A nonlinear robust stochastic full-state feedback control method for perturbed spacecraft attitude tracking

Abstract

The application discloses a kind of nonlinear robust random full-drive control methods of disturbed spacecraft attitude tracking, the method includes the following steps: step 1: in attitude error quaternion coordinates, establish disturbed spacecraft attitude tracking error dynamics and disturbed rigid body dynamics model, and reconstruct attitude tracking error dynamics as second-order random high-order full-drive system;Step 2: under the condition that error position is measurable while error speed is not directly measurable, construct intermediate variable mapping and design intermediate variable observer, establish observation error system, avoid numerical differentiation to attitude measurement signal;Step 3: based on the output of intermediate variable observer, construct nonlinear robust backstepping control law, and map equivalent control quantity as physical torque input by algebraic speed estimation.The application can simultaneously process model uncertainty, input gain perturbation and random diffusion disturbance under unified model framework, and is suitable for disturbed spacecraft attitude tracking control.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft attitude control and stochastic nonlinear system control technology, and relates to a nonlinear robust stochastic full-drive control method for the attitude tracking problem of disturbed spacecraft. Background Technology

[0003] Tracking control is a fundamental problem in spacecraft guidance, navigation, and control systems. For disturbed spacecraft, on the one hand, rotational inertia perturbations, unmodeled coupling terms, and actuator gain biases introduce significant model uncertainties; on the other hand, environmental torques such as gravity gradient torque, aerodynamic torque, and solar radiation pressure have continuous effects, and high-frequency sensing and structural vibrations enter attitude dynamics through random noise channels. If only a deterministic control framework is used, it is difficult to simultaneously handle the combined effects of nominal nonlinearity, multiplicative gain perturbations, and random disturbances in a unified model.

[0004] In existing attitude control designs, error velocities are often difficult to measure directly. Directly differentiating the attitude measurement signal can easily amplify high-frequency noise and cause control command chattering. Furthermore, under conditions of both random disturbances and model uncertainties, providing a rigorous stability analysis of the closed-loop system is a key issue that needs to be addressed in the attitude control of disturbed spacecraft. Summary of the Invention

[0005] To address the challenges of random disturbances, parameter perturbations, input gain mismatch, and the inability to directly measure error velocities in attitude tracking of disturbed spacecraft, this invention provides a nonlinear robust stochastic full-drive control method for attitude tracking of disturbed spacecraft. This method establishes a stochastic full-drive system model in attitude error coordinates and combines an intermediate variable observer, a nonlinear robust backstepping controller, and local probabilistic final bounded stability analysis to achieve attitude tracking control of the disturbed spacecraft. This invention can simultaneously handle model uncertainties, input gain perturbations, and random diffusion disturbances within a unified model framework, making it suitable for attitude tracking control of disturbed spacecraft.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A nonlinear robust stochastic all-drive control method for attitude tracking of a disturbed spacecraft includes the following steps:

[0008] Step 1: Establish the dynamics of the disturbed spacecraft attitude tracking error and the dynamics of the disturbed rigid body in the attitude error quaternion coordinate system, and reconstruct the attitude tracking error dynamics into a second-order stochastic high-order all-drive system. The specific steps are as follows:

[0009] Step 1-1: Assume the spacecraft attitude error kinematics and disturbed dynamics are as follows:

[0010]

[0011]

[0012]

[0013] in, , These are the scalar and vector parts of the attitude error quaternion, respectively. It's angular velocity. It is the error angular velocity. It is a three-dimensional identity matrix. It is an antisymmetric operator. The actual moment of inertia matrix, To control the torque, For external environmental torque, Here is the diffusion matrix. It is a three-dimensional standard Brownian motion;

[0014] Steps 1-2: Considering the influence of uncertainty, according to the stochastic differential rule, it is reconstructed into the following form of a second-order stochastic fully driven system:

[0015]

[0016] in, It is a system state variable. It is the system nominal drift. It is an additive uncertainty term. It is a multiplicative input gain perturbation. It is the nominal input gain matrix. It is a random diffusion term;

[0017] Step 2: Under the condition that the error position is measurable but the error velocity cannot be directly measured, construct an intermediate variable mapping and design an intermediate variable observer to establish an observation error system, avoiding numerical differentiation of the attitude measurement signal. The specific steps are as follows:

[0018] Step 2-1: Define the intermediate variable as:

[0019]

[0020] Step 2-2: Construct intermediate variable observers:

[0021] ;

[0022] in, and To design the matrix, The equivalent control quantity to be designed;

[0023] Steps 2-3: Define observation error , Establish an observation error system;

[0024] Step 3: Construct a nonlinear robust backstepping control law based on the output of the intermediate variable observer, and map the equivalent control quantity to the physical torque input through algebraic velocity estimation. The specific steps are as follows:

[0025] Step 3-1: Undefined first-level backstepping error variable:

[0026] ;

[0027] Step 3-2, Virtual Control Law:

[0028] ;

[0029] Step 3-3: Define the second-level error variables:

[0030] ;

[0031] Steps 3-4: Design equivalent control quantities:

[0032]

[0033] Steps 3-5: To map the equivalent control quantity to the physical torque input, define the algebraic velocity estimate:

[0034]

[0035] Steps 3-6: The physical control law is:

[0036] .

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. The attitude tracking error dynamics are rigorously transformed into the standard form of second-order stochastic full drive, which can simultaneously handle additive uncertainties, multiplicative input gain perturbations and random diffusion disturbances in a unified model;

[0039] 2. By introducing an intermediate variable observer, smooth state estimation can be achieved under the condition that the error position is measurable but the error velocity is not directly measurable, thus avoiding the numerical differentiation of the attitude measurement signal.

[0040] 3. Construct a nonlinear robust backstepping control law to make the tracking error subsystem exhibit an explicit dissipative structure, and prove that the closed-loop error system has the property of local probabilistic eventual boundedness in the working domain. Attached Figure Description

[0041] Figure 1 This is a block diagram of the attitude control system for a disturbed spacecraft based on a random all-drive system.

[0042] Figure 2 The curve showing the total tracking error of the spacecraft attitude when the standard deviation of random noise is 0.01;

[0043] Figure 3 The tracking curves for each attitude angle of the spacecraft are given when the standard deviation of random noise is 0.01.

[0044] Figure 4 The control torque curve of the spacecraft actuator is given when the standard deviation of random noise is 0.01.

[0045] Figure 5 The curves of various process variables of the spacecraft attitude system are shown when the standard deviation of random noise is 0.01.

[0046] Figure 6 The Monte Carlo plot of the spacecraft attitude when the standard deviation of random noise is 0.01.

[0047] Figure 7 The curve showing the total tracking error of the spacecraft attitude when the standard deviation of random noise is 0.03;

[0048] Figure 8 The tracking curves for various attitude angles of the spacecraft are given when the standard deviation of random noise is 0.03.

[0049] Figure 9 The control torque curve of the spacecraft actuator is given when the standard deviation of random noise is 0.03.

[0050] Figure 10 The curves of various process variables of the spacecraft attitude system are shown when the standard deviation of random noise is 0.03.

[0051] Figure 11 The image shows a Monte Carlo plot of the spacecraft's attitude when the standard deviation of random noise is 0.03. Detailed Implementation

[0052] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0053] The invention will now be described in further detail, taking into account specific mathematical modeling, observer design, control law construction, and stability analysis.

[0054] The invention will now be described in further detail, taking into account specific mathematical modeling, observer design, control law construction, and stability analysis.

[0055] Attitude tracking control is a fundamental problem in spacecraft guidance, navigation, and control systems. For disturbed spacecraft, on the one hand, rotational inertia perturbations, unmodeled coupling terms, and actuator gain deviations introduce significant model uncertainties; on the other hand, environmental torques such as gravity gradient torque, aerodynamic torque, and solar radiation pressure have continuous effects, and high-frequency sensing and structural vibrations enter the attitude dynamics through random noise channels. If only a deterministic control framework is used, it is difficult to simultaneously handle the combined effects of nominal nonlinearity, multiplicative gain perturbations, and random disturbances in a unified model. To address this, this invention reconstructs the disturbed spacecraft attitude tracking system into a second-order stochastic high-order fully actuated (SHOFA) system, and designs an intermediate variable observer and a nonlinear robust backstepping controller based on this. The goal of this invention is not to directly linearize the original attitude dynamics locally, but to establish a second-order stochastic fully actuated error system under the attitude error coordinates, then construct observation and control laws for this error system, and prove the local probability ultimately bounded (local PUB) of the closed-loop system in the working domain.

[0056] This invention addresses the following three issues:

[0057] 1. The attitude tracking error dynamics are rigorously transformed into the standard form of a second-order stochastic full-drive system;

[0058] 2. When the error location is measurable but the error velocity cannot be directly measured, design an intermediate variable observer to avoid numerical differentiation of the measurement signal;

[0059] 3. Construct a nonlinear robust backstepping control law based on the observer output, and provide a proof of the local PUB stability of the closed-loop error system.

[0060] Let the unit quaternions corresponding to the spacecraft's current attitude and desired attitude be respectively:

[0061] (1)

[0062] in, , These are the scalar and vector parts of the current attitude quaternion, respectively. , These are the scalar and vector parts of the desired attitude quaternion, respectively.

[0063] Define the attitude error quaternion as:

[0064] (2)

[0065] in, , These are the scalar and vector parts of the attitude error quaternion, respectively. This represents quaternion multiplication. To ensure the single-valuedness of the error parameterization, the scalar part of the error quaternion is taken to satisfy... .

[0066] For any vector Define the antisymmetric operator:

[0067] (3)

[0068] Let the actual angular velocity and the desired angular velocity be respectively Then the error angular velocity is defined as:

[0069] (4)

[0070] in:

[0071] (5)

[0072] From the quaternion error kinematics, we can obtain:

[0073] (6)

[0074] make

[0075] (7)

[0076] but

[0077] (8)

[0078] Suppose that the rigid body dynamics of the disturbed spacecraft satisfy the following Itô-type stochastic differential equations:

[0079] (9)

[0080] in, The actual moment of inertia matrix, To control the torque, For external environmental torque, Here is the diffusion matrix. It is a three-dimensional standard Brownian motion.

[0081] Decompose the real inertia into:

[0082] (10)

[0083] in, Nominal inertia For unknown bounded perturbations.

[0084] From (4), we can obtain:

[0085] (11)

[0086] Because the subsequent control law will use A non-singular working domain needs to be introduced:

[0087] (12)

[0088] Further selection of compact working subdomains:

[0089] (13)

[0090] Note 1. Based on quaternion error relations It can be seen that the conditions This is equivalent to the attitude error angle satisfying:

[0091]

[0092] Therefore, tight working domain This describes not the arbitrary large-attitude roll phase, but rather the fine-tracking working envelope after attitude acquisition is complete. For a typical spacecraft mission flow, unwinding, coarse acquisition, and navigation initialization usually compress the attitude error into a certain preset envelope before switching to fine-tracking control; simultaneously, the reference attitude is updated according to continuous maneuver commands and generally does not cross within adjacent control periods. Singular boundary. Therefore, regarding the on-orbit precision tracking phase studied in this invention, the closed-loop trajectory enters and operates within... The internal working domain is a high-probability engineering event, and the tight working domain assumption has a clear physical context.

[0093] exist superior, Non-singular, its inverse can be explicitly written as:

[0094] (14)

[0095] Differentiate both sides of (8). Since The differential contains only the finite variation term, therefore ,thereby:

[0096] (15)

[0097] Substituting (11) into (15), we get:

[0098] (16)

[0099] Define the nominal drift term:

[0100] (17)

[0101] Nominal input gain matrix:

[0102] (18)

[0103] And define multiplicative input gain perturbation:

[0104] (19)

[0105] Then there is an exact decomposition:

[0106] (20)

[0107] Then, inertia mismatch, coupling error, and external disturbances are incorporated into the additive uncertainty term:

[0108] (twenty one)

[0109] The diffusion term is defined as:

[0110] (twenty two)

[0111] Therefore, (16) can be strictly written in the form of a second-order stochastic total drive:

[0112] (twenty three)

[0113] Assumption 1. Desired attitude trajectory and its induced angular velocity Continuous and bounded, i.e., there exists a constant. , making

[0114] (twenty four)

[0115] Assumption 2. In any given compact working subdomain Above, the input gain perturbation and diffusion terms are bounded, i.e., there exist constants. and , so that:

[0116] (25)

[0117] External disturbance torque Continuous and bounded, i.e., there exists a constant. Make:

[0118] (26)

[0119] Assumption 3. The navigation system can provide continuous measurements of the attitude error vector, that is:

[0120] (27)

[0121] Note 2. Assumption 3 is a modeling convention made for the control layer interface, i.e. This represents the attitude error vector output by the navigation system. In engineering implementation, star sensors, gyroscopes, and filters introduce measurement and estimation errors; if their residual errors remain bounded within the working domain, they can be integrated with external disturbances and random diffusion terms into the uncertainty channel without altering the local analysis structure of this invention. To highlight the intermediate variable observer and the controller core, this invention abstracts the control layer using measurable data as... .

[0122] Lemma 1. For any given compact working subdomain and the upper bound of any velocity Define compact sets:

[0123] (28)

[0124] Then mapping , , , and exist Bounded and smooth; mapping and exist It is bounded above, and Regarding velocity variables Local Lipschitz. That is, the existence of a positive constant. , so that:

[0125] (29)

[0126] (30)

[0127] Proof. In Above ,and about Smooth, therefore , and exist All of the above are smooth and bounded mappings. From the relation...

[0128] (31)

[0129] It can be seen that when hour, and about Smooth and uniformly bounded.

[0130] Equations (17) and (21) show that, and All of these are derived from the above smooth bounded mappings and about It is composed of quadratic polynomial terms, and therefore in compact sets The function remains bounded on the compact set. Furthermore, since a smooth function is necessarily a Lipschitz function on a compact set, there exists a constant. This makes (29) true, and (30) also true.

[0131] Note 3. Gyrocoupling terms in spacecraft attitude dynamics Since angular velocity is a quadratic term, it is generally not advisable to directly assume that it satisfies the global Lipschitz condition over the entire space. The Lipschitz property used subsequently in this invention is limited to the local Lipschitz property in the compact working domain and the bounded velocity domain, and is guaranteed by the smoothness analysis of Lemma 1.

[0132] As can be seen from (23), the controller design requires the use of This information is available, but the quantity is usually not directly measurable. To avoid [further issues]... To perform numerical differentiation, define intermediate variables:

[0133] (32)

[0134] in ,and .

[0135] From (23) and (32), we can obtain:

[0136] (33)

[0137] (34)

[0138] Based on this, an intermediate variable observer is constructed:

[0139] (35)

[0140] in ,and , This is the equivalent control quantity to be designed.

[0141] Define observation error:

[0142] (36)

[0143] From (33), (35) and We can obtain:

[0144] (37)

[0145] Similarly, from (34) and (35), we get:

[0146] (38)

[0147] in

[0148] (39)

[0149] Lemma 2. If , ,and , Then the matrix is:

[0150] (40)

[0151] It is a Hurwitz matrix.

[0152] Proof. Matrix It can be decoupled into three second-order subsystems according to three channels, and their characteristic polynomials are as follows:

[0153] (41)

[0154] because , According to the second-order Hurwitz criterion, All roots lie in the open left half-plane, therefore Hurwitz.

[0155] Since attitude tracking in the error coordinate system is equivalent to making , Therefore, the controller is designed directly around the error system (23). The first-level backstepping error variable is defined as follows:

[0156] (42)

[0157] Selecting a virtual control law:

[0158] (43)

[0159] in ,and Further define the second-level error variables:

[0160] (44)

[0161] From (35) and (43), we can obtain:

[0162] (45)

[0163] because Only depend on Its derivative can be algebraically calculated from the observer equation as follows:

[0164] (46)

[0165] Design equivalent control quantity:

[0166] (47)

[0167] in , , From (35), (44), and (98), we can obtain:

[0168] (48)

[0169] To map the equivalent control quantity to the physical torque input, an algebraic velocity estimate is defined:

[0170] (49)

[0171] From (32) and (36), we can obtain:

[0172] (50)

[0173] Therefore, the physical control law is taken as:

[0174] (51)

[0175] Substituting (51) into (39) and using (20), we get:

[0176] (52)

[0177] Lemma 3. For any given compact analysis domain:

[0178] (53)

[0179] There are positive numbers This makes in Established on:

[0180] (54)

[0181] Proof. We can directly obtain from (50):

[0182] (55)

[0183] (56)

[0184] thereby:

[0185] (57)

[0186] Combining (55), we can obtain:

[0187] (58)

[0188] Therefore, in the analysis domain superior, Uniformly bounded. Its upper bound is denoted as:

[0189] (59)

[0190] Therefore when Sometimes, there are ,in Given by (28) and take .

[0191] Then, by the local Lipschitz conclusion of Lemma 1, we can obtain:

[0192] (60)

[0193] On the other hand, by (98), (49) and It can be seen that the items in square brackets

[0194] (61)

[0195] This can be further expanded explicitly. (From...) From (46) and (56), we get:

[0196] (62)

[0197] (63)

[0198] Substitute (62) and (63) into (61), and use , We can obtain:

[0199] (64)

[0200] Furthermore, from (57), we can see that when Sometimes:

[0201]

[0202] Therefore Furthermore, by Lemma 1, we know that:

[0203] (65)

[0204] Therefore, there exists a constant:

[0205]

[0206] (66)

[0207] Make:

[0208] (67)

[0209] By Lemma 1, we have:

[0210] (68)

[0211] Therefore, from (52), (55), (60) and We can obtain:

[0212] (69)

[0213] In (69), the constant term, Item and The items are collected again, resulting in (54).

[0214] Definition 1. Let the closed-loop error state be:

[0215] (70)

[0216] For any given compact analysis domain Define the first exit time:

[0217] (71)

[0218] If for any There exists a constant This ensures that the stopping process satisfies:

[0219] (72)

[0220] This is called a closed-loop error system in the analysis domain. The above is a locally bounded probability.

[0221] By Lemma 2, there exists a symmetric positive definite matrix. To make it satisfy the Lyapunov equation:

[0222] (73)

[0223] in Let be any given positive definite matrix. Let:

[0224] (74)

[0225] The observation error system (37)–(38) can then be written as:

[0226] (75)

[0227] Theorem 1. Under the conditions that Assumptions 1–3 hold, given a compact analysis domain And assume that the initial value belongs to this analysis domain, that is:

[0228] (76)

[0229] If design parameters satisfy:

[0230] (77)

[0231] in Defined by (94)–(95). Note the constants in Lemma 3. Depends on a given analysis domain The selection of (77) is therefore relative to the analysis domain. The local gain selection condition. Then the stopping process has a Lyapunov function:

[0232] (78)

[0233] satisfy:

[0234] (79)

[0235] in , It is a positive constant. Furthermore, for any... have:

[0236] (80)

[0237] Therefore, the closed-loop error system in the analysis domain Upper local PUB.

[0238] Proof. First, calculate the derivative of the tracking error component. From (45) and (48), we can obtain:

[0239] (81)

[0240] Note the intersection terms and Exact cancellation. Applying Young's inequality to the last term: for any ,

[0241] (82)

[0242] set up:

[0243] (83)

[0244] From (81) and (82), we can obtain:

[0245] (84)

[0246] Then calculate the observation error. From (75) and the definition of Itô generators:

[0247] (85)

[0248] From (73), we immediately obtain:

[0249] (86)

[0250] remember , , By Lemma 3 and Assumption 2, we have:

[0251] (87)

[0252] (88)

[0253] Apply Young's inequality to the first and third terms in (87). For any ,

[0254] (89)

[0255] (90)

[0256] The intermediate term can be directly written as:

[0257] (91)

[0258] Substituting (89)–(91) into (86), we get:

[0259] (92)

[0260] Add (84) and (92) together, and use , ,get:

[0261] (93)

[0262] in:

[0263] (94)

[0264] (95)

[0265] (96)

[0266] Given condition (77), there exists a positive constant. make:

[0267] (97)

[0268] On the other hand, by It can be seen that positive constants exist. ,make:

[0269] (98)

[0270] Substituting (98) into (97), we get:

[0271] (99)

[0272] At the stopping time Applying the Dynkin formula, we have:

[0273] (100)

[0274] From (99), we can obtain:

[0275] (101)

[0276] Then, using Gronwall's inequality, we get:

[0277] (102)

[0278] That is, equation (80) holds true.

[0279] On the other hand, (98) has Therefore, for any From Markov's inequality, we can obtain:

[0280] (103)

[0281] make Then we have:

[0282] (104)

[0283] For any given Simply take:

[0284] (105)

[0285] Then there is:

[0286] (106)

[0287] Therefore, the closed-loop error system in the analysis domain Upper local PUB.

[0288] Corollary 1. Under the conditions of Theorem 1, the algebraic velocity estimation error is:

[0289] (107)

[0290] In any given analysis domain The same applies to local PUBs.

[0291] Proof. From (107), we can obtain:

[0292] (108)

[0293] Theorem 1 has been proven to be a stopping process. In the analysis domain The upper local PUB, and (108) indicates by Linear control, therefore Local PUBs are also present in the same analysis domain.

[0294] This invention addresses the attitude tracking problem of disturbed spacecraft by establishing a nonlinear robust control method based on a stochastic all-drive framework. First, the attitude tracking error dynamics are rigorously reconstructed into a second-order SHOFA form in error quaternion coordinates, and inertial perturbation, external environmental torque, and input gain mismatch are uniformly incorporated into additive and multiplicative uncertainties. Second, considering the characteristic that the error position is measurable but the error velocity is not directly measurable, an intermediate variable observer is introduced to avoid numerical differentiation of the attitude measurement signal. Subsequently, a nonlinear robust backstepping control law is constructed based on the observer output, making the tracking error subsystem exhibit an explicit dissipative structure. Finally, by constructing a composite Lyapunov function and utilizing Itô generator analysis, the local PUB property of the closed-loop error system in the operating domain is proved, and the local PUB conclusion for the algebraic velocity estimation error is also given.

[0295] The parameters for the example are as follows:

[0296] Global simulation parameters: Total simulation duration Simulation step size .

[0297] Spacecraft physical parameters: Nominal moment of inertia matrix The true fundamental value of rotational inertia Rotational inertia cross-coupling deviation .

[0298] Actuator and environmental disturbance parameters: Control torque saturation limit value System process noise standard deviation External disturbance torque direction vector External disturbance torque amplitude External disturbance torque frequency .

[0299] Observer and controller gain design: Observer location layer gain Observer velocity layer gain Backstepping virtual control gain Backstepping actual control gain Robust compensation control gain coefficient .

[0300] Initial state and desired trajectory: desired attitude motion amplitude (converted to) ), desired posture motion frequency The expected trajectory is equivalent to the axis of rotation. Large initial pose error (converted to) ), initial error rotation axis spacecraft's initial physical angular velocity .

[0301] Tracking curves of the spacecraft at various attitude angles (roll, pitch, yaw) Figure 3 , Figure 8 As can be seen, despite the initial large angle error of 45° and unknown system perturbations, the actual attitude trajectory can converge quickly and smoothly to the desired trajectory in about 10 seconds under the control strategy proposed in this invention. The total system attitude tracking error curve ( Figure 2 , Figure 7 The magnified view shows that after entering steady state, the error is strictly bound within a very small envelope; when the standard deviation of random noise increases from 0.01 to 0.03, the fluctuation amplitude of steady-state error increases slightly, but the system still maintains strict local probabilistic eventually bounded (PUB) stability.

[0302] Figure 5 and Figure 10The core process variables of the system are demonstrated. Among them, the position and velocity errors of the intermediate variable observer converge rapidly to near zero within a very short time; the estimated value of the physical angular velocity highly coincides with the true value, indicating that under the condition of error-free direct velocity measurement, the observer successfully achieves high-precision and smooth estimation of angular velocity, effectively avoiding numerical differentiation of position signals with random noise. Thanks to the smooth velocity estimation, Figure 4 and Figure 9 Except for a brief moment when the control torque of the actuator in the initial acquisition phase touches the amplitude limit boundary due to a large error, it exhibits a continuous and stable sinusoidal adjustment pattern during the tracking steady-state phase, effectively suppressing control command chattering caused by high-frequency noise.

[0303] To examine the general reliability of the algorithm under random operating conditions Figure 6 and Figure 11 Box plots for N=200 Monte Carlo experiments are presented. The results show that under multiple random disturbances and parameter perturbations: the root mean square error distribution of attitude tracking accuracy and observer estimation accuracy is concentrated with extremely narrow upper and lower limits; the system settling time (convergence speed) is mostly stable between 10s and 11s; and the actuator control energy consumption is uniformly distributed without divergence. Even under strong noise conditions, the above indicators maintain extremely high consistency, proving that the controller designed based on nonlinear robust backstepping control and Itô stochastic system theory not only has reasonable energy consumption but also possesses excellent comprehensive robust suppression capabilities against multi-source disturbances and uncertainties.

Claims

1. A nonlinear robust stochastic all-drive control method for attitude tracking of a disturbed spacecraft, characterized in that... The method includes the following steps: Step 1: Establish dynamic models of the attitude tracking error of the disturbed spacecraft and dynamic models of the disturbed rigid body in attitude error quaternion coordinates, and reconstruct the attitude tracking error dynamics into a second-order stochastic high-order all-drive system; Step 2: Under the condition that the error position is measurable but the error velocity cannot be directly measured, construct an intermediate variable mapping and design an intermediate variable observer to establish an observation error system, thereby avoiding numerical differentiation of the attitude measurement signal; Step 3: Construct a nonlinear robust backstepping control law based on the output of the intermediate variable observer, and map the equivalent control quantity into a physical torque input through algebraic velocity estimation.

2. The nonlinear robust stochastic all-drive control method for attitude tracking of disturbed spacecraft according to claim 1, characterized in that... The specific steps of step 1 are as follows: Step 1-1: Assume the spacecraft attitude error kinematics and disturbed dynamics are as follows: in, , These are the scalar and vector parts of the attitude error quaternion, respectively. It's angular velocity. It is the error angular velocity. It is a three-dimensional identity matrix. It is an antisymmetric operator. The actual moment of inertia matrix, To control the torque, For external environmental torque, Here is the diffusion matrix. It is a three-dimensional standard Brownian motion; Steps 1-2: Considering the influence of uncertainty, according to the stochastic differential rule, it is reconstructed into the following form of a second-order stochastic fully driven system: in, It is a system state variable. It is the system nominal drift. It is an additive uncertainty term. It is a multiplicative input gain perturbation. It is the nominal input gain matrix. It is a random diffusion term.

3. The nonlinear robust stochastic all-drive control method for attitude tracking of disturbed spacecraft according to claim 2, characterized in that... The specific steps of step 2 are as follows: Step 2-1: Define the intermediate variable as: Step 2-2: Construct intermediate variable observers: ； in, and To design the matrix, The equivalent control quantity to be designed; Steps 2-3: Define observation error , Establish an observation error system.

4. The nonlinear robust stochastic all-drive control method for attitude tracking of disturbed spacecraft according to claim 3, characterized in that... The specific steps of step 3 are as follows: Step 3-1: Undefined first-level backstepping error variable: ； Step 3-2, Virtual Control Law: ； Step 3-3: Define the second-level error variables: ； Steps 3-4: Design equivalent control quantities: Steps 3-5: To map the equivalent control quantity to the physical torque input, define the algebraic velocity estimate: Steps 3-6: The physical control law is: 。

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