ+d V ; Where: f V and g V represents the transformed kinetic model coefficient, d V represents the external disturbance of the speed subsystem, Φ represents the control input of the speed subsystem, i.e., the fuel equivalence ratio; For the height subsystem, in order to deal with the influence of non-minimum phase characteristics on system stability, it is necessary to construct a stable zero dynamic by redefining the output; according to the equal convergence principle, the redefined output H is selected and expressed as: H=h+λ * i(2) Where: * is the combination coefficient to be designed; H * =h * +λ * θ * represents the reference command of the equilibrium point, where h * is the height reference command of the balance point, θ * is the attitude reference instruction of the balance point; make Combined with the velocity V at the equilibrium point * , find the dynamic pressure at the equilibrium point Pitch angle θ * 、Fuel equivalence ratio Φ * , and the elevator command δ e * ; (3) Accurate modeling based on deep Koopman operator theory In order to achieve the learning of the combination coefficient λ within a reasonable operating range * , combined with the deep Koopman operator theory, the deep neural network is trained using the pre-collected data set to accurately model the output redefine dynamic equation; specifically as follows: for the current time k, define the state x corresponding to the state x at time k k , the control input u at time k corresponds to the input u k , and the next state x k+1 , R n represents an n-dimensional vector consisting of real numbers; using the discrete time expression x k+1 =f(x k ,u k ), where The current state quantity, control quantity to the state quantity at the next moment is represented by the mapping R 3 ×R 4 |→R 3 , and the mapping is unknown; therefore, the state of the lift space is described as Construct the Koopman operator structure, define the Koopman function as K, and use Implement a finite-dimensional approximation of K, where x * ∈R 7 The state of being elevated; definition As a set of observations composed of l-dimensional data for actual flight calculation, l is the number of observations, represents the state value of the equilibrium point at time k, Represents the observation information of the i-th dimension data; To evaluate the dynamic expression x k+1 =f(x k ,u k ), the Koopman approximation of , defines the following model: Where: For x k The estimated value of A∈R l×l , B∈R l×4 , C∈R l×4 is the system matrix of the model in formula (3), which is calculated by solving the following optimization problem Where: Represents x k in u k Evolution of the dataset Contains M sequence snapshots, which are used for the optimization process; learn through the original data and solve equation (4) to obtain the A, B, C matrices, while satisfying x k+1 =f(x k ,u k ) and y k =x k +1; Select N groups of initial states randomly generated within the permissible flight range for the construction of the training database; for each initial state, generate a combination coefficient λ of S samples within a custom range that meets the requirements * ; Considering that each set of initial states only stores one combination coefficient λ * , the proportional-integral-differential PID controller with the same simulation environment and simulation parameters is used to test the robustness and tracking performance; finally, the corresponding combination coefficient λ that takes into account both robustness and performance is obtained * , forming the lifting state vector x corresponding to time k k * and observables in x c represents its state reference; on this basis, a deep neural network is trained using a pre-collected data set to obtain the dynamic equation x k+1 =f(x k ,u k ) for accurate reconstruction; for the loss function design of deep neural network training, based on the data pairs obtained in the above process, a weighted K-step prediction error is used It is expressed as: Among them, r∈[0,1] represents the decay factor, Indicates that x is obtained through the deep Koopman operator k+1 The k-th step forward prediction error; The system output is redefined with the help of the deep Koopman operator so that all V * 、h * The root of the zero dynamics is located in the left half plane of the coordinate system, H is the minimum phase output, and the control design for step (4) is obtained; The reconstructed external dynamic structure is as follows: Where: d H (t,x) and d ψ (t, x, u) represent mismatched disturbance and matched disturbance respectively; ψ=Vsinγ+λ * Q,f ψ and g ψ represents the nominal known terms related to the model parameters; (4) Optimizing learning control design based on data-driven output redefinition Define the reference signal of the speed subsystem and reconstruction system as V d and H d , the corresponding tracking error is e V =VV d and e H =HH d ; The design fuel equivalence ratio command, virtual controller and elevator control command are: Where: k V >0,k H >0,k ψ >0 is the positive parameter to be designed; refer to instruction ψ f and its micro-amount By virtual controller ψ d It is obtained by introducing a first-order filter and defining e ψ =ψ-ψ f To redefine the tracking error of the attitude subsystem; and is the observed value of the disturbance term, which is expressed as the following data-driven neural perturbation observer: Where: z V 、z H 、z ψ They represent the observation errors of the velocity subsystem, the redefinition altitude subsystem, and the redefinition attitude subsystem, respectively, and η V =e V –z V , η H =e H –z H , η ψ =e ψ –z ψ ;μ V >0,μ H >0,μ ψ >0 is a positive parameter to be designed; when x=V,H,ψ, use The disturbance term is estimated, where represents the estimated neural network weight vector, S x Denotes the corresponding basis function; defines the identification data storage stack and the overall data storage stack as and Among them l x Indicates the maximum number of rows, J x Indicates the maximum number of columns; select and As the current storage stack, where 0≤j x ≤J x ; Design the following two-step online learning enhancement mechanism to update the state changes of the data stack; Where: S1 and S2 are two online learning enhancement steps; in order to express the characteristics of data-driven, the point As a data-driven update data point, the point The corresponding latest data storage stack and the latest overall data storage stack are defined as and in For point The corresponding tracking error, observation error, neural network weight vector and corresponding basis function; Ψ x (j x )=minSVD(D x (:,j x )) represents the minimum singular value; ρ x is a small positive constant to be designed; Indicates using the latest system data Updated target column; Furthermore, the prediction error is constructed as Where: k x and l x represents the positive parameter to be designed, Indicates the jth x Column reference instructions; and From the jxth column data stack D x (:,j x )get.

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