A method for quantitatively characterizing reconstruction ability based on energy space

Abstract

The application is a kind of reconstruction ability quantitative characterization method based on energy space, belonging to the technical field of spacecraft overall. Firstly, the state space model and fault model of the spacecraft are established; then, the energy function considering the control input constraint is constructed as the quantitative characterization index of the system reconstruction ability; finally, aiming at the problem that the Hamilton-Jacobi-Bellman equation is difficult to solve in the process of calculating the reconstruction ability index of the nonlinear system, a single neural network structure is used to solve the approximate solution of the maximum reconstruction ability according to the ideas of dynamic programming and reinforcement learning, so as to determine the reconstruction ability boundary of the nonlinear system. The application solves the problem that the HJB equation is difficult to solve in the process of solving the reconfigurability evaluation index of the complex nonlinear system, so as to realize the quantitative characterization of the reconfigurability of the nonlinear system.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for quantitatively characterizing reconstruction capability based on energy space, and belongs to the technical field of spacecraft overall design. BACKGROUND

[0002] The fault of actuators will seriously affect the performance and stability of the system, and then threaten the safety of the system. In order to deal with the possible fault, the system needs to be equipped with corresponding reconstruction strategy to maintain or moderately reduce the control target. The traditional research idea mainly focuses on the research of reconstruction algorithm after the fault, however, the system itself does not necessarily have sufficient reconstruction capability, so it is not necessarily able to run complex reconstruction algorithm. The research on reconfigurability can quantitatively analyze whether the redundancy allocation of the system is reasonable, whether the reconstruction measures are effective, and whether the fault system is reconfigurable, etc., so as to provide more valuable information and basis for the designers, thereby targetedly optimizing the reconstruction scheme and system structure, and greatly improving the design efficiency of software and hardware.

[0003] Although the research on reconfigurability evaluation at home and abroad has made certain progress, the main research is on simple linear systems, which can provide some method ideas for the reconfigurability research of complex nonlinear systems, but has certain limitations. For example, the reconfigurability evaluation of the linearized nonlinear system can only get local evaluation results, and the linearized model is difficult to accurately describe the nonlinearity and fault characteristics of the system. In particular, the linearization processing will cause some faults caused by nonlinear factors (such as friction) to be ignored. Because of the complex characteristics and various forms of nonlinear systems, there is still a lack of general mathematical tools for unified analysis and processing, and the existing research on the reconfigurability of nonlinear systems is less, and mostly carried out for a certain specific system (such as bilinear system, linear switching system, etc.), and the applicable range is very limited. Therefore, the research on the reconfigurability evaluation and design of general nonlinear systems is helpful for the practical application of reconfigurability theory and method in the development process of spacecraft and other engineering systems, and has very important practical significance. SUMMARY

[0004] The technical problem to be solved by the present application is that the existing reconfigurability research is mainly applicable to simple linear systems, and a method for quantitatively characterizing reconstruction capability based on energy space is provided to realize the quantitative evaluation of the reconstruction capability of complex nonlinear systems.

[0005] The technical scheme of the present application is: a method for quantitatively characterizing reconstruction capability based on energy space, comprising:

[0006] (1) using the design parameters of a spacecraft, considering the actual limiting factors including control input constraints, establishing a system state space model of the spacecraft in normal mode;

[0007] (2) According to the obtained system state space model under the normal mode, a system state space model under the fault θ s is established;

[0008] (3) An energy function J s containing control input constraints is constructed;

[0009] (4) A mapping relationship between the system state and the estimated value of the energy function is established: wherein, W is the weight matrix of the neural network; Φ(x k ) is the activation function of the neural network;

[0010] (5) Based on the obtained mapping relationship, a training target of neural network iteration is established , that is, the training target W i of the next iteration is calculated using the currently estimated weight W i+1 , and i represents the iteration step number of the neural network;

[0011] (6) Let i = 0, give an initial weight W 0 , and calculate the corresponding initial energy function J

[0012] (7) Based on the current weight, the least square solution of the training target equation in step (5) is determined, the updated network weight W i+1 is obtained, and the current energy function J

[0013] (8) If J go to step (9); otherwise, let the neural network iteration step number i increase by 1 and go to step (7);

[0014] (9) The minimum energy function J is obtained, that is, the system reconstruction ability boundary.

[0015] The state space model is represented as:

[0016]

[0017] wherein, Δt is the telemetry data sampling time, the subscript k represents the number of sampling time, and

[0018]

[0019] wherein, x × is the cross multiplication operator of the vector x in the form of a matrix, ​​The actuator installation matrix, which reflects the torque mapping from the actuator installation coordinate system to the spacecraft body coordinate system, is installed.

[0020] The system state space model under the fault θ s is established according to the obtained system state space model under the normal mode, and includes:

[0021] For the state space model given in step (1), the actuator selection matrix Σ s of the spacecraft under the fault θ s is determined, the matrix Σ s is a diagonal matrix with elements of 0 or 1, and the diagonal elements correspond one-to-one to the actuators, the elements corresponding to the healthy actuators are 1, and the elements corresponding to the faulty actuators are 0, and the system model under the fault θ s is established:

[0022]

[0023] The energy function J in step (3) is: The function reflects the energy consumed by the fault system in step (2) to control the zero-time state x0 back to 0, thereby quantifying the reconstruction ability of the system; wherein u0 is the zero-time control torque, v is the real-time control torque, ρ -1 (·) is the inverse function of the bounded continuous one-to-one real analytic integrable function , satisfying ρ(0)=0; is a positive definite symmetric matrix.

[0024] A single neural network is used to establish the mapping relationship between the system state x k and the energy function J s (x k ,u k ) in step (3) and the mapping relationship between the system state x k and the energy function partial derivative :

[0025]

[0026] Wherein, is the weight matrix of the neural network, which is composed of the weight value related to the energy function and the weight value related to the co-state variable ; is the activation function of the neural network, which is composed of p smooth and linearly independent scalar basis functions, and p is the number of neurons of the neural network, is the energy function J s (x k ,u k) and its partial derivative λ s (x k ,u k The estimated value of ).

[0027] Establish the iterative training objective for the neural network:

[0028]

[0029] Even using the currently estimated weight W i To calculate the training objective W for the next iteration i+1 , where i represents the number of iterations in the neural network.

[0030] Based on the mapping relationship in step (4), the corresponding initial energy function is calculated. The formula is:

[0031]

[0032] Among them, W 0 Given the initial weights W 0 , It is determined by the initial weight W 0 The estimated energy function and its partial derivatives are obtained, where x0 and u0 are the system's state and control torque at time zero.

[0033] The calculation of the current energy function

[0034]

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] (1) The method of the present invention addresses the problem that existing reconfigurability studies are mostly applicable to simple linear systems, and extends the quantitative characterization technique of reconfigurability to general nonlinear systems, thereby improving the practicality of reconfigurability studies and expanding the scope of application.

[0037] (2) The method of the present invention addresses the problem that the reconfigurability index of nonlinear systems is difficult to solve analytically. It introduces the idea of ​​reinforcement learning into the reconfigurability evaluation process, thereby realizing the quantitative characterization of the reconfigurability of complex dynamic systems, which is conducive to realizing the intelligentization and digitalization of aerospace control. Attached Figure Description

[0038] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0039] like Figure 1 As shown, the present invention provides a quantitative characterization method for reconfiguration capability based on energy space, comprising the following steps:

[0040] (1) Using the spacecraft design parameters, a system state space model of the spacecraft in normal mode is established:

[0041]

[0042] where Δt is the telemetry data sampling time, subscript k represents the number of sampling time, and represent the rotational inertia of the spacecraft, the rotational angular velocity at the Kth moment and the control torque vector of the actuator output, respectively, and

[0043]

[0044] The x × is the cross multiplication operator of the vector x in the form of a matrix, is the actuator installation matrix, which reflects the torque mapping from the actuator installation coordinate system to the spacecraft body coordinate system. For the classical four-skewed flywheel configuration, b2a the value is:

[0045]

[0046] (2) For the system state space model given in step (1), the actuator selection matrix Σ s is determined under the fault θ s , Σ s This matrix Σ s is a diagonal matrix with elements of 0 or 1, and the diagonal elements correspond one-to-one with the actuators. The element corresponding to the healthy actuator is 1, and the element corresponding to the faulty actuator is 0. The system state space model under the fault θ s is established:

[0047]

[0048] For a spacecraft attitude control system equipped with four actuators, there are 2 4 = 16 actuator selection schemes, corresponding to 16 possible system models, i.e. s = 0 represents the normal mode, and Σ0 is the unit matrix of the corresponding dimension.

[0049] (3) The energy function

[0050]

[0051] reflects the energy consumed by the fault system to control the zero-time state x0 back to 0 in step (2), thereby quantitatively characterizing the reconstruction ability of the system; where u0 is the control torque at zero time, v is the real-time control torque, and ρ -1 (·) is a bounded continuous one-to-one real analytic integrable function the inverse function of tanh, sat, sgn or other saturation function, satisfying ρ(0) = 0; is a positive definite symmetric matrix.

[0052] (4) A single neural network is adopted to establish the mapping relationship between the system state x k and the energy function J s (x k , u k ) in step (3), the mapping relationship between the system state x k and the partial derivative of the energy function λ :

[0053]

[0054] wherein, W is the weight matrix of the neural network, which is composed of the weight w related to the energy function and the weight w related to the co-state variable z is the activation function of the neural network, which is composed of p smooth and linearly independent scalar basis functions, p is the number of neurons of the neural network, and and are the estimated values of the energy function J s (x k , u k ) and its partial derivative λ s (x k , u k ).

[0055] (5) Based on the mapping relationship in step (4), the iterative training target of the neural network is established:

[0056]

[0057] that is, the current estimated weight W i is used to calculate the training target W (i+1)T of the next iteration, wherein i represents the iteration step number of the neural network.

[0058] (6) Let i = 0, select an initial weight W 0 , and calculate the corresponding initial energy function J

[0059]

[0060] wherein, W 0 is the given initial weight W 0 , is the initial energy function calculated based on the initial weight W 0The estimated energy function and its partial derivative, x0, u0 are the state and control torque of the system at zero time.

[0061] (7) Based on the current weight, the least square solution of the training target equation in step (5) is determined to obtain the updated network weight W i+1 , the current energy function is calculated

[0062]

[0063] (8) Based on the calculation result of step (7), if Go to step 9, where epsilon is the allowable calculation error of the energy function. Otherwise, go to step 6.

[0064] (9) Obtain the minimum energy function That is, the system reconstruction ability boundary.

[0065] In summary, through the above examples, the feasibility and effectiveness of the quantitative reconstruction ability characterization method based on energy space proposed in the application are verified.

[0066] The contents not described in detail in the specification of the application belong to the known technology of those skilled in the art.

Claims

1. A method for quantitatively characterizing reconstruction ability based on energy space, characterized in that, Comprise: (1) using spacecraft design parameters, considering the actual limiting factors including control input constraints, to establish a spacecraft system state space model in normal mode; (2) According to the obtained system state space model under normal mode, the system state space model under fault θ s is established. (3) constructing an energy function J including control input constraints s ; (4) Establish a mapping relationship of the system state to the energy function estimate value where W is the weight matrix of the neural network; Φ(x k ) is the activation function of the neural network;​ (5) Based on the obtained mapping relationship, the training target of neural network iteration is established i.e. using the current estimated weight W i to calculate the training target W i+1 of the next iteration, i represents the iteration step number of the neural network; (6) Let i = 0, give an initial weight W 0 , based on the mapping relationship to calculate the corresponding initial energy function (7) Based on the current weights, determine the least square solution of the training target equation in step (5) to obtain the updated network weights W i +1 and calculate the current energy function (8) If ε denotes the allowable calculation error of the energy function, go to step (9); otherwise, let the iteration step number i of the neural network be increased by 1 and go to step (7); (9) the minimum energy function i.e. the system reconfiguration capability boundary, x0, u0are the system zero-time state and control torque, respectively.

2. The method of claim 1, wherein, The state space model is expressed as: where Δt is the telemetry data sampling time, and the subscript k denotes the sampling time number, and denote the spacecraft's moment of inertia, the system state at the kth time instant, and the control torque vector of the actuator output, respectively, and where x × is the cross multiplication operator of the vector x in matrix form, is the actuator installation matrix, reflecting the moment mapping from the actuator installation coordinate system to the spacecraft body coordinate system.

3. The method of claim 2, wherein, The system state space model under the normal mode is obtained, and a system state space model under the fault θ s is established according to the system state space model under the normal mode. Given the state-space model in step (1), determine the spacecraft's state at fault θ. s The actuator selection matrix Σ s The matrix Σ s It is a diagonal matrix with elements of 0 or 1, and each diagonal element corresponds one-to-one with an actuator. The element corresponding to a healthy actuator is 1, and the element corresponding to a faulty actuator is 0. A fault θ is established. s The following system model:

4. The method of claim 3, wherein, the energy function in step (3) This function reflects the energy consumed by the fault system to control the zero time state x0 back to 0 in step (2), thereby quantifying the reconstruction ability of the system; wherein u0 is the control torque at zero time, v is the real-time control torque, ρ -1 (·) is a bounded continuous one-to-one real analytic integrable function The inverse function of ρ (·) satisfies ρ (0) = 0; is a positive definite symmetric matrix.

5. The method of claim 4, wherein, A single neural network is used to establish the mapping from the system state x k to the energy function J s (x k ,u k ) and the mapping from the system state x k to the energy function partial derivative ​ wherein is a weight matrix of the neural network, composed jointly of weights and weights with respect to the co-state variables is an activation function of the neural network, composed of p smooth and linearly independent scalar basis functions, p being the number of neurons of the neural network, is an estimate of the energy function J s (x k , u k ) and its partial derivative λ s (x k , u k ).

6. The method of claim 5, wherein, The iterative training target of the neural network is established: Even if the current estimated weight W i is used to calculate the training target W i+1 of the next iteration, where i represents the iteration step number of the neural network.

7. The method of claim 6, wherein the method is based on energy space reconstruction capability quantification. Based on the mapping relationship in step (4), the corresponding initial energy function is calculated The formula is: Among them, W 0 Given the initial weights W 0 , It is determined by the initial weight W 0 The estimated energy function and its partial derivatives are obtained, where x0 and u0 are the system's state and control torque at time zero.

8. The method of claim 7, wherein, said computing a current energy function

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