A method and system for attitude safety adaptive state feedback control of a spacecraft

Abstract

The present invention belongs to the technical field of spacecraft attitude safety control, and specifically relates to a spacecraft attitude safety adaptive state feedback control method and system, including: Step 1: Establish a spacecraft attitude tracking error dynamics model with actuator false data injection attacks by using Euler angles; Step 2: According to the spacecraft attitude tracking error dynamics model, estimate the upper bound of the attack signal by using a parameter adaptive law, and propose a virtual controller and a real control law by using the backstepping method; Finally, complete the adaptive safe spacecraft attitude tracking control in the face of unknown actuator false data injection attacks. The present invention can effectively solve the safety control problem of the spacecraft attitude tracking system in the face of false data injection attacks, and ensure the safety and stability of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft attitude safety control, and in particular relates to a spacecraft attitude safety adaptive state feedback control method and system. Background Art

[0002] With the rapid development of aerospace technology, the problem of spacecraft attitude control has been widely studied. The aerospace attitude tracking control system can enable the controlled spacecraft to track the desired state, thereby meeting the requirements of various missions. However, in practical applications, the complex nonlinearity of the spacecraft attitude system places high demands on the design of the control scheme. At the same time, the normal operation of the spacecraft attitude tracking control system depends on the communication network, which may be attacked by false data injection, causing the attitude control actuator to be paralyzed, thereby affecting the normal operation of the spacecraft and even causing great losses. Therefore, it is of practical significance to study the spacecraft attitude tracking control scheme with false data injection attacks.

[0003] Chinese patent publication number CN118170163A discloses a predictor-based fixed-time neural network spacecraft attitude control method, which builds a spacecraft pitch angle motion system model with uncertain state based on the reaction force flywheel, estimates the uncertainty of the system using the state predictor and the fixed-time neural network estimator, builds a virtual controller of the first two order states of the system based on the backstepping method, and designs the actual control law for controlling the pitch angle of the spacecraft based on the Lyapunov theory. This invention can realize fixed-time spacecraft attitude control in complex situations, but does not consider the security control problem of the system being attacked by a network.

[0004] Chinese patent publication number CN114995502A discloses a spacecraft formation flight attitude tracking control method, which uses attitude quaternions to construct a rigid spacecraft attitude motion model, considers external disturbances and parameter uncertainties to establish a formation attitude error system, designs an adaptive control law using a non-singular fast integral terminal sliding surface, and designs an attitude tracking controller using a directed topological graph. This invention can solve the problem of spacecraft attitude tracking control, but it also does not consider the response strategy of the spacecraft attitude tracking system when it is attacked by a network, and cannot solve the security control problem of the system.

[0005] In summary, the existing technology has made some progress in spacecraft attitude tracking control, but there are still problems in security and stability when facing actuator false data injection attacks. Therefore, developing a control method that can effectively resist actuator false data injection attacks and ensure the safe and stable operation of the spacecraft attitude tracking system is a problem that needs to be solved in the current aerospace technology field. Summary of the invention

[0006] The object of the present invention is to provide a spacecraft attitude safety adaptive state feedback control method and system, which can effectively solve the safety control problem of the spacecraft attitude tracking system facing false data injection attacks and ensure the safety and stability of the system.

[0007] The technical solution adopted by the present invention is as follows:

[0008] A spacecraft attitude safety adaptive state feedback control method includes the following steps:

[0009] Step 1: Establish a spacecraft attitude tracking error dynamics model with actuator false data injection attacks by using Euler angles; specifically:

[0010] The specific steps of Step 1 are as follows: Establish a spacecraft attitude tracking system model with actuator false data injection attacks by using Euler angles; taking the inertial coordinate system as the reference system, the spacecraft attitude kinematic equation relative to the inertial space under the 3-1-2 rotation sequence represented by Euler angles is:

[0011]

[0012] Where are the three Euler angles under the 3-1-2 rotation sequence. Let the spacecraft perform small-angle attitude tracking, that is ω = [ω x ω y ω z T ∈R 3×1 is the attitude angular velocity of the spacecraft in the body coordinate system, and R i ∈R 3×3 is the projection matrix from ω to , and its specific expression is:

[0013]

[0014] In Step 1, the spacecraft suffers from an actuator false data injection attack η = [η1 η2 η3] T ∈R 3×1 , and its upper bound is η m = [η m1 η m2 η m3 T ∈R 3×1 , then the attitude dynamics equation of the rigid spacecraft under the false data injection attack can be expressed as:

[0015]

[0016] Where u = [u1 u2 u3] ∈ R 3×1 ​​is the control torque vector, ω × ∈R 3×3 is the cross product matrix of ω, defined as follows:

[0017]

[0018] and l ∈ R 3×3 is the spacecraft moment of inertia matrix in the following form:

[0019]

[0020] where l x ∈R, l y ∈R, l z ∈R are the projections of the spacecraft on the corresponding axes respectively.

[0021] The attitude kinematics and dynamics models of the spacecraft are expressed as:

[0022]

[0023] Define θ r , ψ r as the expected values of the attitude angles θ, ψ respectively, then the attitude tracking error is:

[0024]

[0025] The attitude tracking error equation can be obtained as:

[0026]

[0027] Let x1 = ρ e and x2 = ω, then the attitude tracking error equation of the spacecraft with actuator false data injection attack can be obtained:

[0028]

[0029] Step 2: According to the spacecraft attitude tracking error dynamics model; use the parameter adaptive law to estimate the upper bound of the attack signal, and use the backstepping method to propose the virtual controller and the real control law; finally, complete the adaptive secure spacecraft attitude tracking control against unknown actuator false data injection attacks. Specifically:

[0030] In the said Step 2, first use the parameter adaptive law to estimate the upper bound of the attack signal, and use the backstepping method to propose the virtual controller and the actual control law; first design the coordinate transformation as follows:

[0031]

[0032] where α is the virtual control input;

[0033] Then select the Lyapunov function as:

[0034]

[0035] Design the virtual control input α as:

[0036]

[0037] where k1 is a positive parameter designed; the derivative of the Lyapunov function is obtained as:

[0038]

[0039] Select the Lyapunov function again as:

[0040]

[0041] where γ ∈ R is a positive parameter designed; is the estimation error, is the upper bound η of the false data injection attack η m the estimated value of;

[0042] The designed actual control input u and the parameter adaptation law are respectively:

[0043]

[0044] where k2 ∈ R is a positive parameter designed, and

[0045]

[0046] where z 21 , z 22 , z 23 ∈ R are the 1st, 2nd, and 3rd components of z2 respectively;

[0047] The derivative of the Lyapunov function is obtained as:

[0048]

[0049] where Then the closed-loop system is ultimately uniformly bounded; and by choosing the parameters k1, k2, γ as the corresponding values, making the system tracking error approach the neighborhood of the origin, then the attitude safe adaptive tracking control of the spacecraft with actuator false data injection attack is completed.

[0050] A spacecraft attitude safety adaptive state feedback control system generates a state adaptive law using the system feedback state, generates a virtual control law using the tracking error signal, combines the virtual control signal, the adaptive parameters, and the actual control signal generated by the actual controller to control the spacecraft attitude tracking system with actuator false data injection attacks, and compares the system attitude angle with the reference signal to generate a tracking error signal.

[0051] The technical effects achieved by the present invention are as follows:

[0052] In the present invention, an Euler angle is used to establish a spacecraft attitude tracking error dynamics model with actuator false data injection attacks; then, based on the spacecraft attitude tracking error dynamics model, a parameter adaptive law is used to estimate the upper bound of the attack signal, and a virtual controller and a real control law are proposed using the backstepping method; finally, an adaptive safe spacecraft attitude tracking control in the face of unknown actuator false data injection attacks is completed. The present invention can effectively solve the safety control problem of the spacecraft attitude tracking system facing false data injection attacks and ensure the safety and stability of the system. Description of the Drawings

[0053] Figure 1 is a flowchart of a spacecraft attitude safety adaptive state feedback control method of the present invention;

[0054] Figure 2 is a system operation diagram of a spacecraft attitude safety adaptive state feedback control system of the present invention;

[0055] Figure 3 is a spacecraft tracking error trajectory diagram in the present invention;

[0056] Figure 4 is a curve graph of the parameter adaptive law in the present invention;

[0057] Figure 5 is a curve graph of the actual control law in the present invention. Detailed Embodiments

[0058] In order to make the purpose and advantages of the present invention clearer, the present invention will be specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific implementation manners of the present invention and does not strictly limit the specific protection scope claimed by the present invention.

[0059] Embodiment 1:

[0060] As Figure 1 shown, a spacecraft attitude safety adaptive state feedback control method includes the following steps:

[0061] Step 1: The spacecraft attitude tracking error dynamics model with actuator false data injection attack is established by using Euler angles; specifically:

[0062] First, define the geocentric inertial coordinate system Ox o y o z o , whose origin is fixed at the Earth's center of mass, the Ox o axis points to the vernal equinox point, the Oz o axis points to the North Pole, and the Oy o axis is determined by the right-hand rule. Then define the spacecraft body coordinate system Ox b y b z b , the origin of this coordinate system is fixed at the spacecraft's center of mass, let the Ox b axis be along the spacecraft's longitudinal axis, i.e., the spacecraft's flight direction, the Oy b axis is in the spacecraft's cross-section, and the Oz b axis is determined by the right-hand rule. This system can be obtained from the reference frame by three Euler angles ψ, θ according to the 3-1-2 rotation sequence. First, rotate Ox o y o z o around the Oz o axis by ψ angle to obtain the first coordinate system Ox'y'z':

[0063]

[0064] Then rotate Ox'y'z' around the Ox' axis by angle to the second coordinate system Ox''y''z'':

[0065]

[0066] Finally, rotate Ox''y''z'' around the Oy'' axis by θ angle to obtain this system Ox b y b z b :

[0067]

[0068] From the rotation process, the transformation equation can be obtained:

[0069]

[0070] Then the rotation matrix corresponding to the 3-1-2 rotation sequence is:

[0071]

[0072] Where:

[0073]

[0074] From the transformation process, the angular velocity ω ∈ R in this system can be obtained 3×1 is:

[0075]

[0076] The kinematic equation of the spacecraft's attitude relative to the inertial space under the 3-1-2 rotation sequence finally expressed in Euler angles is:

[0077]

[0078] where are the three Euler angles under the 3-1-2 rotation sequence. Let the spacecraft perform small-angle attitude tracking, that is ω = [ω x ω y ω z T ∈ R 3×1 is the attitude angular velocity of the spacecraft in the body coordinate system, R i ∈ R 3×3 is the projection matrix from ω to Its specific expression is:

[0079]

[0080] In step 1, the spacecraft is subjected to an actuator false data injection attack η = [η1 η2 η3] T ∈ R 3×1 , and its upper bound is η m = [η m1 η m2 η m3 T ∈ R 3×1 , then the attitude dynamics equation of the rigid spacecraft under the false data injection attack can be expressed as:

[0081]

[0082] where u = [u1 u2 u3] ∈ R 3×1 is the control torque vector, ω × ∈ R 3×3 is the cross product matrix of ω, defined as follows:

[0083]

[0084] and l ∈ R 3×3 is the spacecraft moment of inertia matrix with the following form:

[0085]

[0086] ​​where \(l\) x \(\in \mathbb{R}\), \(l\) y \(\in \mathbb{R}\), \(l\) z \(\in \mathbb{R}\) are the projections of the spacecraft on the corresponding axes respectively.

[0087] The attitude kinematics and dynamics models of the spacecraft are expressed as:

[0088]

[0089] Define \(\theta\) r , \(\psi\) r to be the expected values of the attitude angles \(\theta\), \(\psi\) respectively, then the attitude tracking error is:

[0090]

[0091] The attitude tracking error equation can be obtained as:

[0092]

[0093] Let \(x_1 = \rho\) e and \(x_2 = \omega\), then the attitude tracking error equation of the spacecraft with actuator false data injection attack can be obtained:

[0094]

[0095] Step 2: According to the spacecraft attitude tracking error dynamics model; use the parameter adaptive law to estimate the upper bound of the attack signal, and use the backstepping method to propose the virtual controller and the real control law; finally, complete the adaptive secure spacecraft attitude tracking control against unknown actuator false data injection attacks. Specifically:

[0096] In the said Step 2, first use the parameter adaptive law to estimate the upper bound of the attack signal, and use the backstepping method to propose the virtual controller and the actual control law; first design the coordinate transformation as follows:

[0097]

[0098] where \(\alpha\) is the virtual control input;

[0099] Then select the Lyapunov function as:

[0100]

[0101] Obviously, it is positive definite. Take its derivative to get:

[0102]

[0103] Design the virtual control input \(\alpha\) as:

[0104]

[0105] where \(k_1\) is a positive parameter designed; Substitute (12) into (11-1); The derivative of the Lyapunov function is obtained as follows:

[0106]

[0107] Select the Lyapunov function again as:

[0108]

[0109] where \(\gamma\in R\) is a positive parameter designed; is the estimation error, is the upper bound \(\eta\) of the false data injection attack \(\eta\) m estimated value;

[0110] Taking the derivative of \(V_2\) gives:

[0111]

[0112] Combining (14) and (14-1) gives:

[0113]

[0114] Design the actual control input \(u\) as:

[0115]

[0116] where \(k_2\in R\) is a positive parameter designed, and:

[0117]

[0118] where \(z\) 21 , \(z\) 22 , \(z\) 23 \(\in R\) are the 1st, 2nd, and 3rd components of \(z_2\) respectively.

[0119] Substitute the control input (15) into formula (14-2) to get:

[0120]

[0121] From (15-1), we can get:

[0122]

[0123] And design the parameter adaptation law as:

[0124]

[0125] Substitute (16) into (15-2) to get:

[0126]

[0127] Since

[0128]

[0129] we can obtain:

[0130]

[0131] For 1 ≤ i ≤ 3, there is z 2i ≤ z 2i sgn(z 2i );

[0132] Because z 2i sgn(z 2i ) is equivalent to taking the absolute value of z 2i , when z 2i is greater than or equal to zero, they are equal, and when z 2i is less than zero, z 2i <z 2i sgn(z 2i );

[0133] Since η m is the upper bound of the absolute value of η, for 1 ≤ i ≤ 3, there is η i |≤ η im , so we can obtain:

[0134] z 21 η1 + z 22 η2 + z 23 η3 ≤ z 21 sgn(z 21 )η 1m + z 22 sgn(z 22 )η 2m + z 23 sgn(z 23 )η 3m (16 - 4)

[0135] That is:

[0136]

[0137] Combining (16 - 1) and (16 - 5), we can obtain:

[0138]

[0139] From Young's inequality, we can obtain:

[0140]

[0141] Combining (16 - 7) and (16 - 6) gives:

[0142]

[0143] Let Then we can get:

[0144]

[0145] In summary, the derivative of the Lyapunov function is:

[0146]

[0147] Then the closed - loop system is ultimately uniformly bounded; and by choosing the parameters k1, k2, γ as the corresponding values, such that the system tracking error approaches the neighborhood of the origin, the attitude - safe adaptive tracking control of the spacecraft with actuator false data injection attack is completed.

[0148] Example 2:

[0149] In this case, as Figure 2 shown in the overall schematic diagram composed of the parameter adaptive law, virtual controller, real control law, and spacecraft attitude tracking system with actuator false data injection attack, a spacecraft attitude - safe adaptive state - feedback control system uses the system feedback state to generate the state adaptive law, uses the tracking error signal to generate the virtual control law, combines the virtual control signal, adaptive parameters, and the actual control signal generated by the actual controller to control the spacecraft attitude tracking system with actuator false data injection attack, and compares the system attitude angle with the reference signal to generate the tracking error signal.

[0150] To verify the effectiveness of the proposed scheme in this case, set the actuator false data injection attack signal as η = [3 + e -0.3t 3 + e -0.2t 3 + e -0.1t T , the desired trajectory is The initial state of the system is ω(0) = [0 0 0] T , The inertia matrix of the spacecraft is selected as

[0151] Select the parameters k1 = 0.7, k2 = 3.5, γ = 100, then the spacecraft control effect diagram is as Figures 3 - 5 shown. Figure 3 is the spacecraft tracking error trajectory diagram; θ e , ψ e are the three components of the tracking error respectively. According to Figure 3 ​It can be seen that the adaptive safe attitude tracking control method of the present invention can enable the controlled spacecraft to track the desired attitude angle, and the tracking error converges within 10 s, with a very good tracking effect; Figure 4 It is the curve graph of the parameter adaptive law, which are respectively the three components of the parameter adaptive law; Figure 5 It is the curve graph of the actual control law, and u1, u2, and u3 are respectively the three components of the actual control law. It can be seen from this that the adaptive safe attitude tracking control scheme proposed by the present invention can enable the spacecraft attitude tracking system with actuator false data injection attacks to operate safely and stably.

[0152] Through the above specific implementation cases, a spacecraft attitude safety adaptive state feedback control method and system provided by the present invention establish a spacecraft attitude tracking error system model with actuator false data injection attacks by using Euler angles, estimate the upper bound of the attack signal by using the parameter adaptive law, and propose a virtual controller and an actual control law by using the backstepping method, realizing the adaptive safe spacecraft attitude tracking control in the face of unknown actuator false data injection attacks.

[0153] The above is only the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements can be made without departing from the principle of the present invention, and these improvements and refinements should also be regarded as the protection scope of the present invention. The structures, devices, and operation methods not specifically described and explained in the present invention are implemented according to the conventional means in the art without special explanation and limitation.

Claims

1. A method for spacecraft attitude safety adaptive state feedback control, characterized in that: Including the following steps: Step 1: Establish a spacecraft attitude tracking error dynamics model with actuator false data injection attacks using Euler angles; Step 2: According to the spacecraft attitude tracking error dynamics model, estimate the upper bound of the attack signal using a parameter adaptation law, and propose a virtual controller and a real control law using the backstepping method; Finally, complete the adaptive safe spacecraft attitude tracking control against unknown actuator false data injection attacks; In step 2, first estimate the upper bound of the attack signal using a parameter adaptation law, and propose a virtual controller and a real control law using the backstepping method. First, design the coordinate transformation as follows: (10) Wherein: is a virtual control input; Then select the Lyapunov function as: (11) Design virtual control input It is: (12) Wherein: is a positive parameter of the design; the derivative of the Lyapunov function is obtained as follows: (13) Wherein: is a projection matrix; Again, select the Lyapunov function as: (14) Wherein: is the spacecraft moment of inertia matrix; is a designed positive parameter; is the estimation error, is the false data injection attack the upper bound of the estimated value of; Design actual control input and the parameter adaptation law are respectively as follows: (15) (16) Wherein: is a positive parameter of the design, and (17) Wherein: are respectively the 1st, 2nd, and 3rd components of Obtain the derivative of the Lyapunov function as: (18) Wherein: , the closed-loop system is ultimately uniformly bounded; and by selecting the parameter to be the corresponding value, such that the system tracking error approaches the neighborhood of the origin, then the attitude safe adaptive tracking control of the spacecraft with actuator false data injection attack is completed.

2. The method for spacecraft attitude safety adaptive state feedback control according to claim 1, characterized in that: Step 1 specifically includes the following steps: Establish a spacecraft attitude tracking system model with actuator false data injection attacks using Euler angles; taking the inertial coordinate system as the reference system, the spacecraft attitude kinematic equation relative to the inertial space in the 3-1-2 rotation sequence represented by Euler angles is: (1) Wherein: are three Euler angles under the 3-1-2 rotation sequence, and let the spacecraft perform small-angle attitude tracking, that is ; is the attitude angular velocity of the spacecraft in the body coordinate system, is to projection matrix, and its specific expression is: (2)。 3. A spacecraft attitude safety adaptive state feedback control method according to claim 2, characterized in that: In the above step 1, the spacecraft suffers from an actuator false data injection attack with bounded energy , and its upper bound is . Then, the attitude dynamics equation of the rigid spacecraft under the false data injection attack is expressed as: (3) Wherein: is the control torque vector, is 's cross product matrix, defined as follows: (4) and is the spacecraft moment of inertia matrix in the following form: (5) Wherein: They are respectively the projections of the spacecraft on the corresponding axes.

4. The attitude safety adaptive state feedback control method for a spacecraft according to claim 3, wherein: The attitude kinematics and dynamics models of the spacecraft are expressed as: (6) Definition are the expected values of the attitude angles respectively, then the attitude tracking error is as follows: (7) Obtain the attitude tracking error equation as: (8) Let and yield the spacecraft attitude tracking error equation with actuator false data injection attack: (9)。 5. A spacecraft attitude safety adaptive state feedback control system, characterized in that: The spacecraft attitude safety adaptive state feedback control system is the operating system of a spacecraft attitude safety adaptive state feedback control method in claim 1. The spacecraft attitude safety adaptive state feedback control method uses the system feedback state to generate a state adaptation law, uses the tracking error signal to generate a virtual control law, combines the virtual control signal, the adaptive parameter, and the actual controller to generate an actual control signal, controls the spacecraft attitude tracking system with actuator false data injection attacks, and compares the system attitude angle with the reference signal to generate a tracking error signal.

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