Spacecraft attitude safety adaptive state feedback control method and system

Abstract

The invention belongs to the technical field of spacecraft attitude safety control, and particularly relates to a spacecraft attitude safety adaptive state feedback control method and system, and the method comprises the steps: 1, building a spacecraft attitude tracking error dynamic model with an actuator false data injection attack through an Euler angle; 2, tracking the error dynamic model according to the attitude of the spacecraft; estimating the upper bound of the attack signal by using a parameter adaptive law, and proposing a virtual controller and a real control law by using a backstepping method; and finally, adaptive safe spacecraft attitude tracking control facing unknown actuator false data injection attacks is completed. According to the method, the security control problem of the spacecraft attitude tracking system facing the false data injection attack can be effectively solved, and the security and stability of the system are ensured.

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 purpose 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 comprises the following steps:

[0009] Step 1: The dynamic model of spacecraft attitude tracking error with actuator false data injection attack is established using Euler angles; specifically:

[0010] The step 1 specifically includes the following steps: using Euler angles to establish a spacecraft attitude tracking system model with actuator false data injection attack; taking the inertial coordinate system as the reference system, the kinematic equation of the spacecraft attitude relative to the inertial space under the 3-1-2 transformation sequence expressed by Euler angles is:

[0011]

[0012] in are the three Euler angles in the 3-1-2 conversion sequence, allowing the spacecraft to perform small-angle attitude tracking, that is, ω=[ω x ω y ω z ] T ∈R 3×1 is the angular velocity of the spacecraft in the body coordinate system, R i ∈R 3×3 To The projection matrix is ​​expressed as follows:

[0013]

[0014] In step 1, the spacecraft is attacked by an energy-bounded actuator false data injection attack η=[η1 η2 η3] T ∈R 3×1 , whose upper bound is η m =[η m1 η m2 η m3 ] T ∈R 3×1 , then the attitude dynamics equation of the rigid spacecraft attacked by false data injection can be expressed as:

[0015]

[0016] where u=[u1 u2 u3]∈R 3×1is 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 of the form:

[0019]

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

[0021] The attitude kinematics and dynamics model of the spacecraft is expressed as:

[0022]

[0023] definition θ r ,ψ r The attitude angle The expected value of θ, ψ, then the attitude tracking error is:

[0024]

[0025] The attitude tracking error equation is:

[0026]

[0027] Let x1 = ρ e And x2 = ω, we can get the spacecraft attitude tracking error equation with actuator false data injection attack:

[0028]

[0029] Step 2: Based on 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 a virtual controller and a real control law; finally complete the adaptive and safe spacecraft attitude tracking control facing the attack of unknown actuator false data injection, specifically:

[0030] In step 2, the upper bound of the attack signal is estimated by using the parameter adaptive law, and the virtual controller and the actual control law are proposed by using the backstepping method; first, the coordinate transformation is designed as follows:

[0031]

[0032] Where α is the virtual control input;

[0033] Then choose the Lyapunov function as:

[0034]

[0035] Design the virtual control input α as:

[0036]

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

[0038]

[0039] Again, we choose the Lyapunov function as:

[0040]

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

[0042] The actual control input u and parameter adaptive law of the design are:

[0043]

[0044] where k2∈R is a positive parameter of the design, 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] in Then the closed-loop system is ultimately uniformly bounded; and by selecting parameters k1, k2, and γ as corresponding values, the system tracking error is made to approach the neighborhood of the origin, thus completing the spacecraft attitude safety adaptive tracking control with actuator false data injection attack.

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

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

[0052] The present invention uses Euler angles to establish a dynamic model of spacecraft attitude tracking error with actuator false data injection attack; then based on the spacecraft attitude tracking error dynamic model; uses parameter adaptive law to estimate the upper bound of the attack signal, uses backstepping method to propose a virtual controller and a real control law; and finally completes adaptive and safe spacecraft attitude tracking control facing unknown actuator false data injection attack. The present invention can effectively solve the safety control problem of spacecraft attitude tracking system facing false data injection attack, and ensure the safety and stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

[0057] Figure 5 It is the actual control law curve diagram in the present invention. DETAILED DESCRIPTION

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

[0059] Embodiment 1:

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

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

[0062] First, define the geocentric inertial coordinate system Ox o y o z o , whose origin is fixed to the center of mass of the Earth, Ox o The axis points to the vernal equinox, Oz o The axis points to the North Pole, Oy o The axis is determined by the right-hand rule. Then define the spacecraft body coordinate system Ox b y b z b , the origin of the coordinate system is fixed to the center of mass of the spacecraft, let Ox b The axis is along the longitudinal axis of the spacecraft, i.e. the direction of the spacecraft's flight. b Axis is within the spacecraft cross section, Oz b The axis is determined by the right-hand rule. This system can be represented by the reference system with three Euler angles ψ, θ is obtained by following the 3-1-2 sequence. First, Ox o y o z o Around Oz o The axis rotates by angle ψ to obtain the first coordinate system Ox′y′z′:

[0063]

[0064] Then rotate Ox′y′z′ around the Ox' axis Angle, to the second coordinate system Ox″y″z″:

[0065]

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

[0067]

[0068] The transformation equation can be obtained from the rotation process:

[0069]

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

[0071]

[0072] in:

[0073]

[0074] From the transformation process, we can get the angular velocity ω∈R of this system: 3×1 for:

[0075]

[0076] The final kinematic equation of the spacecraft attitude relative to the inertial space under the 3-1-2 transformation sequence expressed by Euler angles is:

[0077]

[0078] in are the three Euler angles in the 3-1-2 conversion sequence, allowing the spacecraft to perform small-angle attitude tracking, that is, ω=[ω x ω y ω z ] T ∈R 3×1 is the angular velocity of the spacecraft in the body coordinate system, R i ∈R 3×3 To The projection matrix is ​​expressed as follows:

[0079]

[0080] In step 1, the spacecraft is attacked by an energy-bounded actuator false data injection attack η=[η1 η2 η3] T ∈R 3×1 , whose upper bound is η m =[η m1 η m2 η m3 ] T ∈R 3×1 , then the attitude dynamics equation of the rigid spacecraft attacked by false data injection 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 of the form:

[0085]

[0086] Among them l x ∈R,l y ∈R,l z ∈R are the projections of the spacecraft on the corresponding axes.

[0087] The attitude kinematics and dynamics model of the spacecraft is expressed as:

[0088]

[0089] definition θ r ,ψ r The attitude angle The expected value of θ, ψ, then the attitude tracking error is:

[0090]

[0091] The attitude tracking error equation is:

[0092]

[0093] Let x1 = ρ e And x2 = ω, we can get the spacecraft attitude tracking error equation with actuator false data injection attack:

[0094]

[0095] Step 2: Based on 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 a virtual controller and a real control law; finally complete the adaptive and safe spacecraft attitude tracking control facing the attack of unknown actuator false data injection, specifically:

[0096] In step 2, the upper bound of the attack signal is estimated by using the parameter adaptive law, and the virtual controller and the actual control law are proposed by using the backstepping method; first, the coordinate transformation is designed as follows:

[0097]

[0098] Where α is the virtual control input;

[0099] Then choose the Lyapunov function as:

[0100]

[0101] Obviously it is positive definite, and taking its derivative we get:

[0102]

[0103] Design the virtual control input α as:

[0104]

[0105] Where k1 is a designed positive parameter; Substitute (12) into (11-1); the derivative of the Lyapunov function is:

[0106]

[0107] Again, we choose the Lyapunov function as:

[0108]

[0109] Where γ∈R is a positive parameter of the design; is the estimation error, is the upper bound of the false data injection attack η m An estimated value of

[0110] Taking the derivative of V2, we get:

[0111]

[0112] Combining (14) and (14-1), we can obtain:

[0113]

[0114] The actual control input u is designed as:

[0115]

[0116] Where k2∈R is a positive parameter of the design, and:

[0117]

[0118] where z 21 ,z 22 ,z 23 ∈R are the 1st, 2nd, and 3rd components of z2 respectively.

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

[0120]

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

[0122]

[0123] And the parameter adaptive law is designed as:

[0124]

[0125] Substituting (16) into (15-2), we obtain:

[0126]

[0127] because

[0128]

[0129] We can get:

[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 z 2i Take the absolute value, when z 2i When z is greater than or equal to zero, they are equal. 2i When z is less than zero, 2i <z 2i sgn(z 2i );

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

[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] Right now:

[0136]

[0137] Combining (16-1) and (16-5) we get:

[0138]

[0139] From Young's inequality we can get:

[0140]

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

[0142]

[0143] make 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 selecting parameters k1, k2, and γ as corresponding values, the system tracking error is made to approach the neighborhood of the origin, thus completing the spacecraft attitude safety adaptive tracking control with actuator false data injection attack.

[0148] Embodiment 2:

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

[0150] In order to verify the effectiveness of the proposed solution in this case, the actuator false data injection attack signal is set to η = [3 + e -0.3t 3+e -0.2t 3+e -0.1t ] T , the expected trajectory is The initial state of the system is ω(0)=[0 0 0] T , The spacecraft's moment of inertia matrix is ​​chosen as

[0151] Select parameters k1=0.7, k2=3.5, γ=100, then the spacecraft control effect diagram is as follows Figure 3-5 shown. Figure 3 is the spacecraft tracking error trajectory diagram; θ e , ψ e They are the three components of tracking error. Figure 3It can be seen that the adaptive safety attitude tracking control method of the present invention can control the spacecraft to track the desired attitude angle, the tracking error converges within 10s, and the tracking effect is very good; Figure 4 is the curve diagram of the parameter adaptive law, They are the three components of the parameter adaptation law; Figure 5 It is the actual control law curve diagram, and u1, u2, and u3 are the three components of the actual control law. It can be seen that the adaptive safety attitude tracking control scheme proposed by the present invention can make the spacecraft attitude tracking system with actuator false data injection attack run safely and stably.

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

[0153] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A spacecraft attitude safety adaptive state feedback control method, characterized by: The following steps are involved: Step 1: The dynamic model of spacecraft attitude tracking error with actuator false data injection attack is established using Euler angles; Step 2: Based on 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 a virtual controller and a real control law; finally complete the adaptive and safe spacecraft attitude tracking control facing the attack of false data injection from unknown actuators.

2. A spacecraft attitude safety adaptive state feedback control method according to claim 1, characterized in that: The step 1 specifically includes the following steps: using Euler angles to establish a spacecraft attitude tracking system model with actuator false data injection attack; taking the inertial coordinate system as the reference system, the kinematic equation of the spacecraft attitude relative to the inertial space under the 3-1-2 transformation sequence expressed by Euler angles is: in are the three Euler angles in the 3-1-2 conversion sequence, allowing the spacecraft to perform small-angle attitude tracking, that is, ω=[ω x ω y ω z ] T ∈R 3×1 is the angular velocity of the spacecraft in the body coordinate system, R i ∈R 3×3 To The projection matrix is ​​expressed as follows:

3. A spacecraft attitude safety adaptive state feedback control method according to claim 2, characterized in that: In step 1, the spacecraft is attacked by an energy-bounded actuator false data injection attack η=[η1 η2 η3] T ∈R 3×1 , whose upper bound is η m =[η m1 η m2 η m3 ] T ∈R 3×1 , then the attitude dynamics equation of the rigid spacecraft attacked by false data injection can be expressed as: 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: And l∈R 3×3 is the spacecraft moment of inertia matrix of the form: Among them l x ∈R,l y ∈R,l z ∈R are the projections of the spacecraft on the corresponding axes.

4. A spacecraft attitude safety adaptive state feedback control method according to claim 3, characterized in that: The attitude kinematics and dynamics model of the spacecraft is expressed as: definition θ r ,ψ r The attitude angle The expected value of θ, ψ, then the attitude tracking error is: The attitude tracking error equation is: Let x1 = ρ e And x2 = ω, we can get the spacecraft attitude tracking error equation with actuator false data injection attack:

5. A spacecraft attitude safety adaptive state feedback control method according to claim 4, characterized in that: In step 2, the parameter adaptive law is used to estimate the upper bound of the attack signal, and the virtual controller and the actual control law are proposed using the backstepping method; the design coordinate transformation is as follows: Where α is the virtual control input; Then choose the Lyapunov function as: Design the virtual control input α as: Where k1 is a designed positive parameter; the derivative of the Lyapunov function is: Again, we choose the Lyapunov function as: Where γ∈R is a positive parameter of the design; is the estimation error, is the upper bound of the false data injection attack η m The estimated value of .

6. A spacecraft attitude safety adaptive state feedback control method according to claim 5, characterized in that: The actual control input u and parameter adaptive law of the design are: where k2∈R is a positive parameter of the design, and where z 21 ,z 22 ,z 23 ∈R are the 1st, 2nd and 3rd components of z2 respectively; The derivative of the Lyapunov function is obtained as: in Then the closed-loop system is ultimately uniformly bounded; by selecting parameters k1, k2, and γ as corresponding values, the system tracking error is made to approach the neighborhood of the origin, and the spacecraft attitude safety adaptive tracking control with actuator false data injection attack is completed.

7. A spacecraft attitude safety adaptive state feedback control system, characterized in that: The system feedback state is used to generate a state adaptive law, and the tracking error signal is used to generate a virtual control law. The virtual control signal, adaptive parameters, and actual control signal generated by the actual controller are combined to control the spacecraft attitude tracking system with actuator false data injection attack, and the system attitude angle is compared with the reference signal to generate a tracking error signal.

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