CN114879515B - Spacecraft attitude reconstruction fault-tolerant control method based on learning neural network - Google Patents

Spacecraft attitude reconstruction fault-tolerant control method based on learning neural network Download PDF

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CN114879515B
CN114879515B CN202210813256.9A CN202210813256A CN114879515B CN 114879515 B CN114879515 B CN 114879515B CN 202210813256 A CN202210813256 A CN 202210813256A CN 114879515 B CN114879515 B CN 114879515B
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neural network
attitude
spacecraft
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fault
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CN114879515A (en
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贾庆贤
马瑞
舒睿
张永康
吴云华
于丹
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Nanjing University of Aeronautics and Astronautics
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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Abstract

The invention discloses a spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network, which comprises the steps of firstly, considering the influences of spacecraft actuating mechanism faults, rotational inertia uncertainty and space disturbance, and establishing a spacecraft attitude tracking dynamics model; then, designing a learning neural network model and a learning neural network observer to carry out accurate reconstruction on the faults of the actuating mechanism; and finally, based on a fault reconstruction result, providing a spacecraft attitude reconstruction fault-tolerant controller method based on a learning neural network sliding mode algorithm, wherein the method can realize high-precision attitude tracking control of spacecraft actuating mechanism faults, uncertainty of rotational inertia and space interference influence. The spacecraft attitude fault-tolerant control scheme based on the learning neural network has the characteristics of small calculated amount, strong fault-tolerant capability, strong robustness and the like.

Description

Spacecraft attitude reconstruction fault-tolerant control method based on learning neural network
Technical Field
The invention relates to a spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network, which is mainly applied to spacecraft attitude fault-tolerant control when the faults of a spacecraft actuating mechanism, uncertainty of rotary inertia and space interference are considered.
Background
The spacecraft is in a complex outer space environment for a long time, is influenced by factors such as solar radiation, a weak magnetic field, particle irradiation, vacuum and the like, and inevitably brings great challenges to the maintenance of safety and high reliability of a spacecraft attitude control system. The attitude control subsystem is one of the most basic and key subsystems of a spacecraft system, and whether the system works stably determines whether a space mission can be carried out smoothly. The fault of the attitude control system causes the control precision of the spacecraft to be reduced and the expected attitude to be lost, and the service life of the spacecraft is shortened and even the task is interrupted, thereby bringing about huge economic loss. Therefore, the reliability and maintainability of the spacecraft are improved by the spacecraft fault diagnosis and fault-tolerant control technology, and the spacecraft fault diagnosis and fault-tolerant control method has important academic research value and practical application value.
In recent years, with the requirement for autonomous development of aerospace intelligence, the application of artificial intelligence in the aerospace field draws attention of all aerospace major countries. Aiming at the development requirement of a high-reliability spacecraft system, the rapid development of artificial intelligence is combined, and the on-orbit intelligent fault diagnosis and fault-tolerant control of the spacecraft become the future development trend. Considering the limited storage space and computing power of the on-board computer, the defects that the existing intelligent learning algorithm is large in calculation amount and needs offline training for diagnosis data, and the like, how to ensure the on-orbit intelligent autonomous diagnosis of the spacecraft is still worth researching. On the other hand, considering increasingly complex space exploration tasks and severe in-orbit environments, how to effectively process unknown nonlinear dynamics and achieve robust spacecraft attitude fault-tolerant control is worthy of research.
Disclosure of Invention
Aiming at the problems of executing mechanism faults, uncertainty of rotary inertia and space interference influence in the process of attitude tracking of an on-orbit spacecraft, the active fault-tolerant control method based on the learning neural network sliding mode is provided, the calculation pressure of an on-board computer can be reduced, and the robustness of attitude fault-tolerant tracking control of the spacecraft can be ensured.
A spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network comprises the following steps:
step 1, considering the influences of faults of a spacecraft actuating mechanism, uncertainty of rotational inertia and space interference, establishing a spacecraft attitude dynamics model, and establishing a spacecraft attitude tracking dynamics model based on the spacecraft attitude dynamics model;
step 2, establishing a learning neural network model for online accurate fitting of a nonlinear function by combining a P-type iterative learning algorithm and a radial basis function RBF neural network model;
step 3, designing a learning neural network observer for spacecraft actuating mechanism fault reconstruction based on the learning neural network model;
step 4, providing existence conditions of the learning neural network observer and calculating related parameters;
step 5, designing a learning neural network sliding mode controller for spacecraft attitude reconstruction fault-tolerant control based on the executing mechanism fault reconstruction information obtained by the learning neural network observer, wherein the controller comprises a feedforward compensation item, an attitude tracking controller and a fault adjustment fault-tolerant controller, and under the conditions of actuator faults and interference, the spacecraft is ensured to stably and accurately realize attitude tracking;
and 6, providing existence conditions of the learning neural network sliding mode controller and calculating related parameters to realize spacecraft attitude reconstruction fault-tolerant control.
Preferably, the spacecraft attitude dynamics model in step 1 is as follows:
Figure DEST_PATH_IMAGE001
（1）
wherein the content of the first and second substances,J S ∈R 3×3 a nominal moment of inertia matrix representing the rigid spacecraft;ω=[ω x , ω y , ω z ] T ∈R 3 representing the attitude angular velocity of the spacecraft body coordinate system relative to the inertial coordinate system, superscript-representing the derivative,
Figure DEST_PATH_IMAGE002
acceleration which is angular velocity;u c =[u x , u y , u z ] T ∈R 3 outputting torque for the actuating mechanism;u f =[u fx , u fy , u fz ] T ∈R 3 failure of the actuator;d=[d x , d y , d z ] T ∈R 3 the spatial disturbance moment is represented by a spatial disturbance moment,△J∈R 3×3 is the uncertainty portion of the moment of inertia matrix; hypothesis joint interference
Figure DEST_PATH_IMAGE003
Taking into account joint interferenceu dJ Its value is unknown but bounded, denoted as ║u dJ ║≤u dJmax , u dJmax Is defined asu dJ The upper bound of (a) is,ω × is composed ofωAn anti-symmetric matrix.
Preferably, based on the spacecraft attitude dynamic model (1), the spacecraft attitude tracking error dynamic model is established as follows:
Figure DEST_PATH_IMAGE004
（2）
wherein the content of the first and second substances,ω e =[ω ex , ω ey , ω ez ] T ∈R 3 is the error of attitude angular velocity, is the actual angular velocityω=[ω x , ω y , ω z ] T ∈R 3 And desired angular velocityω d =[ω dx , ω dy , ω dz ] T ∈R 3 Error therebetween, i.e.ω e =ω-R(Q e )ω d (ii) a Attitude quaternion errorQ e =(q e0 ,q e )∈R 4 Is provided withq e0 ∈R，q e =[q e1 , q e2 , q e3 ]∈R 3 And is andq 2 e0 + q e T q e =1；R(Q e )an attitude transformation matrix from the expected attitude to the actual attitude of the spacecraft meets the following requirements:
Figure DEST_PATH_IMAGE005
；
Figure DEST_PATH_IMAGE006
defined as joint interference, whose value, while unknown but bounded, can be represented as ║u d ║≤u dmax , u dmax Is defined asu d The upper bound of (c).
Preferably, in step 2, a learning neural network model for performing online accurate fitting on the fault of the execution mechanism is constructed by combining a P-type iterative learning algorithm and a Radial Basis Function (RBF) neural network, wherein the learning neural network model is as follows:
Figure DEST_PATH_IMAGE007
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE008
is composed off(x)Is determined by the estimated value of (c),
Figure DEST_PATH_IMAGE009
in the form of a matrix of weights,h(x)in the form of a vector of gaussian basis functions,pandmrespectively node and input number, subscriptjIs a node; the learning neural network model can accurately fit a nonlinear function on linef(x)。
Preferably, the RBF neural network model in step 2 is represented as:
for arbitrary continuous functionsf(x)∈R m There is an ideal weight matrix W∈R m×p Thereby satisfying the following conditions:
f(x)= W T h(x)+ε（3）
whereinx=[x 1 ,…,x n ]Is an input vector;pandmrespectively, a node and an input number;εis an approximation error;h(x)=[h 1 (x)…h p (x)] T is a gaussian basis function vector, the elements of which can be obtained by the following relationship:
Figure DEST_PATH_IMAGE010
（4）
wherein the content of the first and second substances,c i ∈R n representing RBF neural networksiThe central parameter of the individual hidden layers,b i ∈r represents the followingiA Gaussian functionh i (x)A width parameter of (d);
wherein, the weight matrix is subjected to P-type iterative learning algorithm
Figure DEST_PATH_IMAGE011
Carrying out iterative upgrade and update, wherein the structural form of the P-type iterative learning algorithm is as follows:
Figure DEST_PATH_IMAGE012
（5）
whereinαIs the learning rate of the learning rate,ethe observer measures and estimates output deviation or controller control deviation, and gamma is a gain matrix;τfor the learning time interval, the learning interval can be selected to be a system sampling interval or an integral multiple of the sampling interval;
therefore, the nonlinear function online accurate fitting algorithm based on the learning neural network model is as follows:
Figure DEST_PATH_IMAGE013
（6）
based on the RBF neural network model (3) and the P-type iterative learning algorithm (5), the designed learning neural network model (6) can accurately fit a nonlinear function on linef(x)。
Preferably, the learning neural network model in the step 2 gives a design structure of the learning neural network observer; the observer has certain robustness to interference, and can accurately reconstruct actuator faults; the learning neural network observer structure for spacecraft actuator fault reconstruction in step 3 is as follows:
Figure DEST_PATH_IMAGE014
（7）
Figure DEST_PATH_IMAGE015
（8）
Figure DEST_PATH_IMAGE016
（9）
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE017
is an estimated value of the attitude angular velocity of the spacecraft,
Figure DEST_PATH_IMAGE018
the deviation of the actual attitude angular velocity and the estimated attitude angular velocity of the spacecraft is obtained;
Figure DEST_PATH_IMAGE019
is an actuator deviation fault reconstruction value; on-line accurate reconstruction of actuator offset faults based on a learning neural network model (6), wherein
Figure DEST_PATH_IMAGE020
Performing online iterative upgrade updating on the weight matrix by using a P-type iterative learning algorithm (9);
Figure DEST_PATH_IMAGE021
is a Gaussian basis function vector;K 1 ∈R 3×3 andK 2 ∈R 3×3 is an observer gain matrix;γandθ 1 is a positive gain parameter; to ensure robustness of the learning neural network observer, use is made of
Figure DEST_PATH_IMAGE022
Joint interference is handled.
Preferably, step 4 specifically comprises:
step 4.1, the stable existence conditions of the learning neural network observer are given as follows:
Figure DEST_PATH_IMAGE023
（10）
Figure DEST_PATH_IMAGE024
（11）
α 1 (1+ε 1 )θ 1 2 -1＜0 （12）
γ-u dJmax ≥0 （13）
wherein the content of the first and second substances,Pis a positive definite symmetric matrix, a positive scalar quantityα 1 ≥1Scalar quantityε 1 ＞0；
Step 4.2, calculating the parameters of the learning neural network observer based on the learning neural network observer and the existence conditions thereof, and comprising the following steps:
step 4.21, selecting positive definite symmetric matrixPAnd a sufficiently small positive scalar quantityα 1 Calculating a gain matrix by equation (11)K 2 ；
Step 4.22, select the appropriate scalarε 1 Calculating the coefficient to be determined by equation (12)θ 1 ；
Step 4.23, according tou dJmax Selecting a positive gain parameterγSo that the formula (13) holds;
step 4.24, calculate the gain matrix by equation (10)K 1 ；
Step 4.25, selecting a suitable scalar quantity by equation (4)b i Sum vectorc i Building a Gaussian basis function
Figure DEST_PATH_IMAGE025
；
Step 4.26, selecting a proper learning time interval according to the sampling time interval of the attitude control system of the spacecraftτ。
Preferably, the learning neural network sliding mode attitude fault-tolerant controller in step 5 has the following structure:
u c =u com +u smc -u rec （14）
Figure DEST_PATH_IMAGE026
（15）
Figure DEST_PATH_IMAGE027
（16）
Figure DEST_PATH_IMAGE028
（17）
wherein, the superscript represents the estimated value, u com is a feedforward compensation term;u smc an attitude tracking controller;u rec adjusting a fault tolerant controller for a fault based learning neural network model;
Figure DEST_PATH_IMAGE029
defined as combined interferenceu df On-line estimation of (2) using the learning neural network in step (2) and weighting the neural network using a P-type iterative learning algorithm
Figure DEST_PATH_IMAGE030
Performing online upgrade updating;Sfor the designed slip-form surface,g(S)a Gaussian base function vector of the RBF neural network; parameter(s)
Figure DEST_PATH_IMAGE031
，β=diag{β 1 β 2 β 3 Is a positive definite diagonal matrix;K 3 ∈R 3×3 is a controller gain matrix;θ 2 andφis a positive scalar quantity.
Preferably, in step 6, in particular,
step 6.1, aiming at the designed learning neural network sliding mode attitude fault-tolerant controller (14), giving the following stable existence conditions:
P 1 J s -1 =α 3 K 3 T （18）
α 3 （1+ε 2 ）θ 2 2 -1＜0 （19）
wherein the content of the first and second substances,P 1 ∈R 3×3 for positively defining symmetric matrices, scalarsε 2 > 0, scalar quantityα 3 ＞0；
6.2, calculating relevant parameters of the learning neural network sliding mode controller based on the structure and the existing conditions of the learning neural network sliding mode attitude fault-tolerant controller, and comprising the following steps:
step 6.21, select the diagonal matrix with the same elementsP 1 And a sufficiently small scalarα 3 Calculating a gain matrix by equation (18)K 3 ；
Step 6.22, select the appropriate scalarε 2 Calculating the coefficient to be determined by equation (19)θ 2 ；
Step 6.23, select the appropriate positive scalar quantity
Figure DEST_PATH_IMAGE032
；
Step 6.24, selecting a proper scalar according to the formula (4)b i Sum vectorc i Building a Gaussian basis functiong(S)；
Step 6.25, selecting a proper learning time interval according to the sampling time interval of the attitude control system of the spacecraftτ。
Compared with the prior art, the spacecraft attitude tracking fault-tolerant control strategy designed by the invention, which takes the iterative learning algorithm, the RBF neural network and the sliding mode algorithm into consideration, has the advantages that:
(1) The method utilizes a learning neural network strategy to accurately reconstruct the failure of the spacecraft actuating mechanism; the P-type iterative learning algorithm is used for replacing the existing self-adaptive learning algorithm to update the weight matrix on line, and the provided strategy has the characteristic of small calculated amount. Therefore, the method is more suitable for the on-orbit spacecraft with limited satellite-borne computing capacity.
(2) According to the invention, on the basis of learning a neural network, a sliding mode control algorithm is introduced, and a learning neural network sliding mode fault-tolerant controller for spacecraft attitude tracking control is constructed, so that the robustness and high precision of spacecraft attitude tracking control are ensured, and the calculation amount can be effectively reduced.
Drawings
FIG. 1 is a flow chart of a spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network;
fig. 2 is a schematic block diagram of a learning neural network-based spacecraft attitude reconstruction fault-tolerant control principle of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network. Aiming at the problems of executing mechanism faults, uncertainty of rotational inertia and space environment interference in the process of tracking and controlling the attitude of the on-orbit spacecraft, the design of a learning neural network observer and the design of a learning neural network sliding mode controller for reconstructing fault-tolerant control of the attitude of the spacecraft are provided, and the method is mainly used for solving the problems of reconstructing the fault of the attitude-controlled executing mechanism of the spacecraft and reconstructing the fault-tolerant control of the robust attitude.
The invention carries out random precision reconstruction on the faults of the actuating mechanism through the RBF neural network, and replaces the self-adaptive learning algorithm with the P-type iterative learning algorithm to continuously iteratively update the RBF neural network weight matrix. Compared with a fault reconstruction method based on an adaptive neural network and a posture fault-tolerant control method based on an adaptive neural network sliding mode, the method has the advantages that the calculation pressure of the spaceborne computer is reduced, and meanwhile the robustness of the posture fault-tolerant tracking control of the spacecraft can be guaranteed.
As shown in fig. 1 to 2, a spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network includes the following steps:
step 1, considering the influence of faults, uncertainty of rotational inertia and space interference of a spacecraft actuating mechanism, establishing a spacecraft attitude tracking dynamics model based on a spacecraft attitude dynamics model, specifically,
step 1.1, establishing a spacecraft attitude kinematics model and a spacecraft dynamics model as follows:
Figure DEST_PATH_IMAGE033
（20）
Figure DEST_PATH_IMAGE034
（21）
for quaternionQ=(q 0 ,q)∈R 4 Whereinq 0 ∈R，q=[q 1 , q 2 , q 3 ] T ∈R 3 Is full ofLaw of foot operationq 2 0 + q T q=1；ω=[ω x , ω y , ω z ] T ∈R 3 Representing the attitude angular velocity of the spacecraft body coordinate system relative to the inertial coordinate system;J ∈R 3×3 a matrix of moments of inertia representing the rigid spacecraft;u=[u, u, u] T ∈R 3 outputting torque for a fault actuating mechanism;d=[d x , d y , d z ] T ∈R 3 representing space disturbance moments such as gravity gradient moment, solar radiation moment, geomagnetic moment and the like, and being bounded although specific numerical values of the space disturbance moments are unknown; non-linear termω × JωSatisfaction assumptions
Figure DEST_PATH_IMAGE035
，ηIs a positive parameter; antisymmetric matrix
Figure DEST_PATH_IMAGE036
；I 3 Is a third order identity matrix.
Step 1.2, based on the spacecraft attitude dynamics model, the spacecraft attitude tracking error kinematics model and the dynamics model are as follows:
Figure DEST_PATH_IMAGE037
（22）
Figure DEST_PATH_IMAGE038
（23）
ω e =ω- R(Q e ) ω d （24）
wherein, the posture is quaternaryNumber errorQ e =(q e0 ,q e )∈R 4 Is provided withq e0 ∈R，q e =[q e1 , q e2 , q e3 ]∈R 3 And is andq 2 e0 + q e T q e =1。Q e defined as the quaternion of the actual attitudeQAnd desired attitude quaternionQ d =(q d0 ,q d )∈R 4 An error therebetween; quaternion for desired attitudeQ d Whereinq d0 ∈R，q d =[q d1 ，q d2 ，q d3 ]∈R 3 Satisfy the following requirementsq 2 d0 + q d T q d =1(ii) a Furthermore, there is a relationship between the attitude quaternion error and the attitude angular velocity error:q e0 = q d T q+q 0 q d0 ，q e = q d0 q-q d × q- q 0 q d 。ω e =[ω ex , ω ey , ω ez ] T ∈R 3 is the error of attitude angular velocity, which is the actual angular velocityωAnd desired angular velocityω d =[ω dx , ω dy , ω dz ] T ∈ R 3 The error between;
Figure DEST_PATH_IMAGE039
representing an error attitude angular acceleration vector of the spacecraft;R(Q e )is defined as a transformation matrix from the expected attitude to the actual attitude of the spacecraft, and the expression is
Figure 487103DEST_PATH_IMAGE005
And is
Figure DEST_PATH_IMAGE040
；
Figure DEST_PATH_IMAGE041
Representing the spacecraft expected attitude angular acceleration vector.
Considering uncertainty of the rotational inertia, the rotational inertia of the spacecraftJ = J S +△JWhereinJ S In the case of the nominal part,△Jis an indeterminate portion. Considering the failure of the spacecraft actuating mechanism and considering the uncertainty item as external interference, the spacecraft attitude dynamics model and the attitude tracking error dynamics mathematical model can be rewritten as follows:
Figure DEST_PATH_IMAGE042
（25）
Figure DEST_PATH_IMAGE043
（26）
wherein the content of the first and second substances,u c in order to output the instructions to the controller,u f in order to cause the failure of the actuating mechanism of the spacecraft,
Figure DEST_PATH_IMAGE044
，
Figure DEST_PATH_IMAGE045
are defined as joint interference.u dJ Andu d although unknown, there areBoundary, i.e. ║u dJ ║≤u dJmax And ║u d ║≤u dmax Therein, whereinu dJmax Andu dmax defined as joint interference, respectivelyu dJ Andu d the upper bound of (c).
And 2, establishing a learning neural network model for online accurate fitting of the nonlinear function based on a P-type iterative learning algorithm and a Radial Basis Function (RBF) neural network model.
RBF neural network model: for arbitrary continuous functionsf(x)∈R m There exists an ideal weight matrix W∈R m ×p Thereby satisfying the following conditions:
f(x)= W T h(x)+ε （27）
whereinx=[x 1 ,…,x n ]Is an input vector;pandmrespectively, a node and an input number;εis an approximation error;h(x)=[h 1 (x)…h p (x)] T is a gaussian basis function vector, the elements of which can be obtained by the following relationship:
Figure 607505DEST_PATH_IMAGE010
（28）
wherein the content of the first and second substances,c i ∈R n representing RBF neural networksiThe central parameter of the individual hidden layers,b i ∈r represents the followingiA Gaussian functionh i (x)The width parameter of (2).
In addition, it is assumed that there exists an optimal weight matrix
Figure DEST_PATH_IMAGE046
Thereby minimizing approximation errors, such as:
Figure DEST_PATH_IMAGE047
（29）
therefore, the temperature of the molten metal is controlled,
Figure 59346DEST_PATH_IMAGE008
is an on-line accurate fitting term of a nonlinear function, and can be obtainedεIs an optimal weight matrix
Figure 720135DEST_PATH_IMAGE046
Corresponding minimization of the approximation error. In the existing RBF neural network technology, the weight matrix is usually performed by using an adaptive learning algorithm
Figure 737770DEST_PATH_IMAGE009
If an integral type self-adaptive learning algorithm is adopted:
Figure DEST_PATH_IMAGE048
（30）
orσ-modification adaptive learning algorithm:
Figure DEST_PATH_IMAGE049
（31）
wherein Γ is the gain matrix and,σis a normal number, and is,eis the observer measured output deviation or the controller controlled deviation.
Compared with the self-adaptive learning algorithm, the P-type iterative learning algorithm has the characteristics of small calculation amount, no need of continuous measurement output and the like. Therefore, the P-type iterative learning algorithm has a better application prospect by considering the limited computing power of the spaceborne computer. Based on the above, the patent proposes to replace the adaptive algorithm with the P-type iterative learning algorithm for the weight matrix
Figure 29074DEST_PATH_IMAGE009
And performing iterative upgrade updating. The structural form of the P-type iterative learning algorithm is as follows:
Figure DEST_PATH_IMAGE050
（32）
whereinαIs the learning rate of the learning rate,eis the observer measuring and estimating the output deviation or the controller controlling deviation, and gamma is the gain matrix.τTo learn the time interval, the learning time interval may be chosen to be the system sampling interval or an integer multiple of the sampling interval. Then the nonlinear function online accurate fitting algorithm based on the learning neural network model is as follows:
Figure DEST_PATH_IMAGE051
（33）
the nonlinear function accurate fitting capability of the learning neural network model (33) is considered, and the method can be applied to online accurate identification of spacecraft attitude control nonlinear dynamics, space disturbance moment or actuator faults.
And 3, designing a learning neural network observer for spacecraft actuating mechanism fault reconstruction based on the learning neural network model in the step 2, and realizing spacecraft attitude angular velocity estimation and spacecraft actuating mechanism fault reconstruction.
Aiming at a spacecraft attitude dynamics model (25), designing the following learning neural network observer structure:
Figure 764948DEST_PATH_IMAGE014
（34）
Figure 229428DEST_PATH_IMAGE015
（35）
Figure 101569DEST_PATH_IMAGE016
（36）
wherein the content of the first and second substances,
Figure 360512DEST_PATH_IMAGE017
is an estimated value of the attitude angular velocity of the spacecraft,
Figure 318104DEST_PATH_IMAGE018
estimating an angular velocity difference value for the actual attitude angular velocity of the spacecraft and the observer;
Figure 320695DEST_PATH_IMAGE019
the method is characterized in that a fault reconstruction value of an execution mechanism is accurately reconstructed on line by using a learning neural network model;
Figure 844080DEST_PATH_IMAGE020
performing online iterative upgrade updating on the weight matrix by using a P-type iterative learning algorithm (36);
Figure 477187DEST_PATH_IMAGE021
in the form of a vector of gaussian basis functions,K 1 ∈R 3×3 andK 2 ∈R 3×3 is the gain matrix of the observer;γandθ 1 is a positive gain parameter; in order to achieve the robustness of the learning neural network observer,
Figure 984391DEST_PATH_IMAGE022
is used to handle joint interference, the sign function sgn (.) is defined as
Figure DEST_PATH_IMAGE052
。
Step 4, providing the existing condition of the learning neural network observer and the parameter calculation step thereof, specifically,
and 4.1, proving the stability of the learning neural network observer by using a Lyapunov stability theory. If the parameters of the learning neural network observer meet the following conditions:
Figure 728356DEST_PATH_IMAGE023
（37）
Figure 371827DEST_PATH_IMAGE024
（38）
α 1 (1+ε 1 )θ 1 2 -1＜0 （39）
γ-u dJmax ≥0 （40）
the learning neural network observer formula (34) -formula (36) ensures that the estimated deviation of the attitude angular velocity of the spacecraft and the reconstruction deviation of the fault of the spacecraft actuator are finally and consistently bounded. In the presence condition of the observer,Pin order to positively determine the symmetric matrix,α 1 ≥1，ε 1 ＞0。
step 4.2, based on the structure and the existence condition of the learning neural network observer, the calculation steps of the parameters of the learning neural network observer are as follows:
1) Selecting a positive definite symmetry matrixPAnd a sufficiently small positive scalar quantityα 1 Calculating a gain matrix by equation (38)K 2 ；
2) Selecting an appropriate scalar quantityε 1 Calculating the parameters by equation (39)θ 1 ；
3) According tou dJmax Selecting appropriate parametersγSo that the formula (40) is established;
4) Calculating the gain matrix by equation (37)K 1 ；
5) Selecting an appropriate scalar quantity by equation (28)b i Sum vectorc i Building a Gaussian base function
Figure 910256DEST_PATH_IMAGE025
；
6) Selecting a proper learning time interval according to the sampling time interval of the attitude control system of the spacecraftτ。
And step 5, further designing a learning neural network sliding mode attitude fault-tolerant controller for realizing fault-tolerant control based on the fault reconstruction result obtained by the learning neural network observer established in the step 3.
The controller comprises three parts of a feedforward compensation item, an attitude tracking controller and a fault-tolerant controller for fault adjustment, the spacecraft attitude tracking system can ensure that the spacecraft stably and accurately realizes attitude tracking under the conditions of actuator faults and interference.
The sliding mode structure and the design of each part of the controller are given as follows:
first, the results are reconstructed based on actuator faults
Figure DEST_PATH_IMAGE053
The spacecraft attitude tracking error dynamics model (26) may be further adapted as follows:
Figure DEST_PATH_IMAGE054
（41）
wherein the content of the first and second substances,u df =u d +e f in order to integrate the interference,e f errors are reconstructed for actuator faults.
Secondly, the following slip form surfaces are givenSDesigning:
Figure DEST_PATH_IMAGE055
（42）
wherein the content of the first and second substances,β=diag{β 1 β 2 β 3 the positive definite diagonal matrix is used as the positive definite diagonal matrix; symbolic function
Figure DEST_PATH_IMAGE056
Is defined as:
Figure DEST_PATH_IMAGE057
，α 1 ∈(1,2)
the sliding mode surface (42) is known to be composed of a spacecraft attitude angular velocity tracking error and a spacecraft attitude quaternion tracking error. From the spacecraft attitude tracking error kinematic model (22) and the spacecraft attitude tracking error kinematic model (26), it is possible to obtain:
Figure DEST_PATH_IMAGE058
（43）
next, the sliding mode approach is given as follows:
Figure DEST_PATH_IMAGE059
（44）
wherein, the positive scalar quantity
Figure 311282DEST_PATH_IMAGE031
。
Finally, based on the sliding mode surface (42) and the approximation rule (44), the following learning neural network sliding mode attitude fault-tolerant controller design is provided:
u c =u com +u smc -u rec （45）
Figure 593358DEST_PATH_IMAGE026
（46）
Figure 91336DEST_PATH_IMAGE027
（47）
Figure 128562DEST_PATH_IMAGE028
（48）
wherein, the superscript represents the estimated value, u com is a feedforward compensation term;u smc an attitude tracking controller;u rec adjusting a fault tolerant controller for a fault based learning neural network model;
Figure 282463DEST_PATH_IMAGE029
defined as combined interferenceu df On-line estimation of the neural network using a learning neural network and weighting of the neural network using a P-type iterative learning algorithm
Figure DEST_PATH_IMAGE060
Performing online upgrade updating; g(S)a Gaussian base function vector of the RBF neural network;K 3 ∈R 3 a controller gain matrix;θ 2 andøis a positive scalar quantity.
And 6, providing the existing conditions and parameter calculation steps of the learning neural network sliding mode controller.
And 6.1, proving the stability of the learning neural network sliding mode attitude fault-tolerant controller (45) by utilizing a Lyapunov stability theory. If learning the neural network sliding mode attitude fault-tolerant controller parameter and satisfying the following condition:
P 1 J s -1 =α 3 K 3 T （49）
α 3 （1+ε 2 ）θ 2 2 -1＜0 （50）
the learning neural network sliding mode attitude fault-tolerant controller can ensure that the spacecraft attitude angular velocity tracking error and the spacecraft attitude quaternion tracking error are finally bounded. In the above-mentioned conditions, the first and second,P 1 ∈R 3×3 in order to define the symmetric matrix positively,ε 2 ＞0，α 3 ＞0。
step 6.2, based on the existence condition of the learning neural network sliding mode attitude fault-tolerant controller, providing parameters of the learning neural network sliding mode attitude fault-tolerant controller, which comprise the following steps:
1) Selecting diagonal matrices of identical elementsP 1 And a sufficiently small scalarα 3 Calculating a gain matrix by equation (49)K 3 ；
2) Selecting an appropriate scalar quantityε 2 Calculating the parameters by equation (50)θ 2 ；
3) Selecting an appropriate positive scalar quantity
Figure 633810DEST_PATH_IMAGE032
；
4) Selecting an appropriate scalar by equation (28)b i Sum vectorc i Building a Gaussian base functiong(S)；
5) Selecting a proper learning time interval according to the sampling time interval of the attitude control system of the spacecraftτ。
The above embodiments are specific supports for the spacecraft attitude reconstruction fault-tolerant control method based on the learning neural network, and the scope of the present invention is not limited thereto, and it is still possible for those skilled in the art to modify the technical solutions described in the foregoing embodiments or to substitute part of the technical features of the foregoing embodiments. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (2)

1. A spacecraft attitude reconstruction fault-tolerant control method based on a learning neural network is characterized by comprising the following steps:
step 1, considering the influence of faults, uncertainty of rotational inertia and space interference of a spacecraft actuating mechanism, establishing a spacecraft attitude dynamics model, establishing a spacecraft attitude tracking dynamics model based on the spacecraft attitude dynamics model, specifically,
the spacecraft attitude dynamics model is as follows:
Figure FDA0003836962550000011
wherein, J S ∈R 3×3 A nominal moment of inertia matrix representing the rigid spacecraft; ω = [ ω =) x ,ω y ,ω z ] T ∈R 3 Representing the attitude angular velocity of a spacecraft body coordinate system relative to an inertial coordinate system, and indicating a derivative by using a superscript, wherein omega is the acceleration of the angular velocity; u. of c ＝[u x ,u y ,u z ] T ∈R 3 Outputting torque for the actuating mechanism; u. of f ＝[u fx ,u fy ,u fz ] T ∈R 3 Is an actuator failure; d = [ d ] x ,d y ,d z ] T ∈R 3 Represents the space disturbance moment, delta J epsilon R 3×3 Is the uncertainty portion of the moment of inertia matrix; hypothesis joint interference
Figure FDA0003836962550000012
Taking into account joint interference u dJ Its value is unknown but bounded, denoted as ║ u dJ ║≤u dJmax ,u dJmax Is defined as u dJ Upper bound of (a), ω × Is a ω antisymmetric matrix;
based on the spacecraft attitude dynamic model (1), the spacecraft attitude tracking error dynamic model is established as follows:
Figure FDA0003836962550000013
wherein, ω is e ＝[ω ex ,ω ey ,ω ez ] T ∈R 3 For the attitude angular velocity error, the actual angular velocity ω = [ ω = ] for the attitude angular velocity error x ,ω y ,ω z ] T ∈R 3 And a desired angular velocity ω d ＝[ω dx ,ω dy ,ω dz ] T ∈R 3 Error therebetween, i.e. ω e ＝ω-R(Q e )ω d (ii) a Attitude quaternion error Q e ＝(q e0 ,q e )∈R 4 Having q of e0 ∈R，q e ＝[q e1 ,q e2 ,q e3 ]∈R 3 And q is 2 e0 +q e T q e ＝1；R(Q e ) The attitude transformation matrix from the expected attitude to the actual attitude of the spacecraft is satisfied
Figure FDA0003836962550000014
Figure FDA0003836962550000015
Defined as joint interference, whose value, while unknown but bounded, can be expressed as ║ u d ║≤u dmax ,u dmax Is defined as u d The upper bound of (c);
step 2, combining a P-type iterative learning algorithm and a radial basis function RBF neural network model, establishing a learning neural network model for online accurate fitting of a nonlinear function, specifically, if the RBF neural network model is an arbitrary continuous function represented based on an ideal weight vector and an approximate error, when the function is estimated based on the learning neural network model, the function is represented as a product of a weight matrix and a Gaussian basis function vector, and the weight matrix is iteratively updated based on the P-type iterative learning algorithm;
step 3, designing a learning neural network observer for spacecraft actuating mechanism fault reconstruction based on the learning neural network model, wherein the observer specifically comprises the following steps:
Figure FDA0003836962550000021
Figure FDA0003836962550000022
Figure FDA0003836962550000023
in the formula, J S Is a matrix of the nominal moment of inertia,
Figure FDA0003836962550000024
the method is an estimation value of the attitude angular velocity of the spacecraft, the superscript is used for solving the derivative, and the superscript is multiplied to represent an antisymmetric matrix; u. of c (t) the output torque of the actuating mechanism,
Figure FDA0003836962550000025
accurately reconstructing the error fault reconstruction value of the executing mechanism on line through a model combining P-type iterative learning and an RBF neural network, wherein the RBF neural network algorithm is right
Figure FDA0003836962550000026
Carrying out accurate fitting, and carrying out P-type iterative learning on a weight matrix W (t) of the RBF neural network, wherein the weight matrix W (t) belongs to R 3×3 Iterative learning to obtain reconstruction weight parameters
Figure FDA0003836962550000027
The specific steps are to utilize
Figure FDA0003836962550000028
Sequentially and iteratively updating the value at the moment before the sampling time t-tau and the current angular velocity reconstruction error;
Figure FDA0003836962550000029
is a Gaussian basis function vector;
Figure FDA00038369625500000210
the deviation of the actual attitude angular velocity and the estimated attitude angular velocity of the spacecraft is obtained; k 1 ∈R 3×3 And K 2 ∈R 3×3 Is an observer gain matrix; gamma and theta 1 Is a positive gain parameter; to ensure the robustness of learning a neural network observer, use is made of
Figure FDA00038369625500000211
Processing the joint interference;
step 4, providing existence conditions of the learning neural network observer and calculating related parameters to enable observer stability theoretical proof to be satisfied, specifically:
step 4.1, the stable existence conditions of the learning neural network observer are given as follows:
Figure FDA00038369625500000212
Figure FDA00038369625500000213
α 1 (1+ε 1 )θ 1 2 -1＜0 (8)
γ-u dJmax ≥0 (9)
wherein P is a positive definite symmetric matrix and a positive scalar alpha 1 ≧ 1, scalar ε 1 ＞0；
Step 4.2, calculating the parameters of the learning neural network observer based on the learning neural network observer and the existence conditions thereof, and comprising the following steps:
step 4.21, selecting positive definite symmetric matrix P and small enough positive scalar alpha 1 Calculating the gain matrix K by equation (7) 2 ；
Step 4.22, select the appropriate scalar ε 1 Calculating the coefficient of waiting for determination theta by the formula (8) 1 ；
Step 4.23, according to u dJmax Selecting a positive gain parameter gamma such that equation (9) holds;
step 4.24, calculating the gain matrix K by the formula (6) 1 ；
Step 4.25, selecting a proper scalar b by the formula (17) i Sum vector c i Building a Gaussian basis function
Figure FDA0003836962550000031
Step 4.26, selecting a proper learning time interval tau according to the sampling time interval of the spacecraft attitude control system;
step 5, designing a learning neural network sliding mode attitude fault-tolerant controller for spacecraft attitude reconstruction fault-tolerant control based on the executing mechanism fault reconstruction information obtained by the learning neural network observer, wherein the controller comprises a feedforward compensation item, an attitude tracking controller and a fault adjustment fault-tolerant controller, and under the conditions of actuator faults and interference, the spacecraft is ensured to stably and accurately realize attitude tracking, and the fault-tolerant controller is as follows:
u c ＝u com +u smc -u rec ， (10)
in the formula u com Is a feedforward compensation term; u. of smc An attitude tracking controller; u. u rec Fault-tolerant controllers are regulated for faults based on a learning neural network model, in which,
Figure FDA0003836962550000032
Figure FDA0003836962550000033
Figure FDA0003836962550000034
ω e representing the error of the attitude angular velocity as an actual angular velocity omega and a desired angular velocity omega d Error between, R (Q) e ) Attitude transformation matrix, Q, for the desired attitude to the actual attitude of a spacecraft e ＝(q e0 ,q e )∈R 4 Having q of e0 ∈R，q e ＝[q e1 ,q e2 ,q e3 ]∈R 3 The index i denotes the ith q e Value of,
Figure FDA0003836962550000035
defined as the combined interference u df Is estimated online by using the learning neural network in step 2On-line estimation and neural network weight using P-type iterative learning algorithm
Figure FDA0003836962550000041
Carrying out online upgrade updating; s is a designed sliding mode surface, and g (S) is a Gaussian basis function vector of the RBF neural network; parameter k 1 ＞0,κ 2 ＞0,γ 1 ∈(0,1)，β＝diag{β 1 β 2 β 3 Is a positive definite diagonal matrix; k is 3 ∈R 3×3 Is a controller gain matrix; theta 2 、
Figure FDA0003836962550000042
α 1 Is a positive scalar quantity;
step 6, providing existence conditions of the learning neural network sliding mode controller and calculating related parameters, so that a controller stability theoretical proof is met, and spacecraft attitude reconstruction fault-tolerant control is realized, specifically:
step 6.1, aiming at the designed learning neural network sliding mode attitude fault-tolerant controller, providing the following stable existing conditions:
P 1 J s -1 ＝α 3 K 3 T (14)
α 3 (1+ε 2 )θ 2 2 -1＜0 (15)
wherein, P 1 ∈R 3×3 Is a positive definite symmetric matrix, a scalar epsilon 2 > 0, scalar α 3 ＞0；
6.2, calculating relevant parameters of the learning neural network sliding mode controller based on the structure and the existing conditions of the learning neural network sliding mode attitude fault-tolerant controller, and comprising the following steps:
step 6.21, select diagonal matrix P with same elements 1 And a sufficiently small scalar α 3 By (14) calculating a gain matrix K 3 ；
Step 6.22, select the appropriate scalar ε 2 Calculating the coefficient of waiting for determination theta by the formula (15) 2 ；
Step 6.23, select the appropriate positive scalar κ 1 、κ 2 ；
Step 6.24, select the appropriate scalar b by (17) i Sum vector c i Constructing a Gaussian basis function g (S);
and 6.25, selecting a proper learning time interval tau according to the sampling time interval of the spacecraft attitude control system.
2. The spacecraft attitude reconstruction fault-tolerant control method based on the learning neural network of claim 1, characterized in that: the RBF neural network model in the step 2 is expressed as:
for any continuous function f (x) e R m There exists an ideal weight matrix W ∈ R m×p Thereby satisfying the following conditions:
f(x)＝W T h(x)+ε (16)
wherein x = [ x ] 1 ,…,x n ]Is an input vector; p and m are respectively a node and an input number; ε is the approximation error; h (x) = [ h 1 (x)…h p (x)] T Is a gaussian basis function vector, the elements of which can be obtained by the following relationship:
Figure FDA0003836962550000051
wherein, c i ∈R n Central parameter representing the ith hidden layer of the RBF neural network, b i E R denotes the ith Gaussian function h i (x) A width parameter of (d); the learning neural network model is as follows:
Figure FDA0003836962550000052
wherein the content of the first and second substances,
Figure FDA0003836962550000053
is an estimate of f (x),
Figure FDA0003836962550000054
is a weight matrix, h (x) is a Gaussian basis function vector, p and m are respectively a node and an input number, and subscript j is a node;
wherein, the weight matrix is subjected to P-type iterative learning algorithm
Figure FDA0003836962550000055
Carrying out iterative upgrade and update, wherein the structural form of the P-type iterative learning algorithm is as follows:
Figure FDA0003836962550000056
wherein alpha is a learning rate, e is an observer measurement estimation output deviation or a controller control deviation, and gamma is a gain matrix; tau is a learning time interval, and the learning interval can be selected as a system sampling interval or an integral multiple of the sampling interval;
therefore, the nonlinear function online accurate fitting algorithm based on the learning neural network model is as follows:
Figure FDA0003836962550000057
based on the RBF neural network model (16) and the P-type iterative learning algorithm (19), the designed learning neural network model (20) can accurately fit the nonlinear function f (x) on line.
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