Random iterative learning control method for repeated tasks of spacecraft

Abstract

The invention relates to a random iterative learning control method for repeated tasks of a spacecraft, belongs to the technical field of control, solves the problem of low trajectory tracking control precision of the spacecraft under the influence of random interference in the prior art, and comprises the following steps: S1, determining an expected target trajectory of the spacecraft, and determining the target trajectory of the spacecraft according to the expected target trajectory; establishing a random noise model; s2, acquiring a system matrix corresponding to a spacecraft dynamic model, obtaining a corresponding block Toplitz matrix, establishing a model of a random iterative learning control law, and obtaining control input of the spacecraft under current iteration; s3, according to the control input of the spacecraft under the current iteration, the tracking error and the selected learning gain matrix, the control input of the spacecraft during the next iteration is updated, the spacecraft is controlled to execute the next iteration process, and the position of the spacecraft under the next iteration is obtained; and S4, carrying out iteration operation for multiple times until the accurate tracking of the target trajectory is completed.

Description

Technical Field

[0001] The present invention relates to the field of control technology, and in particular to a random iterative learning control method for spacecraft repetitive tasks. Background Art

[0002] In recent years, with the increasing demand for earth observation data in fields such as global climate change, natural disaster monitoring, and agricultural management, research on repeated missions for spacecraft has become a hot topic. Advances in satellite technology, especially the development of small satellites and satellite constellations, have significantly improved the frequency and resolution of observations, and the demand for scheduling and optimizing repeated missions has become more urgent. In addition, international cooperation and data sharing play an important role in the global observation system, and more efficient repeated observation missions can be achieved by coordinating satellite resources from different countries and organizations. Therefore, research on repeated tracking missions for spacecraft has important practical significance and broad application prospects.

[0003] Existing spacecraft tracking mission control methods include traditional ground control, autonomous control and joint control. Traditional ground control methods have the advantages of high precision and high reliability, but have the disadvantages of time delay and poor flexibility. Autonomous control methods can quickly respond to environmental changes and reduce dependence on ground control, but their implementation is complex and their reliability needs to be improved. Joint control methods combine the advantages of ground control and autonomous control, taking into account both timeliness and precision, but the system complexity and cost are relatively high.

[0004] The solution ideas of the above control methods are all based on time-domain feedback control. In this case, it is difficult to achieve complete trajectory tracking within a limited time. If the historical information carried by the repeated system can be used, the transient tracking performance can be effectively improved. Therefore, the random iterative learning control method for spacecraft repeated tracking tasks is a key and difficult problem that needs to be solved urgently. Summary of the invention

[0005] In order to overcome the deficiencies of the prior art, the present invention aims to propose a random iterative learning control method applied to repeated trajectory tracking tasks of spacecraft. Specifically, considering that the spacecraft will inevitably be affected by random noise during operation, and the non-zero Markov parameter matrix of the spacecraft usually does not meet the full rank condition, a random iterative learning control method based on traceability is proposed, which breaks through the shortcomings of the traditional iterative learning control method that requires the non-zero Markov parameter matrix of the controlled system to meet the column full rank condition, and the traditional iterative learning control requires that the control environment does not have iterative changes. The problem of high-precision complete trajectory tracking control of the trajectory of the spacecraft under the influence of random interference is solved, so as to improve the control performance of the spacecraft and enhance the robustness and reliability of the system.

[0006] According to an embodiment of the present invention, a random iterative learning control method for spacecraft repetitive tasks is provided, characterized in that it includes the following steps:

[0007] Step S1, establishing a spacecraft dynamics model, determining the expected target trajectory of the spacecraft, and establishing a random noise model;

[0008] Step S2, according to the spacecraft dynamics model established in step S1, obtain the corresponding block Toplitz matrix, establish a model of the random iterative learning control law, and obtain the control input, tracking error and learning gain matrix of the spacecraft under the current iteration;

[0009] Step S3, according to the control input, tracking error and learning gain matrix of the spacecraft in the current iteration, the control input of the spacecraft in the next iteration is updated, the spacecraft is controlled to execute the next iteration process, and the position of the spacecraft in the next iteration is obtained;

[0010] Step S4, repeat step S3 for multiple iterations to obtain the trajectory of the spacecraft's position along the time axis, and compare the trajectory of the spacecraft's position along the time axis with the expected target trajectory of the spacecraft. If precise tracking is not achieved, continue to repeat step S3. If the spacecraft completes precise tracking of the target trajectory, the result of the precise tracking is output and saved.

[0011] In an optional implementation, step S1 specifically includes the following steps:

[0012] Step S1.1, establish a spacecraft dynamics model, and establish a multi-input multi-output time-varying spacecraft dynamics model based on the state information obtained from the database:

[0013]

[0014] Among them, t∈{0,1,2,…,N} is the running time, N is the running cycle, is the number of iterations, x k (t),u k (t) and y k (t) are the state, input and position of the spacecraft at time t in the kth iteration, A(t), B(t) and C(t) are the time-varying system matrices of the spacecraft at time t; v k (t) represents the random noise at the tth time of the kth iteration;

[0015] Step S1.2, determine the expected target trajectory of the spacecraft, and obtain the expected target trajectory of the spacecraft as y d (t), t∈{1,2,…,N};

[0016] Step S1.3, establish a random noise model, and calculate the random noise v in the spacecraft dynamics model (1) k (t) Before modeling, we first define σ as a type of algebra,

[0017]

[0018] in, represents a watershed, express The elements in v i (t) represents the random noise at the tth time of the i-th iteration;

[0019] On this basis, the random noise v1(t) is modeled: for any t∈{0,1,2,…,N}, the random noise v k (t) forms a relative Martingale difference sequence

[0020]

[0021] That is, the random noise model is established as

[0022]

[0023] In an optional implementation, step S2 specifically includes the following steps:

[0024] Step S2.1, based on the established multi-input multi-output time-varying spacecraft dynamics model, establish the block Toeplitz matrix corresponding to the spacecraft dynamics model (1)

[0025]

[0026] Without loss of generality, G represents the block Toeplitz matrix corresponding to the spacecraft. Let the rank of G be m. Based on this, construct a matrix H1 with the same generation space as G;

[0027] Step S2.2, determine the learning gain matrix and obtain the position y of the spacecraft at the current iteration k (t), calculate the tracking error under the current iteration, and on this basis establish the model of random iterative learning control law to obtain the control input under the current iteration.

[0028] In an optional implementation, step S2.2 specifically includes the following steps:

[0029] Step S2.2.1, using the attenuation factor a k Overcome the influence of random noise, where a k Needs to be satisfied

[0030]

[0031] Among them, the attenuation factor α k A scalar indicating the decay along the iteration axis;

[0032] Step 2.2.2, use the learning parameter J to solve the spacecraft trackability problem, select

[0033] J=(H1(J1 T H1) -1 ) T ;

[0034] Step 2.2.3, use the learning parameter Γ to ensure the convergence of the random iterative learning control law, and Γ satisfies the condition

[0035] Re(λ i ((H1(H1 T H1) -1 ) T GΓ))>0

[0036] Among them, λ i (.) represents the i-th eigenvalue of the matrix. This condition means that the matrix (H1(H1 T H1) -1 ) T The eigenvalues ​​of GΓ all have positive real parts;

[0037] Step 2.2.4, based on the results obtained in the above steps, determine the learning gain matrix and establish the model of the random iterative learning control law for the repeated mission of the spacecraft as follows

[0038]

[0039] Among them, U k =[u k T (0),u k T (1),…,u k T (N-1)] T is the system control input augmented vector for k iterations, and is used as the control input for the current iteration. k-1 =[u k-1 T (0),u k-1 T (1),…,u k-1 T (N-1)] T is the system control input augmented vector under k-1 iterations, E k =[e k T (1),ek T (2),…,e k T (N)] T is the augmented vector of the system position error after k iterations, indicating the tracking error under the current iteration, e k (t)=

[0040] y d (t)-y k (t) is the position error vector of the system at time t after k iterations, ∏ k-1 is the learning gain matrix of the previous iteration, where Π k =a k The form of ΓJ determines the learning gain matrix Π in the current iteration k ;

[0041] Step 2.2.5, obtain the control input U of the spacecraft in the current iteration through the above random iterative learning control law model k .

[0042] In an optional implementation, step S3 specifically includes the following steps:

[0043] Step S3.1, according to the control input U of the spacecraft at the current iteration k , Tracking error E k And the selected learning gain matrix Π k Update the control input U of the spacecraft for the next iteration k+1 , control the spacecraft dynamics model (1), and determine the control input of the spacecraft in the next iteration by the following formula:

[0044]

[0045] Among them, U k+1 =[u k+1 T (0),u k+1 T (1),…,u k+1 T (N-1)] T is the system control input augmented vector for k+1 iterations;

[0046] Step S3.2, according to the control input of the spacecraft at the next iteration and the corresponding block Toeplitz matrix, the position of the spacecraft at the next iteration is determined by the following formula:

[0047] Y k+1 =GU k+1 +V k+1

[0048] in, is the system position augmentation vector for k+1 iterations, is the random noise augmented vector under k+1 iterations;

[0049] Step S3.3: The spacecraft updates and adjusts its position according to the control input obtained for the next iteration of the spacecraft, and finally realizes the complete tracking of the expected specified trajectory by the spacecraft, that is,

[0050]

[0051] Among them, Ε(.) represents the expectation of the random variable.

[0052] According to another embodiment of the present invention, a random iterative learning control method for spacecraft repetitive tasks is provided, and the specific steps are as follows:

[0053] The first step is random noise modeling: when a spacecraft performs repeated trajectory tracking missions, random noise is difficult to avoid, and it mainly comes from the following aspects: sensor noise, such as measurement errors of gyroscopes, accelerometers and star sensors; atmospheric disturbances, especially atmospheric density inhomogeneities and short-term changes in low Earth orbit; and manufacturing and assembly errors, which are generated during satellite manufacturing and assembly and accumulated during orbital operation. In an embodiment of the present invention, the above-mentioned random noise is modeled as a martingale difference sequence. Compared with the traditional Gaussian white noise modeling method, the modeling method adopted in the embodiment of the present invention is more general and includes the traditional Gaussian white noise modeling method. This broader modeling method can more accurately describe various random noise sources and improve the applicability and accuracy of the model.

[0054] The second step is to design the random iterative learning control law: In the embodiment of the present invention, the random iterative learning control law includes three parts. The first part is used to overcome the influence of random noise and ensure the stability and accuracy of the system in the presence of noise; the second part is used to ensure the convergence of the spacecraft learning process; the third part is used to solve the problem that the non-zero Markov parameter matrix in the spacecraft does not meet the full rank condition.

[0055] The third step is to ensure the precise tracking effect of the spacecraft: the implementation method of the present invention uses the Lyapunov function and the random approximation method to analyze the convergence of the random iterative learning control method for repetitive tasks of spacecraft in the mean square sense and in the probability 1 sense, so as to ensure the precise tracking effect of the spacecraft.

[0056] Among them, the specific method of the first step of random noise modeling is as follows.

[0057] The embodiment of the present invention establishes the following multi-input multi-output time-varying spacecraft dynamics model by using the state information obtained from the database:

[0058]

[0059] Among them, t∈{0,1,2,…,N} is the running time, N is the running cycle, is the number of iterations, represents the set of non-negative integers {0,1,2,…}; x k (t),u k (t) and y k (t) are the state, input and position of the spacecraft at time t in the kth iteration; A(t), B(t) and C(t) are the time-varying system matrices of the spacecraft at time t; v k (t) is random noise.

[0060] And, the expected target trajectory of the spacecraft is y d (t), t∈{1,2,…,N}.

[0061] For the random noise v in the spacecraft dynamics model (1), k (t) is used for modeling. First, we define σ as a type of algebra,

[0062]

[0063] in, represents a watershed, express The elements in v i (t) represents the random noise at the tth time of the i-th iteration.

[0064] On this basis, the random noise v k (t) is modeled: For any t∈{0,1,2,…,N}, the random noise v k (t) forms a relative Martingale difference sequence

[0065]

[0066] Right now

[0067]

[0068] Among them, v k (t) represents the random noise at the tth time of the kth iteration.

[0069] The specific method of establishing the second step random iterative learning control law is as follows.

[0070] Establish the spacecraft dynamics model (1) and the corresponding block Toeplitz matrix is

[0071]

[0072] Without loss of generality, G represents the block Toeplitz matrix corresponding to the spacecraft, and the rank of G is set to m. Based on this, a matrix H1 with the same generation space as G is constructed. Thus, the specific form of the random iterative learning control law for spacecraft repetitive tasks can be established:

[0073]

[0074] Among them, U k =[u k T (0),u k T (1),…,u k T (N-1)] T is the system control input augmented vector under k iterations, U k-1 =[u k-1 T (0),u k-1 T (1),…,i k-1 T (N-1)] T is the system control input augmented vector under k-1 iterations, E k =[e k T (1),e k T (2),…,e k T (N)] T is the augmented vector of the system position error after k iterations, e k (t) = y d (t)-y k (t) is the position error vector of the system at time t after k iterations. k-1 is the learning gain matrix to be designed. Specifically, the embodiment of the present invention is based on Π k =a k The form of ΓJ determines Π k , where the attenuation factor a k It is used to overcome the influence of random noise. The learning parameter Γ is used to ensure the convergence of the random iterative learning control law (2). The learning parameter J = (H1(H1 T H1) -1 ) T Used to overcome spacecraft trackability issues.

[0075] The specific methods for ensuring the precise tracking effect of spacecraft in the third step are as follows.

[0076] First, the establishment process of the random iterative learning control law (2) for spacecraft repetitive tasks is given:

[0077] 1) Using the attenuation factor a k Overcome the problems caused by random noise, where a k Needs to be satisfied

[0078]

[0079] Among them, α k A scalar indicating the decay along the iteration axis;

[0080] 2) Use the learning parameter J to solve the spacecraft trackability problem. Here we select

[0081] J=(H1(H1 T H1) -1 ) T ;

[0082] 3) Use the learning parameter Γ to ensure the convergence of the random iterative learning control method, where Γ satisfies the condition:

[0083] Re(λ i ((H1(H1 T H1) -1 ) T GΓ))>0,

[0084] Among them, λ i (.) represents the i-th eigenvalue of the matrix. This condition means that the matrix (H1(H1 T H1) -1 ) T The eigenvalues ​​of GΓ all have positive real parts.

[0085] Through the above method, the precise tracking effect of the spacecraft is guaranteed.

[0086] The random iterative learning control method for spacecraft repetitive tasks provided according to the embodiments of the present invention has at least the following advantages over the prior art:

[0087] 1. In the proposed random iterative learning control framework for spacecraft repetitive tasks, the random iterative learning control method proposed in the present invention can effectively overcome the influence of random noise on the tracking effect and realize the spacecraft's accurate tracking of the specified trajectory.

[0088] 2. Compared with the traditional iterative learning control method, the iterative learning control method provided by the embodiment of the present invention is applicable to the scenario where the non-zero Markov parameter matrix of the system does not satisfy the full rank condition, and is thus applicable to more general spacecraft.

[0089] 3. The random iterative learning control method for spacecraft repetitive tasks provided according to the embodiment of the present invention ensures that the spacecraft completely tracks the specified trajectory from beginning to end over a long period of time with extremely high tracking accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. The features and advantages of the present invention can be more clearly understood by referring to the drawings. The drawings are schematic and should not be understood as limiting the present invention in any way. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0091] Figure 1 A schematic diagram of the process of a random iterative learning control method for spacecraft repetitive tasks provided according to an embodiment of the present invention.

[0092] Figure 2 The present invention is a flowchart of a random iterative learning control method for spacecraft repetitive tasks according to an embodiment of the present invention.

[0093] Figure 3 A spacecraft trajectory tracking simulation diagram obtained by applying an embodiment of a random iterative learning control method for spacecraft repetitive tasks provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0094] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0095] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0096] The random iterative learning control method for spacecraft repetitive tasks provided according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings. Figure 1 A schematic diagram of the process of a random iterative learning control method for spacecraft repetitive tasks provided according to an embodiment of the present invention. Figure 2 The present invention is a flowchart of a random iterative learning control method for spacecraft repetitive tasks according to an embodiment of the present invention.

[0097] refer to Figure 1 and Figure 2According to one embodiment of the present invention, a random iterative learning control method for spacecraft repetitive tasks includes the following steps.

[0098] Step S1, determining the expected target trajectory of the spacecraft and performing random noise modeling, specifically includes the following steps.

[0099] Step S1.1, establish a spacecraft model. Establish a multi-input multi-output time-varying spacecraft dynamic model based on the state information obtained from the database:

[0100]

[0101] Among them, t∈{0,1,2,…,N} is the running time, N is the running cycle, is the number of iterations, represents the set of non-negative integers {0,1,2,…}; x k (t),u k (t) and y k (t) are the state, input and position of the spacecraft at time t in the kth iteration; A(t), B(t) and C(t) are the time-varying system matrices of the spacecraft at time t; v k (t) represents the random noise at the tth time of the kth iteration.

[0102] Step S1.2, determine the expected target trajectory of the spacecraft. The expected target trajectory of the spacecraft is y d (t), t∈{1,2,…,N}.

[0103] Step S1.3, based on the above steps, model the random noise. k (t) Before modeling, we first define σ as a type of algebra

[0104]

[0105] in, represents a watershed, express The elements in v i (t) represents the random noise at the tth time of the i-th iteration.

[0106] On this basis, the random noise v k (t) is modeled. For any t∈{0,1,2,…,N}, the random noise v k (t) forms a relative Martingale difference sequence

[0107]

[0108] That is, the random noise model is established as

[0109]

[0110] When a spacecraft performs repeated trajectory tracking missions, random noise is difficult to avoid, and it mainly comes from the following aspects: sensor noise, such as measurement errors of gyroscopes, accelerometers and star sensors; atmospheric disturbances, especially atmospheric density inhomogeneities and short-term changes in low Earth orbit; and manufacturing and assembly errors, which are generated during satellite manufacturing and assembly and accumulated during orbital operation. In this embodiment, the above-mentioned random noise is modeled as a martingale difference sequence. Compared with the traditional Gaussian white noise modeling method, the modeling method adopted by the embodiment of the present invention is more general and includes the traditional Gaussian white noise modeling method. This broader modeling method can more accurately describe various random noise sources and improve the applicability and accuracy of the model.

[0111] Step S2, based on the established multi-input multi-output time-varying spacecraft dynamics model, as the corresponding system matrix of the spacecraft, obtain the corresponding block Toplitz matrix, establish the model of the random iterative learning control law, and obtain the control input under the current iteration. Specifically, it includes the following steps.

[0112] Step S2.1, based on the established multi-input multi-output time-varying spacecraft dynamics model, establish a block Toeplitz matrix corresponding to the spacecraft dynamics model (1).

[0113] The block Toeplitz matrix corresponding to the spacecraft dynamics model (1) is:

[0114]

[0115] Without loss of generality, G represents the block Toeplitz matrix corresponding to the spacecraft. Let the rank of G be m. Based on this, construct a matrix H1 with the same generation space as G.

[0116] Step S2.2, determine the learning gain matrix corresponding to the control law and obtain the position y of the spacecraft at the current iteration k (t), calculate the tracking error under the current iteration, and on this basis establish the model of the random iterative learning control law to obtain the control input under the current iteration. Specifically, the following steps are included.

[0117] Step S2.2.1, using the attenuation factor a k Overcome the influence of random noise, where a k Needs to be satisfied

[0118]

[0119] Among them, the attenuation factor α k A scalar representing the falloff along the iteration axis.

[0120] Step 2.2.2, use the learning parameter J to solve the spacecraft trackability problem, select

[0121] J=(H1(H1 T H1) -1 ) T .

[0122] Step 2.2.3, use the learning parameter Γ to ensure the convergence of the random iterative learning control law, where Γ satisfies the condition

[0123] Re(λ i ((H1(H1 T H1) -1 ) T GΓ))>0

[0124] Among them, λ i (.) represents the i-th eigenvalue of the matrix. This condition means that the matrix (H1(H1 T H1) -1 ) T The eigenvalues ​​of GΓ all have positive real parts.

[0125] Step 2.2.4, based on the results obtained in the above steps, determine the learning gain matrix and establish the model of the random iterative learning control law for spacecraft repetitive tasks as follows

[0126]

[0127] Among them, U k =[u k T (0),u k T (1),…,u k T (N-1)] T is the system control input augmented vector for k iterations, and is used as the control input for the current iteration. k-1 =[u k-1 T (0),u k-1 T (1),…,u k-1 T (N-1)] T is the system control input augmented vector under k-1 iterations, E k =[e k T (1),e k T (2),…,e kT (N)] T is the augmented vector of the system position error after k iterations, indicating the tracking error under the current iteration, e k (t) = y d (t)-y k (t) is the position error vector of the system at time t after k iterations. E k It means the tracking error in the current iteration. k-1 is the learning gain matrix of the previous iteration, where Π k =a k The form of ΓJ determines the learning gain matrix Π at the current iteration k .

[0128] Step 2.2.5, obtain the control input of the satellite system through the above random iterative learning control law model.

[0129] In the above steps of this implementation method, the random iterative learning control law overcomes the influence of random noise by introducing an attenuation factor to ensure the stability and accuracy of the system in the presence of noise; introduces learning parameters to ensure the convergence of the spacecraft learning process; and uses learning parameters to solve the trackability problem of the spacecraft and the problem that the non-zero Markov parameter matrix in the spacecraft does not satisfy the full rank condition.

[0130] Step S3, according to the control input of the spacecraft in the current iteration, the tracking error and the selected learning gain matrix, the control input of the spacecraft in the next iteration is updated, the spacecraft is controlled to execute the next iteration process, and the position of the spacecraft in the next iteration is obtained. Specifically, the following steps are included.

[0131] Step S3.1, according to the control input U of the spacecraft at the current iteration k , Tracking error E k And the selected learning gain matrix Π k Update the control input U of the spacecraft for the next iteration k+1 , control the spacecraft dynamics model (1), and determine the control input of the spacecraft at the next iteration by the following formula:

[0132]

[0133] Among them, U k+1 =[u k+1 T (0),u k+1 T (1),…,u k+1 T (N-1)] T is the augmented vector of the system control input under k+1 iterations.

[0134] Step S3.2, according to the control input of the spacecraft at the next iteration and the corresponding block Toeplitz matrix, the position of the spacecraft at the next iteration is determined by the following formula:

[0135] Y k+1 =GU k+1 +V k+1

[0136] in, is the system position augmentation vector for k+1 iterations, is the random noise augmented vector under k+1 iterations.

[0137] Step S3.3: The spacecraft updates and adjusts its own position according to the control input obtained in the next iteration of the spacecraft, and finally achieves complete tracking of the expected specified trajectory, that is, Where Ε(.) represents the expectation of the random variable.

[0138] Step S4, perform multiple iterations of step S3 to obtain the trajectory of the spacecraft's position along the time axis, and compare the trajectory of the spacecraft's position along the time axis with the spacecraft's expected target trajectory, until the spacecraft completes accurate tracking of the target trajectory, and outputs and saves the accurate tracking result. Specifically, by comparing the spacecraft's position with the expected target trajectory along the time axis, the actual position information y k (t) and the expected trajectory y d (t) compare to confirm whether the accurate tracking is completed. If the accurate tracking is not completed, repeat step S3. If the accurate tracking is completed, output and save the result of the accurate tracking.

[0139] The random iterative learning control method for spacecraft repetitive tasks provided above according to the embodiment of the present invention can be applied to any type of spacecraft, including, for example, observation satellites, etc.

[0140] refer to Figure 3 ,In order to verify the effectiveness of the random iterative learning control method for ,spacecraft repetitive tasks proposed in the present invention, the spacecraft is ,firstly integrated designed in Matlab, and a simulation experiment is ,performed. The simulation process is as follows.

[0141] 1) Set the parameters.

[0142] Here, a simulation case of applying the precise tracking iterative learning control system and method of the spacecraft under the influence of random noise provided by the present invention is provided. A spacecraft with the following linear dynamics is used:

[0143]

[0144] The system matrix is

[0145]

[0146] Random Noise k (t) is modeled as a martingale difference sequence according to the above modeling method. Considering the operation period N = 20, the rank of the Markov parameter matrix C(1)B(0) of the spacecraft is 1, which does not meet the row full rank condition or the column full rank condition. Here, the attenuation factor is selected Learning parameters The learning parameter J=0.3I, where I is the unit matrix.

[0147] From the above, the target trajectory of the spacecraft can be obtained as:

[0148]

[0149] 2) Analyze the results obtained above.

[0150] To further illustrate the effectiveness of the random iterative learning control method for spacecraft repetitive tasks provided by the present invention, see Figure 3 , showing the dynamic evolution of the spacecraft position and the expected target trajectory along the time axis after 100 iterations. The figure shows that the position output of the spacecraft can track the expected target trajectory in real time at any time, and has extremely high tracking accuracy. Therefore, the application of the above-mentioned random iterative learning control method for spacecraft repetitive tasks provided by the present invention can overcome the influence of random noise of the spacecraft, so that any linear time-varying spacecraft with a Markov parameter matrix of insufficient rank can track the trackable target trajectory in real time at all times within a limited time period, and has extremely high tracking accuracy.

[0151] All the above optional technical solutions can be arbitrarily combined to form optional embodiments of the present application, which will not be described one by one here.

[0152] It should be understood that the order of execution of the steps in the above embodiment does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present invention.

[0153] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A random iterative learning control method for spacecraft repetitive tasks, characterized in that: The following steps are involved: Step S1, establishing a spacecraft dynamics model, determining the expected target trajectory of the spacecraft, and establishing a random noise model; Step S2, according to the spacecraft dynamics model established in step S1, obtain the corresponding block Toplitz matrix, establish a model of the random iterative learning control law, and obtain the control input, tracking error and learning gain matrix of the spacecraft under the current iteration; Step S3, according to the control input, tracking error and learning gain matrix of the spacecraft in the current iteration, the control input of the spacecraft in the next iteration is updated, the spacecraft is controlled to execute the next iteration process, and the position of the spacecraft in the next iteration is obtained; Step S4, repeat step S3 for multiple iterations to obtain the trajectory of the spacecraft's position along the time axis, and compare the trajectory of the spacecraft's position along the time axis with the expected target trajectory of the spacecraft. If precise tracking is not achieved, continue to repeat step S3. If the spacecraft completes precise tracking of the target trajectory, the result of the precise tracking is output and saved.

2. The random iterative learning control method for spacecraft repetitive tasks according to claim 1, characterized in that: Step S1 specifically includes the following steps: Step S1.1, establish a spacecraft dynamics model, and establish a multi-input multi-output time-varying spacecraft dynamics model based on the state information obtained from the database: Among them, t∈{0,1,2,…,N} is the running time, N is the running cycle, is the number of iterations, x k (t),u k (t) and y k (t) are the state, input and position of the spacecraft at time t in the kth iteration, A(t), B(t) and C(t) are the time-varying system matrices of the spacecraft at time t; v k (t) represents the random noise at the tth time of the kth iteration; Step S1.2, determine the expected target trajectory of the spacecraft, and obtain the expected target trajectory of the spacecraft as y d (t), t∈{1,2,…,n}; Step S1.3, establish a random noise model, and calculate the random noise v in the spacecraft dynamics model (1) k (t) Before modeling, we first define σ as a type of algebra, in, represents a watershed, express The elements in v i (t) represents the random noise at the tth time of the i-th iteration; On this basis, the random noise v k (t) Modeling: For any t∈{0,1,2,…,N}, the random noise v k (t) forms a relative Martingale difference sequence That is, the random noise model is established as 3. The random iterative learning control method for spacecraft repetitive tasks according to claim 2, characterized in that: Step S2 specifically includes the following steps: Step S2.1, based on the established multi-input multi-output time-varying spacecraft dynamics model, establish the block Toeplitz matrix corresponding to the spacecraft dynamics model (1) Without loss of generality, G represents the block Toeplitz matrix corresponding to the spacecraft. Let the rank of G be m. Based on this, construct a matrix H1 with the same generation space as G; Step S2.2, determine the learning gain matrix and obtain the position y of the spacecraft at the current iteration k (t), calculate the tracking error under the current iteration, and on this basis establish the model of random iterative learning control law to obtain the control input under the current iteration.

4. The random iterative learning control method for spacecraft repetitive tasks according to claim 3, characterized in that: Step S2.2 specifically includes the following steps: Step S2.2.1, using the attenuation factor a k Overcome the influence of random noise, where a k Needs to be satisfied Among them, the attenuation factor α k A scalar indicating the decay along the iteration axis; Step 2.2.2, use the learning parameter J to solve the spacecraft trackability problem, select J=(H1(H1 T H1) -1 ) T ; Step 2.2.3, use the learning parameter Γ to ensure the convergence of the random iterative learning control law, and Γ satisfies the condition Re(λ i ((H1(H1 T H1) -1 ) T GΓ))>0 Among them, λ i (.) represents the i-th eigenvalue of the matrix. This condition means that the matrix (H1(H1 T H1) -1 ) T The eigenvalues ​​of GΓ all have positive real parts; Step 2.2.4, based on the results obtained in the above steps, determine the learning gain matrix and establish the model of the random iterative learning control law for the repeated mission of the spacecraft as follows Among them, U k =[u k T (0),u k T (1),…,u k T (N-1)] T is the system control input augmented vector for k iterations, and is used as the control input for the current iteration. k-1 =[u k-1 T (0),u k-1 T (1),…,u k-1 T (N-1)] T is the system control input augmented vector under k-1 iterations, E k =[e k T (1),e k T (2),…,e k T (N)] T is the augmented vector of the system position error after k iterations, indicating the tracking error under the current iteration, e k (t)= y d (t)-y k (t) is the position error vector of the system at time t after k iterations, Π k-1 is the learning gain matrix of the previous iteration, where Π k =a k The form of ΓJ determines the learning gain matrix ∏ in the current iteration k ; Step 2.2.5, obtain the control input U of the spacecraft in the current iteration through the above random iterative learning control law model k .

5. The random iterative learning control method for spacecraft repetitive tasks according to claim 4, characterized in that: Step S3 specifically includes the following steps: Step S3.1, according to the control input U of the spacecraft at the current iteration k , Tracking error E k And the selected learning gain matrix Π k Update the control input U of the spacecraft for the next iteration k+1 , control the spacecraft dynamics model (1), and determine the control input of the spacecraft in the next iteration by the following formula: Among them, U k+1 =[u k+1 T (0),u k+1 T (1),...,u k+1 T (N-1)] T is the system control input augmented vector for k+1 iterations; Step S3.2, according to the control input of the spacecraft at the next iteration and the corresponding block Toeplitz matrix, the position of the spacecraft at the next iteration is determined by the following formula: Y k+1 =GU k+1 +V k+1 in, is the system position augmentation vector for k+1 iterations, is the random noise augmented vector under k+1 iterations; Step S3.3: The spacecraft updates and adjusts its position according to the control input obtained for the next iteration of the spacecraft, and finally realizes the complete tracking of the expected specified trajectory by the spacecraft, that is, Among them, Ε(.) represents the expectation of the random variable.

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