Reconstruction capability quantitative characterization method based on energy space

Abstract

The invention discloses a reconstruction capability quantitative characterization method based on an energy space, and belongs to the technical field of overall spacecrafts. Firstly, a state space model and a fault model of a spacecraft are established; then, constructing an energy function considering control input constraint as a quantitative characterization index of the system reconstruction capability; and finally, aiming at the problem that a Hamilton-Jacobi-Bellman equation is difficult to analyze and solve in the reconstruction capability index calculation process of the nonlinear system, solving an approximate solution of the maximum reconstruction capability by using a single neural network structure in combination with the idea of dynamic planning and reinforcement learning, thereby determining the reconstruction capability boundary of the nonlinear system. According to the method, the problem that the HJB equation is difficult to analyze and solve in the reconfigurability evaluation index solving process of the complex nonlinear system is solved, so that the reconfigurability quantitative characterization of the nonlinear system is realized.

Description

Technical Field

[0001] The invention relates to a quantitative characterization method of reconstruction capability based on energy space, belonging to the technical field of overall spacecraft design. Background Art

[0002] Actuator failures can seriously affect the performance and stability of the system, and thus threaten the safety of the system. In order to cope with possible failures, the system needs to be equipped with corresponding reconstruction strategies to maintain or moderately reduce the control objectives. Traditional research ideas mainly focus on the study of reconstruction algorithms after failures. However, the system itself does not necessarily have sufficient reconstruction capabilities, so it may not be able to run complex reconstruction algorithms. Research on reconfigurability can quantitatively analyze whether the system redundancy allocation is reasonable, whether the reconstruction measures are effective, and whether the faulty system is reconfigurable. It can provide designers with more valuable information and basis, so as to optimize the reconstruction scheme and system structure in a targeted manner, greatly improving the design efficiency of software and hardware.

[0003] At present, although some progress has been made in the research on reconfigurability evaluation at home and abroad, the research mainly focuses on simple linearized systems, which can provide some methods and ideas for the research on the reconfigurability of complex nonlinear systems, but it has certain limitations. For example, the reconfigurability evaluation of linearized nonlinear systems can only obtain partial evaluation results, and the linearized model is difficult to accurately describe the nonlinearity and fault characteristics of the system; in particular, the linearization process will cause some faults caused by nonlinear factors (such as friction, etc.) to be ignored. Because of the complex characteristics and diverse forms of nonlinear systems, there is still a lack of general mathematical tools to analyze and process them uniformly. There are few existing studies on the reconfigurability of nonlinear systems, and most of them are carried out for a specific system (such as bilinear systems, linear switching systems, etc.), and the scope of application is very limited. Therefore, studying the reconfigurability evaluation and design problems of general nonlinear systems will help the reconfigurability theory method to be applied in the development process of engineering systems such as spacecraft, which is of great practical significance. Summary of the invention

[0004] The technical problem to be solved by the present invention is: in view of the problem that existing reconfigurability research is mostly applicable to simple linear systems, a quantitative characterization method of reconstruction capability based on energy space is provided to realize quantitative evaluation of reconstruction capability of complex nonlinear systems.

[0005] The technical solution of the present invention is: a quantitative characterization method of reconstruction capability based on energy space, comprising:

[0006] (1) Using the spacecraft design parameters and considering the actual constraints including control input constraints, a system state space model of the spacecraft in normal mode is established;

[0007] (2) Based on the obtained system state space model under normal mode, establish the fault θ s The system state space model under ;

[0008] (3) Construct an energy function J containing control input constraints s ;

[0009] (4) Establishing the estimated value of the system state to energy function The mapping relationship is: Where 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, establish the training target of neural network iteration That is, using the current estimated weight W i To calculate the training target W for the next iteration i+1 , i represents the number of iterations of the neural network;

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

[0012] (7) Based on the current weights, determine the least squares solution of the training objective equation in step (5) to obtain the updated network weights W i+1 , and calculate the current energy function

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

[0014] (9) Obtain the minimum energy function That is, the boundary of the system's reconstruction capabilities.

[0015] The state space model is expressed as:

[0016]

[0017] Where Δt is the telemetry data sampling time, and the subscript k represents the sampling time number. and represent the spacecraft’s moment of inertia, the angular velocity at the Kth moment, and the control torque vector output by the actuator, respectively, and

[0018]

[0019] Among them, x × is the cross product operator of a vector x in matrix form, is the actuator installation matrix, which reflects the torque mapping from the actuator installation coordinate system to the spacecraft body coordinate system.

[0020] According to the system state space model obtained in the normal mode, the fault θ s The system state space model under , includes:

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

[0022]

[0023] The energy function in step (3) is This function reflects the energy consumed by the faulty system in step (2) to control the zero-time state x0 back to 0, thereby quantifying the system's reconstruction capability; 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 satisfies ρ(0)=0; is a positive definite symmetric matrix.

[0024] A single neural network is used to establish the system state x based on the reinforcement learning method. k To step (3) the energy function J s (x k ,u k ) and the system state x k To the partial derivative of the energy function The mapping relationship is:

[0025]

[0026] in, is the weight matrix of the neural network, which is composed of the weights of the energy function and about comorphic variables The weights of are composed of; is the activation function of the neural network, which consists of p smooth and linearly independent scalar basis functions, where p is the number of neurons in the neural network. is the energy function J s (x k ,u k) and its partial derivative λ s (x k ,u k ) is an estimated value.

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

[0028]

[0029] That is, using the current estimated weight W i To calculate the training target W for the next iteration i+1 , where i represents the number of iterations of 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 For the given initial weight W 0 , is the initial weight W 0 The estimated energy function and its partial derivatives, x0, u0 are the state and control torque of the system at time zero.

[0033] The calculation of the current energy function

[0034]

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

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

[0037] (2) The method of the present invention aims to solve the problem that the reconfiguration capability index of nonlinear systems is difficult to solve analytically. The method 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 the realization of intelligent and digital aerospace control. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0039] like Figure 1 As shown, the present invention provides a quantitative characterization method of reconstruction capability based on energy space, and the steps are as follows:

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

[0041]

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

[0043]

[0044] The x × is the cross product operator of a vector x in matrix form, is the actuator installation matrix, which reflects the torque mapping from the actuator installation coordinate system to the spacecraft body coordinate system. For the classic four-oblique flywheel configuration, C b2a The values ​​are:

[0045]

[0046] (2) For the system state space model given in step (1), determine its s The actuator selection matrix Σ under s ,Σ s , the matrix Σ s is a diagonal matrix with elements of 0 or 1, and the diagonal elements correspond to the actuators one by one. The elements corresponding to the healthy actuators are 1, and the elements corresponding to the faulty actuators are 0. s The state space model of the system is:

[0047]

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

[0049] (3) Construct an energy function that includes control input constraints

[0050]

[0051] Reflects the energy consumed by the faulty system in step (2) to control the zero-time state x0 back to 0, thereby quantitatively characterizing the system's reconstruction capability; 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 satisfies ρ(0) = 0. This function can be a saturation function such as tanh, sat, sgn, etc. is a positive definite symmetric matrix.

[0052] (4) Using a single neural network, the system state x is established based on the reinforcement learning method. k To step (3) the energy function J s (x k ,u k ) mapping relationship, system state x k To the partial derivative of the energy function The mapping relationship is:

[0053]

[0054] in, is the weight matrix of the neural network, which is composed of the weights of the energy function and about comorphic variables The weights of are composed of; is the activation function of the neural network, which consists of p smooth and linearly independent scalar basis functions, where p is the number of neurons in the neural network. and is the energy function J s (x k ,u k ) and its partial derivative λ s (x k ,u k ) is an estimated value.

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

[0056]

[0057] That is, using the current estimated weight W i To calculate the training target W for the next iteration (i+1)T , where i represents the number of iterations of the neural network.

[0058] (6) Let i = 0 and select an initial weight W 0 , based on the mapping relationship in step (4), calculate the corresponding initial energy function

[0059]

[0060] Among them, W 0 For the given initial weight W 0 , is the initial weight W 0The estimated energy function and its partial derivatives, x0, u0 are the state and control torque of the system at time zero.

[0061] (7) Based on the current weights, determine the least squares solution of the training objective equation in step (5) to obtain the updated network weights W i+1 , calculate the current energy function

[0062]

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

[0064] (9) Obtain the minimum energy function That is, the boundary of the system's reconstruction capabilities.

[0065] In summary, the above embodiments verify the feasibility and effectiveness of the method for quantitatively characterizing reconstruction capability based on energy space proposed in the present invention.

[0066] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A quantitative characterization method of reconstruction capability based on energy space, characterized in that: include: (1) Using the spacecraft design parameters and considering the actual constraints including control input constraints, a system state space model of the spacecraft in normal mode is established; (2) Based on the obtained system state space model under normal mode, establish the fault θ s The system state space model under ; (3) Construct an energy function J containing control input constraints s ; (4) Establishing the estimated value of the system state to energy function The mapping relationship is: 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, establish the training target of neural network iteration That is, using the current estimated weight W i To calculate the training target W for the next iteration i+1 , i represents the number of iterations of the neural network; (6) Let i = 0 and give an initial weight W 0 , calculate the corresponding initial energy function based on the mapping relationship (7) Based on the current weights, determine the least squares solution of the training objective equation in step (5) to obtain the updated network weights W i+1 , and calculate the current energy function (8) If Go to step (9); otherwise, increase the number of neural network iterations i by 1 and go to step (7); (9) Obtain the minimum energy function That is, the boundary of system reconstruction capability.

2. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 1, characterized in that: The state space model is expressed as: Where Δt is the telemetry data sampling time, and the subscript k represents the sampling time number. and represent the spacecraft’s moment of inertia, the angular velocity at the Kth moment, and the control torque vector output by the actuator, respectively, and Among them, x × is the cross product operator of a vector x in matrix form, is the actuator installation matrix, which reflects the torque mapping from the actuator installation coordinate system to the spacecraft body coordinate system.

3. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 2, characterized in that: According to the system state space model obtained in the normal mode, the fault θ s The system state space model under , includes: For the state space model given in step (1), determine the spacecraft under fault θ s The actuator selection matrix Σ under s , the matrix Σ s is a diagonal matrix with elements of 0 or 1, and the diagonal elements correspond to the actuators one by one. The elements corresponding to the healthy actuators are 1, and the elements corresponding to the faulty actuators are 0. s The following system model:

4. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 3, characterized in that: The energy function in step (3) is This function reflects the energy consumed by the faulty system in step (2) to control the zero-time state x0 back to 0, thereby quantifying the system's reconstruction capability; 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 ρ(·): The inverse function of satisfies ρ(0)=0; is a positive definite symmetric matrix.

5. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 4, characterized in that: A single neural network is used to establish the system state x based on the reinforcement learning method. k To step (3) the energy function J s (x k ,u k ) and the system state x k To the partial derivative of the energy function The mapping relationship is: in, is the weight matrix of the neural network, which is composed of the weights of the energy function and about comorphic variables The weights of k ): is the activation function of the neural network, which consists of p smooth and linearly independent scalar basis functions, where p is the number of neurons in the neural network. is the energy function J s (x k ,u k ) and its partial derivative λ s (x k ,u k ) is an estimated value.

6. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 5, characterized in that: Establish an iterative training objective for the neural network: That is, using the current estimated weight W i To calculate the training target W for the next iteration i+1 , where i represents the number of iterations of the neural network.

7. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 6, characterized in that: Based on the mapping relationship in step (4), the corresponding initial energy function is calculated The formula is: Among them, W 0 For the given initial weight W 0 , is the initial weight W 0 The estimated energy function and its partial derivatives, x0, u0 are the state and control torque of the system at time zero.

8. The method for quantitatively characterizing reconstruction capability based on energy space according to claim 7, characterized in that: The calculation of the current energy function

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